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DTU Compute

Introduction to Medical Image Analysis

Plenty of slides adapted from Thomas Moeslunds lectures

Rasmus R PaulsenDTU Compute

rapadtudk

httpwwwcomputedtudkcourses02511httpwwwcomputedtudkcourses02512

DTU Compute

2122018Introduction to Medical Image Analysis2 DTU Compute Technical University of Denmark

Lecture 4 ndash Neighbourhood Processing

800 ndash 900 Exercises900 ndash 11ish Lecture

11ish - Exercises

1200 ndash 1300 Lunch break

1300 - Exercises

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What can you do after today Describe the difference between point processing and neighbourhood

processing Compute a rank filtered image using the min max median and

difference rank filters Compute a mean filtered image Decide if median or average filtering should be used for noise removal Choose the appropriate image border handling based on a given input

image Implement and apply template matching Compute the normalised cross correlation and explain why it should be

used Apply given image filter kernels to images Use edge filters on images Describe finite difference approximation of image gradients Describe the concept of edge detection

DTU Compute

2122018Introduction to Medical Image Analysis4 DTU Compute Technical University of Denmark

Point processing

0 2

1 2

1 2 1

2 5 3

1 3

2 2

0 1

1 2 0

2 1 4

1 0 19

12

Input Output

bull The value of the output pixel is only dependent on the value of one input pixel

bull A global operation ndash changes all pixels

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Point processing Grey level enhancement

ndash Process one pixel at a time independent of all other pixelsndash For example used to correct Brightness and Contrast

Too lowcontrastCorrect

Too highcontrast

Too high brightness

Too low brightness

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Neighbourhood processing

0 2

1 2

1 2 1

2 5 3

1 3

2 2

0 1

1 2 0

2 1 4

1 0 19

12

Input Output

bull Several pixels in the input has an effect on the output

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Use of filtering

Noise removal Enhance edges Smoothing

bull Image processing

bull Typically done before actual image analysis

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Salt and pepper noise Pixel values that are very

different from their neighbours

Very bright or very dark spots

Scratches in X-rays

What is that

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Salt and pepper noise Fake example

ndash Let us take a closer look at noise pixels

They are all 0 or 255

Should we just remove all the 0rsquos and 255rsquos from the image

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2122018Introduction to Medical Image Analysis10 DTU Compute Technical University of Denmark

What is so special about noise What is the value of the pixel

compared to the neighbours Average of the neighbours

ndash 170 Can we compare to the

averagendash Difficult ndash should we remove

all values bigger than average+1

It is difficult to detect noise

172 169 171 168 0 169 172 173 168

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Noise ndash go away We can not tell what pixels

are noise One solution

ndash Set all pixels to the average of the neighbours (and the pixel itself)

Oh nondash Problemsndash The noise ldquopollutesrdquo the

good pixels

172 169 171 168 0 169 172 173 168

170

169 168 0 170 172173 170 172 170

149

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What is the median ValueA) 170B) 173C) 169D) 171E) 172

13

0 0 02

A B C D E

169 168 0 170172 173 170 172 170

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The median value The values are sorted from low to high The middle number is picked

ndash The median value

169 168 0 170172 173 170 172 170

0168 169 170 170 170172 172173

Median

Noise has no influence on the median

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Noise away ndash the median filter All pixels are set to the

median of its neighbourhood Noise pixels do not pollute

good pixels

172 169 171 168 0 169 172 173 168

170

169 168 0 170 172173 170 172 170

170

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Noise removal ndash average filter

Scanned X-ray with salt and pepper noise

Average filter (3x3)

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Noise removal ndash median filter

Scanned X-ray with salt and pepper noise

Median filter (3x3)

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Image Filtering Creates a new filtered image Output pixel is computed based

on a neighbourhood in the input image

3 x 3 neighbourhoodndash Filter size 3 x 3ndash Kernel size 3 x 3ndash Mask size 3 x 3

Larger filters often usedndash Size

7 x 7ndash Number of elements

49

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Median filterA) 25B) 90C) 198D) 86E) 103

0

13

1 0 0

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Rank filters Based on sorting the pixel

values in the neighbouring region

Minimum rank filterndash Darker image Noise problems

Maximum rank filterndash Lighter image Noise problems

Difference filterndash Enhances changes (edges)

0168 169 170 170 170172 172173

-

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Median filter

A) 3B) 84C) 112D) 73E) 202

0

12

10 0

A B C D E

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Correlation What is it Two measurements

ndash Low correlationndash High correlation

High correlation means that there is a relation between the values

They look the same Correlation is a measure of

similarity

Low

High

Muscles

Mat

h Ski

lls

Muscles

Ben

ch P

ress

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Why do we need similarity Image analysis is also about recognition of patterns Often an example pattern is used We need something to tell us if there is a high match

between our pattern and a part of the image

Example pattern

Image

Find matches

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Correlation (1D)

1 1 2 2 1 1 2 2 1 1

1 2 1

45

41

1 1 + 2 1 + 1 2 = 5

Normalise

Kernel

Signal (1D image)

41

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Correlation (1D)

1 1 2 2 1 1 2 2 1 1

1 2 1

45

47

47

45

45

47

47

45

41

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Normalisation

1 1 2 2 1 1 2 2 1 1

1 2 1

45

41

1 1 + 2 1 + 1 2 = 5

Normalise41

bull The sum of the kernel elements is used

bull Keep the values in the same range as the input image

Sum is 4

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Normalisation Normalisation factor

ndash Sum of kernel coefficients

1 2 1h(x)

119909119909

ℎ 119909119909 = 1 + 2 + 1

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Correlation on images The filter is now 2D 1 1 1

1 1 1

1 1 1

0 2 4

1 2 2

1 6 3

1 2 12 5 3

2 1 3

1 3 1

2 2 2

0 1 3

1 2 0

2 1 4

1 0 1

912

91

Input OutputKernel

Kernel coefficients

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Correlation on images

1 1 11 1 11 1 1

0 2 4

1 2 2

1 6 3

1 2 0

2 1 4

1 0 1

912

911

91

Input Output

1 3 1

2 2 2

0 1 3

1 2 12 5 3

2 1 3

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Correlation on images

Input Output

The mask is moved row by row

No values at the border

0 2 4

1 2 2

1 6 3

1 2 0

2 1 4

1 0 1

1 3 1

2 2 2

0 1 3

1 2 12 5 3

2 1 3

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1 2 1

1 3 1

1 2 1

-1 -2 -1

0 0 0

1 2 1

Draw your filter

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Correlation on images ndash no normalisationA) 4B) 7C) 16D) 23E) 25

1 2 11 3 11 2 1

0 2 41 2 2

1 6 3

1 2 12 5 3

2 1 3

1 3 1

2 2 2

0 1 3

1 2 0

2 1 4

1 0 11 0

14

0 0

A B C D E

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Correlation on images ndash no normalisation 2A) 010B) 3 3C) 6 2D) 10 15E) 11 32

13

0 0 0 0

A B C D E

-1 -2 -10 0 01 2 1

0 2 41 2 2

1 6 3

1 2 12 5 3

2 1 3

1 3 1

2 2 2

0 1 3

1 2 0

2 1 4

1 0 1

Chart1

13
0
0
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Mathematics of 2D Correlation

h

f

Correlation operator

1 2 11 3 11 2 1

0 2 4

1 2 2

1 6 3

1 2 1

2 5 3

2 1 3

1 3 1

2 2 2

0 1 3

1 2 0

2 1 4

1 0 1

119892119892 119909119909119910119910 = 119891119891 119909119909119910119910 ∘ ℎ(119909119909119910119910)

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Mathematics of 2D Correlation

1 2 11 3 11 2 1

0 2 4

1 2 2

1 6 3

1 2 1

2 5 3

2 1 3

1 3 1

2 2 2

0 1 3

1 2 0

2 1 4

1 0 1

h

fh(00)

f(21)

Example g(21)

i = -1 j = -1

i = 1 j = 0

119892119892 119909119909119910119910 = 119895119895=minus119877119877

119877119877

119894119894=minus119877119877

119877119877

ℎ(119894119894 119895119895) 119891119891(119909119909 + 119894119894119910119910 + 119895119895)

DTU Compute

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Mathematics of 2D Correlation

1 2 11 3 11 2 1

0 2 4

1 2 2

1 6 3

1 2 1

2 5 3

2 1 3

1 3 1

2 2 2

0 1 3

1 2 0

2 1 4

1 0 1

h

f

119892119892 119909119909119910119910 = 119895119895=minus119877119877

119877119877

119894119894=minus119877119877

119877119877

ℎ(119894119894 119895119895) 119891119891(119909119909 + 119894119894119910119910 + 119895119895)

119892119892(119909119909119910119910 = 1 2 + 2 0 + 1 1 + 1 1 + 3 4 + 1 2 + 1 0 + 2 1 + 1 0

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119892119892 119909119909 119910119910 = 119895119895=minus119877119877

119877119877

119894119894=minus119877119877

119877119877

ℎ(119894119894 119895119895) 119891119891(119909119909 + 119894119894119910119910 + 119895119895)

119892119892 22 =ℎ minus1minus1 sdot 119891119891 11 + ℎ 0minus1 sdot 119891119891 21 + ℎ 1minus1 sdot 119891119891 31 +ℎ minus10 sdot 119891119891 12 + ℎ 00 sdot 119891119891 22 + ℎ 10 sdot 119891119891 32 +ℎ minus11 sdot 119891119891 13 + ℎ 01 sdot 119891119891 23 + ℎ 11 sdot 119891119891 33

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2D Kernel Normalisation

1 2 11 3 11 2 1

h

Normalisation factor

1 + 2 + 1 + 1 + 3 + 1 + 1 + 2 + 1 = 13

119909119909

119910119910

ℎ(119909119909119910119910)

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CorrelationA) 50122B) 123001C) 11233D) 2550E) 90454

0 0 0 0

13

A B C D E

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0
0
0
0
13

Sheet1

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Smoothing filters

Also know as ndash Smoothing kernel Mean filter Low pass filter blurring

The simplest filter ndash Spatial low pass filterndash Removes high frequencies

Another mask ndash Gaussian filter

1 1 1

1 1 1

1 1 191

1 2 1

2 4 2

1 2 1161

Why Gaussian

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Use of smoothing

3x3 7x7 11x11 15x15

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Use of smoothing Large kernels smooth more Removes high frequency information Good at enhancing big structures

3x3 15x15

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Mean filterA) 166B) 113C) 12D) 51E) 245

0 0 0 0

A B C D E

Chart1

12
0
0
0
0

Sheet1

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Border handling

0 2 41 2 2

1 6 3

1 2 12 5 3

2 1 3

1 3 1

2 2 2

0 1 3

1 2 0

2 1 4

1 0 1

Input Output

No values at the border

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Border handling ndash extend the input

0 2 41 2 2

1 6 3

1 2 12 5 3

2 1 3

1 3 1

2 2 2

0 1 3

1 2 0

2 1 4

1 0 1

Input

0 0 0 0 000000

bull Zero padding ndash what happens

bull Zero is black ndash creates dark border around the image

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Correlation with zero paddingA) 5 8B) 12 16C) 13 3D) 15 21E) 17 12

1 2 11 3 11 2 1

0 2 41 2 2

1 6 3

1 2 12 5 3

2 1 3

1 3 1

2 2 2

0 1 3

1 2 0

2 1 4

1 0 1

0

13

0 0 0

A B C D E

Chart1

0
13
0
0
0

Sheet1

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Border handling ndash extend the input

0 2 41 2 2

1 6 3

1 2 12 5 3

2 1 3

1 3 1

2 2 2

0 1 3

1 2 0

2 1 4

1 0 1

Input

1 2 0 1 311211

bull Reflection

bull Normally better than zero padding

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Template Matching Template

ndash Skabelon paring dansk Locates objects in images

Input

Template

Output Correlation image

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Template Matching The correlation between the template and the input

image is computed for each pixel

Input

Template

Output Correlation image

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Template Matching The pixel with the highest value is found in the

output imagendash Here is the highest correlation

Input

Template

Output Correlation image

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Template Matching This corresponds to the found pattern in the input

image

Input

Template

Output Correlation image

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Problematic Correlation Correlation matching has problem with light areas ndash

why

Input (f)

Template (h)

Output Correlation imageFake max

Real max

Very High119892119892 119909119909119910119910 = 119895119895=minus119877119877

119877119877

119894119894=minus119877119877

119877119877

ℎ(119894119894 119895119895) 119891119891(119909119909 + 119894119894119910119910 + 119895119895)

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2122018Introduction to Medical Image Analysis59 DTU Compute Technical University of Denmark

Normalised Cross Correlation

Input (f)

Template (h)

Output Correlation image

Real max

NCC x y =Correlation

Length of image patch sdot Length of template

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2122018Introduction to Medical Image Analysis60 DTU Compute Technical University of Denmark

Length of template Vector length

ndash Put all pixel values into a vectorndash Compute the length of this vector

Describes the intensity of the templatendash Bright template has a large lengthndash Dark template has a small length

Template (h)

Length of template = 119895119895=minus119877119877

119877119877

119894119894=minus119877119877

119877119877

ℎ(119894119894 119895119895) ℎ(119894119894 119895119895)

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2122018Introduction to Medical Image Analysis61 DTU Compute Technical University of Denmark

Length of image patch Vector length based on pixel values in image patch Describes the intensity of the image patch

Template (h)

Input (f) with patch

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Normalised Cross Correlation The length of the image patch and the length of

template normalise the NCC If the image is very bright the NCC will be ldquopulled

downrdquo

NCC x y =Correlation

Length of image patch sdot Length of template

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2122018Introduction to Medical Image Analysis63 DTU Compute Technical University of Denmark

Normalised Cross Correlation NCC will be between

ndash 0 No similarity between template and image patchndash 1 Template and image patch are identical

Input (f)

Template (h)

Output Correlation image

Real max

NCC x y =Correlation

Length of image patch sdot Length of template

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2122018Introduction to Medical Image Analysis64 DTU Compute Technical University of Denmark

Normalised Cross Correlation

A) 010B) 033C) 083D) 062E) 098

Der udfoslashres template matching med og normalized crosscorrelation (NCC) beregnes Hvad bliver NNC i den markerede pixel

1

2 2

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Edges An edge is where there is a

high change in gray level values

Objects are often separated from the background by edgesGray level profile

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Edges The profile as a function f(d) What value is high when there

is an edgendash The slope of fndash The slope of the tangent at d

f(d)

119891119891prime(119889119889)

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2122018Introduction to Medical Image Analysis68 DTU Compute Technical University of Denmark

Finite Difference Definition of slope

Approximation

Simpler approximationh = 1

119891119891prime 119889119889 = limℎrarr0

119891119891 119889119889 + ℎ minus 119891119891(119889119889)ℎ

119891119891prime 119889119889 asymp119891119891 119889119889 + ℎ minus 119891119891(119889119889)

ℎ

119891119891prime 119889119889 asymp 119891119891 119889119889 + 1 minus 119891119891(119889119889)

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2122018Introduction to Medical Image Analysis69 DTU Compute Technical University of Denmark

Edges Discrete approximation of frsquo(d) Can be implemented as a filter

-1 0 1

f(d-2) f(d-1) f(d) f(d+1) f(d+2) f(d+3)

f(d)

119891119891prime 119889119889 asymp 119891119891 119889119889 + 1 minus 119891119891(119889119889)

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Edges in 2D Changes in gray level values

ndash Image gradientndash Gradient is the 2D derivative of a 2D function f(xy)ndash Equal to the slope of the imagendash A steep slope is equal to an edge

120571120571119891119891 119909119909119910119910 = 119866(119892119892119909119909119892119892119910119910)

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Edge filter kernel The Prewitt filter is a typical

edge filter Output image has high

values where there are edges

-1 0 1

-1 0 1

-1 0 1Vertical Prewitt filter

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Prewitt filter

Original Prewitt Prewitt

Hot colormapSmooth 15x15

Smooth 15x15

Prewitt

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Edge detection Edge filter

ndash Prewitt for example Thresholding

ndash Separate edges from non-edges

Output is binary imagendash Edges are white

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Edge filtering

A) MeanB) Horizontal SobelC) Vertical PrewittD) Horisontal PrewittE) Median

Der udfoslashres en filtrering (correlation) med et filter paring billedet Der bruges ikke coefficient normalization Den filtrerede vaeligrdi i den markerede pixel bliver -119 Hvilket et 3x3 filter blev benyttet

0

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02511 - Niveau af dagens emne forelaeligsingA) Meget letB) LetC) PassendeD) SvaeligrtE) Meget svaeligrt

23

6

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02512 - Niveau af dagens emne forelaeligsingA) Meget letB) LetC) PassendeD) SvaeligrtE) Meget svaeligrt

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02511 - Mit eget udbytte af dagenA) Jeg har laeligrt meget lidtB) Lidt laeligringC) PassendeD) God laeligringE) Jeg har laeligrt meget

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02512 - Mit eget udbytte af dagenA) Jeg har laeligrt meget lidtB) Lidt laeligringC) PassendeD) God laeligringE) Jeg har laeligrt meget

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02511 - Sidste uges oslashvelser (pixelwiseoperations)A) Meget letteB) LetteC) PassendeD) SvaeligreE) Meget svaeligre

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02512 - Sidste uges oslashvelser (pixelwiseoperations)A) Meget letteB) LetteC) PassendeD) SvaeligreE) Meget svaeligre

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Denne uges brug af clickersA) click click click ndash jeg bliver

sindssygB) For meget clickC) PassendeD) Jeg vil gerne have lidt mereE) Jeg kan ikrsquo faring nok

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What can you do after today Describe the difference between point processing and neighbourhood

processing Compute a rank filtered image using the min max median and

difference rank filters Compute a mean filtered image Decide if median or average filtering should be used for noise removal Choose the appropriate image border handling based on a given input

image Implement and apply template matching Compute the normalised cross correlation and explain why it should be

used Apply given image filter kernels to images Use edge filters on images Describe finite difference approximation of image gradients Describe the concept of edge detection

DTU Compute

2122018Introduction to Medical Image Analysis84 DTU Compute Technical University of Denmark

Oslashvelsesrapport over oslashvelse 4 - 02511 Oslashvelser taeligller cirka 30 af karakteren Skal afleveres senest den 7 marts kl 2359 Kan afleveres af 1 eller 2 personer

ndash I skal skrive jeres egen oslashvelsesrapportndash Brug mindst et af jeres egne billeder

Afleveres som PDF Lad vaeligre med at kopiere opgaveteksten ind i jeres

opgave Put Matlab kode i et Appendix og henvis fra teksten Eksempel rapport over oslashvelse findes paring

hjemmesiden under eksamen

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2122018Introduction to Medical Image Analysis85 DTU Compute Technical University of Denmark

Exercises

  • Introduction to Medical Image Analysis
  • Lecture 4 ndash Neighbourhood Processing
  • What can you do after today
  • Point processing
  • Point processing
  • Neighbourhood processing
  • Use of filtering
  • Salt and pepper noise
  • Salt and pepper noise
  • What is so special about noise
  • Noise ndash go away
  • What is the median Value
  • The median value
  • Noise away ndash the median filter
  • Noise removal ndash average filter
  • Noise removal ndash median filter
  • Image Filtering
  • Median filter
  • Rank filters
  • Median filter
  • Correlation
  • Why do we need similarity
  • Correlation (1D)
  • Correlation (1D)
  • Normalisation
  • Normalisation
  • Correlation on images
  • Correlation on images
  • Correlation on images
  • Draw your filter
  • Correlation on images ndash no normalisation
  • Correlation on images ndash no normalisation 2
  • Mathematics of 2D Correlation
  • Mathematics of 2D Correlation
  • Mathematics of 2D Correlation
  • Slide Number 40
  • 2D Kernel Normalisation
  • Correlation
  • Smoothing filters
  • Use of smoothing
  • Use of smoothing
  • Mean filter
  • Border handling
  • Border handling ndash extend the input
  • Correlation with zero padding
  • Border handling ndash extend the input
  • Template Matching
  • Template Matching
  • Template Matching
  • Template Matching
  • Problematic Correlation
  • Normalised Cross Correlation
  • Length of template
  • Length of image patch
  • Normalised Cross Correlation
  • Normalised Cross Correlation
  • Normalised Cross Correlation
  • Edges
  • Edges
  • Finite Difference
  • Edges
  • Edges in 2D
  • Edge filter kernel
  • Prewitt filter
  • Edge detection
  • Edge filtering
  • 02511 - Niveau af dagens emne forelaeligsing
  • 02512 - Niveau af dagens emne forelaeligsing
  • 02511 - Mit eget udbytte af dagen
  • 02512 - Mit eget udbytte af dagen
  • 02511 - Sidste uges oslashvelser (pixelwise operations)
  • 02512 - Sidste uges oslashvelser (pixelwise operations)
  • Denne uges brug af clickers
  • What can you do after today
  • Oslashvelsesrapport over oslashvelse 4 - 02511
  • Exercises
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    D
    E

    DTU Compute

    2122018Introduction to Medical Image Analysis2 DTU Compute Technical University of Denmark

    Lecture 4 ndash Neighbourhood Processing

    800 ndash 900 Exercises900 ndash 11ish Lecture

    11ish - Exercises

    1200 ndash 1300 Lunch break

    1300 - Exercises

    DTU Compute

    2122018Introduction to Medical Image Analysis3 DTU Compute Technical University of Denmark

    What can you do after today Describe the difference between point processing and neighbourhood

    processing Compute a rank filtered image using the min max median and

    difference rank filters Compute a mean filtered image Decide if median or average filtering should be used for noise removal Choose the appropriate image border handling based on a given input

    image Implement and apply template matching Compute the normalised cross correlation and explain why it should be

    used Apply given image filter kernels to images Use edge filters on images Describe finite difference approximation of image gradients Describe the concept of edge detection

    DTU Compute

    2122018Introduction to Medical Image Analysis4 DTU Compute Technical University of Denmark

    Point processing

    0 2

    1 2

    1 2 1

    2 5 3

    1 3

    2 2

    0 1

    1 2 0

    2 1 4

    1 0 19

    12

    Input Output

    bull The value of the output pixel is only dependent on the value of one input pixel

    bull A global operation ndash changes all pixels

    DTU Compute

    2122018Introduction to Medical Image Analysis5 DTU Compute Technical University of Denmark

    Point processing Grey level enhancement

    ndash Process one pixel at a time independent of all other pixelsndash For example used to correct Brightness and Contrast

    Too lowcontrastCorrect

    Too highcontrast

    Too high brightness

    Too low brightness

    DTU Compute

    2122018Introduction to Medical Image Analysis6 DTU Compute Technical University of Denmark

    Neighbourhood processing

    0 2

    1 2

    1 2 1

    2 5 3

    1 3

    2 2

    0 1

    1 2 0

    2 1 4

    1 0 19

    12

    Input Output

    bull Several pixels in the input has an effect on the output

    DTU Compute

    2122018Introduction to Medical Image Analysis7 DTU Compute Technical University of Denmark

    Use of filtering

    Noise removal Enhance edges Smoothing

    bull Image processing

    bull Typically done before actual image analysis

    DTU Compute

    2122018Introduction to Medical Image Analysis8 DTU Compute Technical University of Denmark

    Salt and pepper noise Pixel values that are very

    different from their neighbours

    Very bright or very dark spots

    Scratches in X-rays

    What is that

    DTU Compute

    2122018Introduction to Medical Image Analysis9 DTU Compute Technical University of Denmark

    Salt and pepper noise Fake example

    ndash Let us take a closer look at noise pixels

    They are all 0 or 255

    Should we just remove all the 0rsquos and 255rsquos from the image

    DTU Compute

    2122018Introduction to Medical Image Analysis10 DTU Compute Technical University of Denmark

    What is so special about noise What is the value of the pixel

    compared to the neighbours Average of the neighbours

    ndash 170 Can we compare to the

    averagendash Difficult ndash should we remove

    all values bigger than average+1

    It is difficult to detect noise

    172 169 171 168 0 169 172 173 168

    DTU Compute

    2122018Introduction to Medical Image Analysis11 DTU Compute Technical University of Denmark

    Noise ndash go away We can not tell what pixels

    are noise One solution

    ndash Set all pixels to the average of the neighbours (and the pixel itself)

    Oh nondash Problemsndash The noise ldquopollutesrdquo the

    good pixels

    172 169 171 168 0 169 172 173 168

    170

    169 168 0 170 172173 170 172 170

    149

    DTU Compute

    2122018Introduction to Medical Image Analysis12 DTU Compute Technical University of Denmark

    What is the median ValueA) 170B) 173C) 169D) 171E) 172

    13

    0 0 02

    A B C D E

    169 168 0 170172 173 170 172 170

    Chart1

    13
    0
    0
    0
    2

    Sheet1

    DTU Compute

    2122018Introduction to Medical Image Analysis13 DTU Compute Technical University of Denmark

    The median value The values are sorted from low to high The middle number is picked

    ndash The median value

    169 168 0 170172 173 170 172 170

    0168 169 170 170 170172 172173

    Median

    Noise has no influence on the median

    DTU Compute

    2122018Introduction to Medical Image Analysis14 DTU Compute Technical University of Denmark

    Noise away ndash the median filter All pixels are set to the

    median of its neighbourhood Noise pixels do not pollute

    good pixels

    172 169 171 168 0 169 172 173 168

    170

    169 168 0 170 172173 170 172 170

    170

    DTU Compute

    2122018Introduction to Medical Image Analysis15 DTU Compute Technical University of Denmark

    Noise removal ndash average filter

    Scanned X-ray with salt and pepper noise

    Average filter (3x3)

    DTU Compute

    2122018Introduction to Medical Image Analysis16 DTU Compute Technical University of Denmark

    Noise removal ndash median filter

    Scanned X-ray with salt and pepper noise

    Median filter (3x3)

    DTU Compute

    2122018Introduction to Medical Image Analysis17 DTU Compute Technical University of Denmark

    Image Filtering Creates a new filtered image Output pixel is computed based

    on a neighbourhood in the input image

    3 x 3 neighbourhoodndash Filter size 3 x 3ndash Kernel size 3 x 3ndash Mask size 3 x 3

    Larger filters often usedndash Size

    7 x 7ndash Number of elements

    49

    DTU Compute

    2122018Introduction to Medical Image Analysis18 DTU Compute Technical University of Denmark

    Median filterA) 25B) 90C) 198D) 86E) 103

    0

    13

    1 0 0

    A B C D E

    Chart1

    0
    13
    1
    0
    0

    Sheet1

    DTU Compute

    2122018Introduction to Medical Image Analysis20 DTU Compute Technical University of Denmark

    Rank filters Based on sorting the pixel

    values in the neighbouring region

    Minimum rank filterndash Darker image Noise problems

    Maximum rank filterndash Lighter image Noise problems

    Difference filterndash Enhances changes (edges)

    0168 169 170 170 170172 172173

    -

    DTU Compute

    2122018Introduction to Medical Image Analysis21 DTU Compute Technical University of Denmark

    Median filter

    A) 3B) 84C) 112D) 73E) 202

    0

    12

    10 0

    A B C D E

    Chart1

    0
    12
    1
    0
    0

    Sheet1

    DTU Compute

    2122018Introduction to Medical Image Analysis23 DTU Compute Technical University of Denmark

    Correlation What is it Two measurements

    ndash Low correlationndash High correlation

    High correlation means that there is a relation between the values

    They look the same Correlation is a measure of

    similarity

    Low

    High

    Muscles

    Mat

    h Ski

    lls

    Muscles

    Ben

    ch P

    ress

    DTU Compute

    2122018Introduction to Medical Image Analysis24 DTU Compute Technical University of Denmark

    Why do we need similarity Image analysis is also about recognition of patterns Often an example pattern is used We need something to tell us if there is a high match

    between our pattern and a part of the image

    Example pattern

    Image

    Find matches

    DTU Compute

    2122018Introduction to Medical Image Analysis25 DTU Compute Technical University of Denmark

    Correlation (1D)

    1 1 2 2 1 1 2 2 1 1

    1 2 1

    45

    41

    1 1 + 2 1 + 1 2 = 5

    Normalise

    Kernel

    Signal (1D image)

    41

    DTU Compute

    2122018Introduction to Medical Image Analysis26 DTU Compute Technical University of Denmark

    Correlation (1D)

    1 1 2 2 1 1 2 2 1 1

    1 2 1

    45

    47

    47

    45

    45

    47

    47

    45

    41

    DTU Compute

    2122018Introduction to Medical Image Analysis27 DTU Compute Technical University of Denmark

    Normalisation

    1 1 2 2 1 1 2 2 1 1

    1 2 1

    45

    41

    1 1 + 2 1 + 1 2 = 5

    Normalise41

    bull The sum of the kernel elements is used

    bull Keep the values in the same range as the input image

    Sum is 4

    DTU Compute

    2122018Introduction to Medical Image Analysis28 DTU Compute Technical University of Denmark

    Normalisation Normalisation factor

    ndash Sum of kernel coefficients

    1 2 1h(x)

    119909119909

    ℎ 119909119909 = 1 + 2 + 1

    DTU Compute

    2122018Introduction to Medical Image Analysis29 DTU Compute Technical University of Denmark

    Correlation on images The filter is now 2D 1 1 1

    1 1 1

    1 1 1

    0 2 4

    1 2 2

    1 6 3

    1 2 12 5 3

    2 1 3

    1 3 1

    2 2 2

    0 1 3

    1 2 0

    2 1 4

    1 0 1

    912

    91

    Input OutputKernel

    Kernel coefficients

    DTU Compute

    2122018Introduction to Medical Image Analysis30 DTU Compute Technical University of Denmark

    Correlation on images

    1 1 11 1 11 1 1

    0 2 4

    1 2 2

    1 6 3

    1 2 0

    2 1 4

    1 0 1

    912

    911

    91

    Input Output

    1 3 1

    2 2 2

    0 1 3

    1 2 12 5 3

    2 1 3

    DTU Compute

    2122018Introduction to Medical Image Analysis31 DTU Compute Technical University of Denmark

    Correlation on images

    Input Output

    The mask is moved row by row

    No values at the border

    0 2 4

    1 2 2

    1 6 3

    1 2 0

    2 1 4

    1 0 1

    1 3 1

    2 2 2

    0 1 3

    1 2 12 5 3

    2 1 3

    DTU Compute

    2122018Introduction to Medical Image Analysis32 DTU Compute Technical University of Denmark

    1 2 1

    1 3 1

    1 2 1

    -1 -2 -1

    0 0 0

    1 2 1

    Draw your filter

    DTU Compute

    2122018Introduction to Medical Image Analysis33 DTU Compute Technical University of Denmark

    Correlation on images ndash no normalisationA) 4B) 7C) 16D) 23E) 25

    1 2 11 3 11 2 1

    0 2 41 2 2

    1 6 3

    1 2 12 5 3

    2 1 3

    1 3 1

    2 2 2

    0 1 3

    1 2 0

    2 1 4

    1 0 11 0

    14

    0 0

    A B C D E

    Chart1

    1
    0
    14
    0
    0

    Sheet1

    DTU Compute

    2122018Introduction to Medical Image Analysis34 DTU Compute Technical University of Denmark

    Correlation on images ndash no normalisation 2A) 010B) 3 3C) 6 2D) 10 15E) 11 32

    13

    0 0 0 0

    A B C D E

    -1 -2 -10 0 01 2 1

    0 2 41 2 2

    1 6 3

    1 2 12 5 3

    2 1 3

    1 3 1

    2 2 2

    0 1 3

    1 2 0

    2 1 4

    1 0 1

    Chart1

    13
    0
    0
    0
    0

    Sheet1

    DTU Compute

    2122018Introduction to Medical Image Analysis37 DTU Compute Technical University of Denmark

    Mathematics of 2D Correlation

    h

    f

    Correlation operator

    1 2 11 3 11 2 1

    0 2 4

    1 2 2

    1 6 3

    1 2 1

    2 5 3

    2 1 3

    1 3 1

    2 2 2

    0 1 3

    1 2 0

    2 1 4

    1 0 1

    119892119892 119909119909119910119910 = 119891119891 119909119909119910119910 ∘ ℎ(119909119909119910119910)

    DTU Compute

    2122018Introduction to Medical Image Analysis38 DTU Compute Technical University of Denmark

    Mathematics of 2D Correlation

    1 2 11 3 11 2 1

    0 2 4

    1 2 2

    1 6 3

    1 2 1

    2 5 3

    2 1 3

    1 3 1

    2 2 2

    0 1 3

    1 2 0

    2 1 4

    1 0 1

    h

    fh(00)

    f(21)

    Example g(21)

    i = -1 j = -1

    i = 1 j = 0

    119892119892 119909119909119910119910 = 119895119895=minus119877119877

    119877119877

    119894119894=minus119877119877

    119877119877

    ℎ(119894119894 119895119895) 119891119891(119909119909 + 119894119894119910119910 + 119895119895)

    DTU Compute

    2122018Introduction to Medical Image Analysis39 DTU Compute Technical University of Denmark

    Mathematics of 2D Correlation

    1 2 11 3 11 2 1

    0 2 4

    1 2 2

    1 6 3

    1 2 1

    2 5 3

    2 1 3

    1 3 1

    2 2 2

    0 1 3

    1 2 0

    2 1 4

    1 0 1

    h

    f

    119892119892 119909119909119910119910 = 119895119895=minus119877119877

    119877119877

    119894119894=minus119877119877

    119877119877

    ℎ(119894119894 119895119895) 119891119891(119909119909 + 119894119894119910119910 + 119895119895)

    119892119892(119909119909119910119910 = 1 2 + 2 0 + 1 1 + 1 1 + 3 4 + 1 2 + 1 0 + 2 1 + 1 0

    DTU Compute

    2122018Introduction to Medical Image Analysis40 DTU Compute Technical University of Denmark

    119892119892 119909119909 119910119910 = 119895119895=minus119877119877

    119877119877

    119894119894=minus119877119877

    119877119877

    ℎ(119894119894 119895119895) 119891119891(119909119909 + 119894119894119910119910 + 119895119895)

    119892119892 22 =ℎ minus1minus1 sdot 119891119891 11 + ℎ 0minus1 sdot 119891119891 21 + ℎ 1minus1 sdot 119891119891 31 +ℎ minus10 sdot 119891119891 12 + ℎ 00 sdot 119891119891 22 + ℎ 10 sdot 119891119891 32 +ℎ minus11 sdot 119891119891 13 + ℎ 01 sdot 119891119891 23 + ℎ 11 sdot 119891119891 33

    DTU Compute

    2122018Introduction to Medical Image Analysis41 DTU Compute Technical University of Denmark

    2D Kernel Normalisation

    1 2 11 3 11 2 1

    h

    Normalisation factor

    1 + 2 + 1 + 1 + 3 + 1 + 1 + 2 + 1 = 13

    119909119909

    119910119910

    ℎ(119909119909119910119910)

    DTU Compute

    2122018Introduction to Medical Image Analysis42 DTU Compute Technical University of Denmark

    CorrelationA) 50122B) 123001C) 11233D) 2550E) 90454

    0 0 0 0

    13

    A B C D E

    Chart1

    0
    0
    0
    0
    13

    Sheet1

    DTU Compute

    2122018Introduction to Medical Image Analysis44 DTU Compute Technical University of Denmark

    Smoothing filters

    Also know as ndash Smoothing kernel Mean filter Low pass filter blurring

    The simplest filter ndash Spatial low pass filterndash Removes high frequencies

    Another mask ndash Gaussian filter

    1 1 1

    1 1 1

    1 1 191

    1 2 1

    2 4 2

    1 2 1161

    Why Gaussian

    DTU Compute

    2122018Introduction to Medical Image Analysis45 DTU Compute Technical University of Denmark

    Use of smoothing

    3x3 7x7 11x11 15x15

    DTU Compute

    2122018Introduction to Medical Image Analysis46 DTU Compute Technical University of Denmark

    Use of smoothing Large kernels smooth more Removes high frequency information Good at enhancing big structures

    3x3 15x15

    DTU Compute

    2122018Introduction to Medical Image Analysis47 DTU Compute Technical University of Denmark

    Mean filterA) 166B) 113C) 12D) 51E) 245

    0 0 0 0

    A B C D E

    Chart1

    12
    0
    0
    0
    0

    Sheet1

    DTU Compute

    2122018Introduction to Medical Image Analysis49 DTU Compute Technical University of Denmark

    Border handling

    0 2 41 2 2

    1 6 3

    1 2 12 5 3

    2 1 3

    1 3 1

    2 2 2

    0 1 3

    1 2 0

    2 1 4

    1 0 1

    Input Output

    No values at the border

    DTU Compute

    2122018Introduction to Medical Image Analysis50 DTU Compute Technical University of Denmark

    Border handling ndash extend the input

    0 2 41 2 2

    1 6 3

    1 2 12 5 3

    2 1 3

    1 3 1

    2 2 2

    0 1 3

    1 2 0

    2 1 4

    1 0 1

    Input

    0 0 0 0 000000

    bull Zero padding ndash what happens

    bull Zero is black ndash creates dark border around the image

    DTU Compute

    2122018Introduction to Medical Image Analysis51 DTU Compute Technical University of Denmark

    Correlation with zero paddingA) 5 8B) 12 16C) 13 3D) 15 21E) 17 12

    1 2 11 3 11 2 1

    0 2 41 2 2

    1 6 3

    1 2 12 5 3

    2 1 3

    1 3 1

    2 2 2

    0 1 3

    1 2 0

    2 1 4

    1 0 1

    0

    13

    0 0 0

    A B C D E

    Chart1

    0
    13
    0
    0
    0

    Sheet1

    DTU Compute

    2122018Introduction to Medical Image Analysis53 DTU Compute Technical University of Denmark

    Border handling ndash extend the input

    0 2 41 2 2

    1 6 3

    1 2 12 5 3

    2 1 3

    1 3 1

    2 2 2

    0 1 3

    1 2 0

    2 1 4

    1 0 1

    Input

    1 2 0 1 311211

    bull Reflection

    bull Normally better than zero padding

    DTU Compute

    2122018Introduction to Medical Image Analysis54 DTU Compute Technical University of Denmark

    Template Matching Template

    ndash Skabelon paring dansk Locates objects in images

    Input

    Template

    Output Correlation image

    DTU Compute

    2122018Introduction to Medical Image Analysis55 DTU Compute Technical University of Denmark

    Template Matching The correlation between the template and the input

    image is computed for each pixel

    Input

    Template

    Output Correlation image

    DTU Compute

    2122018Introduction to Medical Image Analysis56 DTU Compute Technical University of Denmark

    Template Matching The pixel with the highest value is found in the

    output imagendash Here is the highest correlation

    Input

    Template

    Output Correlation image

    DTU Compute

    2122018Introduction to Medical Image Analysis57 DTU Compute Technical University of Denmark

    Template Matching This corresponds to the found pattern in the input

    image

    Input

    Template

    Output Correlation image

    DTU Compute

    2122018Introduction to Medical Image Analysis58 DTU Compute Technical University of Denmark

    Problematic Correlation Correlation matching has problem with light areas ndash

    why

    Input (f)

    Template (h)

    Output Correlation imageFake max

    Real max

    Very High119892119892 119909119909119910119910 = 119895119895=minus119877119877

    119877119877

    119894119894=minus119877119877

    119877119877

    ℎ(119894119894 119895119895) 119891119891(119909119909 + 119894119894119910119910 + 119895119895)

    DTU Compute

    2122018Introduction to Medical Image Analysis59 DTU Compute Technical University of Denmark

    Normalised Cross Correlation

    Input (f)

    Template (h)

    Output Correlation image

    Real max

    NCC x y =Correlation

    Length of image patch sdot Length of template

    DTU Compute

    2122018Introduction to Medical Image Analysis60 DTU Compute Technical University of Denmark

    Length of template Vector length

    ndash Put all pixel values into a vectorndash Compute the length of this vector

    Describes the intensity of the templatendash Bright template has a large lengthndash Dark template has a small length

    Template (h)

    Length of template = 119895119895=minus119877119877

    119877119877

    119894119894=minus119877119877

    119877119877

    ℎ(119894119894 119895119895) ℎ(119894119894 119895119895)

    DTU Compute

    2122018Introduction to Medical Image Analysis61 DTU Compute Technical University of Denmark

    Length of image patch Vector length based on pixel values in image patch Describes the intensity of the image patch

    Template (h)

    Input (f) with patch

    DTU Compute

    2122018Introduction to Medical Image Analysis62 DTU Compute Technical University of Denmark

    Normalised Cross Correlation The length of the image patch and the length of

    template normalise the NCC If the image is very bright the NCC will be ldquopulled

    downrdquo

    NCC x y =Correlation

    Length of image patch sdot Length of template

    DTU Compute

    2122018Introduction to Medical Image Analysis63 DTU Compute Technical University of Denmark

    Normalised Cross Correlation NCC will be between

    ndash 0 No similarity between template and image patchndash 1 Template and image patch are identical

    Input (f)

    Template (h)

    Output Correlation image

    Real max

    NCC x y =Correlation

    Length of image patch sdot Length of template

    DTU Compute

    2122018Introduction to Medical Image Analysis64 DTU Compute Technical University of Denmark

    Normalised Cross Correlation

    A) 010B) 033C) 083D) 062E) 098

    Der udfoslashres template matching med og normalized crosscorrelation (NCC) beregnes Hvad bliver NNC i den markerede pixel

    1

    2 2

    3

    2

    A B C D E

    Chart1

    1
    2
    2
    3
    2

    Sheet1

    DTU Compute

    2122018Introduction to Medical Image Analysis66 DTU Compute Technical University of Denmark

    Edges An edge is where there is a

    high change in gray level values

    Objects are often separated from the background by edgesGray level profile

    DTU Compute

    2122018Introduction to Medical Image Analysis67 DTU Compute Technical University of Denmark

    Edges The profile as a function f(d) What value is high when there

    is an edgendash The slope of fndash The slope of the tangent at d

    f(d)

    119891119891prime(119889119889)

    DTU Compute

    2122018Introduction to Medical Image Analysis68 DTU Compute Technical University of Denmark

    Finite Difference Definition of slope

    Approximation

    Simpler approximationh = 1

    119891119891prime 119889119889 = limℎrarr0

    119891119891 119889119889 + ℎ minus 119891119891(119889119889)ℎ

    119891119891prime 119889119889 asymp119891119891 119889119889 + ℎ minus 119891119891(119889119889)

    ℎ

    119891119891prime 119889119889 asymp 119891119891 119889119889 + 1 minus 119891119891(119889119889)

    DTU Compute

    2122018Introduction to Medical Image Analysis69 DTU Compute Technical University of Denmark

    Edges Discrete approximation of frsquo(d) Can be implemented as a filter

    -1 0 1

    f(d-2) f(d-1) f(d) f(d+1) f(d+2) f(d+3)

    f(d)

    119891119891prime 119889119889 asymp 119891119891 119889119889 + 1 minus 119891119891(119889119889)

    DTU Compute

    2122018Introduction to Medical Image Analysis70 DTU Compute Technical University of Denmark

    Edges in 2D Changes in gray level values

    ndash Image gradientndash Gradient is the 2D derivative of a 2D function f(xy)ndash Equal to the slope of the imagendash A steep slope is equal to an edge

    120571120571119891119891 119909119909119910119910 = 119866(119892119892119909119909119892119892119910119910)

    DTU Compute

    2122018Introduction to Medical Image Analysis71 DTU Compute Technical University of Denmark

    Edge filter kernel The Prewitt filter is a typical

    edge filter Output image has high

    values where there are edges

    -1 0 1

    -1 0 1

    -1 0 1Vertical Prewitt filter

    DTU Compute

    2122018Introduction to Medical Image Analysis72 DTU Compute Technical University of Denmark

    Prewitt filter

    Original Prewitt Prewitt

    Hot colormapSmooth 15x15

    Smooth 15x15

    Prewitt

    DTU Compute

    2122018Introduction to Medical Image Analysis73 DTU Compute Technical University of Denmark

    Edge detection Edge filter

    ndash Prewitt for example Thresholding

    ndash Separate edges from non-edges

    Output is binary imagendash Edges are white

    DTU Compute

    2122018Introduction to Medical Image Analysis74 DTU Compute Technical University of Denmark

    Edge filtering

    A) MeanB) Horizontal SobelC) Vertical PrewittD) Horisontal PrewittE) Median

    Der udfoslashres en filtrering (correlation) med et filter paring billedet Der bruges ikke coefficient normalization Den filtrerede vaeligrdi i den markerede pixel bliver -119 Hvilket et 3x3 filter blev benyttet

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    DTU Compute

    2122018Introduction to Medical Image Analysis76 DTU Compute Technical University of Denmark

    02511 - Niveau af dagens emne forelaeligsingA) Meget letB) LetC) PassendeD) SvaeligrtE) Meget svaeligrt

    23

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    10

    A B C D E

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    2122018Introduction to Medical Image Analysis77 DTU Compute Technical University of Denmark

    02512 - Niveau af dagens emne forelaeligsingA) Meget letB) LetC) PassendeD) SvaeligrtE) Meget svaeligrt

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    DTU Compute

    2122018Introduction to Medical Image Analysis78 DTU Compute Technical University of Denmark

    02511 - Mit eget udbytte af dagenA) Jeg har laeligrt meget lidtB) Lidt laeligringC) PassendeD) God laeligringE) Jeg har laeligrt meget

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    DTU Compute

    2122018Introduction to Medical Image Analysis79 DTU Compute Technical University of Denmark

    02512 - Mit eget udbytte af dagenA) Jeg har laeligrt meget lidtB) Lidt laeligringC) PassendeD) God laeligringE) Jeg har laeligrt meget

    2

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    DTU Compute

    2122018Introduction to Medical Image Analysis80 DTU Compute Technical University of Denmark

    02511 - Sidste uges oslashvelser (pixelwiseoperations)A) Meget letteB) LetteC) PassendeD) SvaeligreE) Meget svaeligre

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    2122018Introduction to Medical Image Analysis81 DTU Compute Technical University of Denmark

    02512 - Sidste uges oslashvelser (pixelwiseoperations)A) Meget letteB) LetteC) PassendeD) SvaeligreE) Meget svaeligre

    3

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    DTU Compute

    2122018Introduction to Medical Image Analysis82 DTU Compute Technical University of Denmark

    Denne uges brug af clickersA) click click click ndash jeg bliver

    sindssygB) For meget clickC) PassendeD) Jeg vil gerne have lidt mereE) Jeg kan ikrsquo faring nok

    0 0

    5

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    A B C D E

    Chart1

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    DTU Compute

    2122018Introduction to Medical Image Analysis83 DTU Compute Technical University of Denmark

    What can you do after today Describe the difference between point processing and neighbourhood

    processing Compute a rank filtered image using the min max median and

    difference rank filters Compute a mean filtered image Decide if median or average filtering should be used for noise removal Choose the appropriate image border handling based on a given input

    image Implement and apply template matching Compute the normalised cross correlation and explain why it should be

    used Apply given image filter kernels to images Use edge filters on images Describe finite difference approximation of image gradients Describe the concept of edge detection

    DTU Compute

    2122018Introduction to Medical Image Analysis84 DTU Compute Technical University of Denmark

    Oslashvelsesrapport over oslashvelse 4 - 02511 Oslashvelser taeligller cirka 30 af karakteren Skal afleveres senest den 7 marts kl 2359 Kan afleveres af 1 eller 2 personer

    ndash I skal skrive jeres egen oslashvelsesrapportndash Brug mindst et af jeres egne billeder

    Afleveres som PDF Lad vaeligre med at kopiere opgaveteksten ind i jeres

    opgave Put Matlab kode i et Appendix og henvis fra teksten Eksempel rapport over oslashvelse findes paring

    hjemmesiden under eksamen

    DTU Compute

    2122018Introduction to Medical Image Analysis85 DTU Compute Technical University of Denmark

    Exercises

    • Introduction to Medical Image Analysis
    • Lecture 4 ndash Neighbourhood Processing
    • What can you do after today
    • Point processing
    • Point processing
    • Neighbourhood processing
    • Use of filtering
    • Salt and pepper noise
    • Salt and pepper noise
    • What is so special about noise
    • Noise ndash go away
    • What is the median Value
    • The median value
    • Noise away ndash the median filter
    • Noise removal ndash average filter
    • Noise removal ndash median filter
    • Image Filtering
    • Median filter
    • Rank filters
    • Median filter
    • Correlation
    • Why do we need similarity
    • Correlation (1D)
    • Correlation (1D)
    • Normalisation
    • Normalisation
    • Correlation on images
    • Correlation on images
    • Correlation on images
    • Draw your filter
    • Correlation on images ndash no normalisation
    • Correlation on images ndash no normalisation 2
    • Mathematics of 2D Correlation
    • Mathematics of 2D Correlation
    • Mathematics of 2D Correlation
    • Slide Number 40
    • 2D Kernel Normalisation
    • Correlation
    • Smoothing filters
    • Use of smoothing
    • Use of smoothing
    • Mean filter
    • Border handling
    • Border handling ndash extend the input
    • Correlation with zero padding
    • Border handling ndash extend the input
    • Template Matching
    • Template Matching
    • Template Matching
    • Template Matching
    • Problematic Correlation
    • Normalised Cross Correlation
    • Length of template
    • Length of image patch
    • Normalised Cross Correlation
    • Normalised Cross Correlation
    • Normalised Cross Correlation
    • Edges
    • Edges
    • Finite Difference
    • Edges
    • Edges in 2D
    • Edge filter kernel
    • Prewitt filter
    • Edge detection
    • Edge filtering
    • 02511 - Niveau af dagens emne forelaeligsing
    • 02512 - Niveau af dagens emne forelaeligsing
    • 02511 - Mit eget udbytte af dagen
    • 02512 - Mit eget udbytte af dagen
    • 02511 - Sidste uges oslashvelser (pixelwise operations)
    • 02512 - Sidste uges oslashvelser (pixelwise operations)
    • Denne uges brug af clickers
    • What can you do after today
    • Oslashvelsesrapport over oslashvelse 4 - 02511
    • Exercises
      A0
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      C1
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      E
      A1
      B2
      C2
      D3
      E2
      A
      B
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      D
      E
      A0
      B13
      C0
      D0
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      A12
      B0
      C0
      D0
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      B0
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      B12
      C1
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      A
      B
      C
      D
      E
      A13
      B0
      C0
      D0
      E2
      A
      B
      C
      D
      E

      DTU Compute

      2122018Introduction to Medical Image Analysis3 DTU Compute Technical University of Denmark

      What can you do after today Describe the difference between point processing and neighbourhood

      processing Compute a rank filtered image using the min max median and

      difference rank filters Compute a mean filtered image Decide if median or average filtering should be used for noise removal Choose the appropriate image border handling based on a given input

      image Implement and apply template matching Compute the normalised cross correlation and explain why it should be

      used Apply given image filter kernels to images Use edge filters on images Describe finite difference approximation of image gradients Describe the concept of edge detection

      DTU Compute

      2122018Introduction to Medical Image Analysis4 DTU Compute Technical University of Denmark

      Point processing

      0 2

      1 2

      1 2 1

      2 5 3

      1 3

      2 2

      0 1

      1 2 0

      2 1 4

      1 0 19

      12

      Input Output

      bull The value of the output pixel is only dependent on the value of one input pixel

      bull A global operation ndash changes all pixels

      DTU Compute

      2122018Introduction to Medical Image Analysis5 DTU Compute Technical University of Denmark

      Point processing Grey level enhancement

      ndash Process one pixel at a time independent of all other pixelsndash For example used to correct Brightness and Contrast

      Too lowcontrastCorrect

      Too highcontrast

      Too high brightness

      Too low brightness

      DTU Compute

      2122018Introduction to Medical Image Analysis6 DTU Compute Technical University of Denmark

      Neighbourhood processing

      0 2

      1 2

      1 2 1

      2 5 3

      1 3

      2 2

      0 1

      1 2 0

      2 1 4

      1 0 19

      12

      Input Output

      bull Several pixels in the input has an effect on the output

      DTU Compute

      2122018Introduction to Medical Image Analysis7 DTU Compute Technical University of Denmark

      Use of filtering

      Noise removal Enhance edges Smoothing

      bull Image processing

      bull Typically done before actual image analysis

      DTU Compute

      2122018Introduction to Medical Image Analysis8 DTU Compute Technical University of Denmark

      Salt and pepper noise Pixel values that are very

      different from their neighbours

      Very bright or very dark spots

      Scratches in X-rays

      What is that

      DTU Compute

      2122018Introduction to Medical Image Analysis9 DTU Compute Technical University of Denmark

      Salt and pepper noise Fake example

      ndash Let us take a closer look at noise pixels

      They are all 0 or 255

      Should we just remove all the 0rsquos and 255rsquos from the image

      DTU Compute

      2122018Introduction to Medical Image Analysis10 DTU Compute Technical University of Denmark

      What is so special about noise What is the value of the pixel

      compared to the neighbours Average of the neighbours

      ndash 170 Can we compare to the

      averagendash Difficult ndash should we remove

      all values bigger than average+1

      It is difficult to detect noise

      172 169 171 168 0 169 172 173 168

      DTU Compute

      2122018Introduction to Medical Image Analysis11 DTU Compute Technical University of Denmark

      Noise ndash go away We can not tell what pixels

      are noise One solution

      ndash Set all pixels to the average of the neighbours (and the pixel itself)

      Oh nondash Problemsndash The noise ldquopollutesrdquo the

      good pixels

      172 169 171 168 0 169 172 173 168

      170

      169 168 0 170 172173 170 172 170

      149

      DTU Compute

      2122018Introduction to Medical Image Analysis12 DTU Compute Technical University of Denmark

      What is the median ValueA) 170B) 173C) 169D) 171E) 172

      13

      0 0 02

      A B C D E

      169 168 0 170172 173 170 172 170

      Chart1

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      2122018Introduction to Medical Image Analysis13 DTU Compute Technical University of Denmark

      The median value The values are sorted from low to high The middle number is picked

      ndash The median value

      169 168 0 170172 173 170 172 170

      0168 169 170 170 170172 172173

      Median

      Noise has no influence on the median

      DTU Compute

      2122018Introduction to Medical Image Analysis14 DTU Compute Technical University of Denmark

      Noise away ndash the median filter All pixels are set to the

      median of its neighbourhood Noise pixels do not pollute

      good pixels

      172 169 171 168 0 169 172 173 168

      170

      169 168 0 170 172173 170 172 170

      170

      DTU Compute

      2122018Introduction to Medical Image Analysis15 DTU Compute Technical University of Denmark

      Noise removal ndash average filter

      Scanned X-ray with salt and pepper noise

      Average filter (3x3)

      DTU Compute

      2122018Introduction to Medical Image Analysis16 DTU Compute Technical University of Denmark

      Noise removal ndash median filter

      Scanned X-ray with salt and pepper noise

      Median filter (3x3)

      DTU Compute

      2122018Introduction to Medical Image Analysis17 DTU Compute Technical University of Denmark

      Image Filtering Creates a new filtered image Output pixel is computed based

      on a neighbourhood in the input image

      3 x 3 neighbourhoodndash Filter size 3 x 3ndash Kernel size 3 x 3ndash Mask size 3 x 3

      Larger filters often usedndash Size

      7 x 7ndash Number of elements

      49

      DTU Compute

      2122018Introduction to Medical Image Analysis18 DTU Compute Technical University of Denmark

      Median filterA) 25B) 90C) 198D) 86E) 103

      0

      13

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      2122018Introduction to Medical Image Analysis20 DTU Compute Technical University of Denmark

      Rank filters Based on sorting the pixel

      values in the neighbouring region

      Minimum rank filterndash Darker image Noise problems

      Maximum rank filterndash Lighter image Noise problems

      Difference filterndash Enhances changes (edges)

      0168 169 170 170 170172 172173

      -

      DTU Compute

      2122018Introduction to Medical Image Analysis21 DTU Compute Technical University of Denmark

      Median filter

      A) 3B) 84C) 112D) 73E) 202

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      DTU Compute

      2122018Introduction to Medical Image Analysis23 DTU Compute Technical University of Denmark

      Correlation What is it Two measurements

      ndash Low correlationndash High correlation

      High correlation means that there is a relation between the values

      They look the same Correlation is a measure of

      similarity

      Low

      High

      Muscles

      Mat

      h Ski

      lls

      Muscles

      Ben

      ch P

      ress

      DTU Compute

      2122018Introduction to Medical Image Analysis24 DTU Compute Technical University of Denmark

      Why do we need similarity Image analysis is also about recognition of patterns Often an example pattern is used We need something to tell us if there is a high match

      between our pattern and a part of the image

      Example pattern

      Image

      Find matches

      DTU Compute

      2122018Introduction to Medical Image Analysis25 DTU Compute Technical University of Denmark

      Correlation (1D)

      1 1 2 2 1 1 2 2 1 1

      1 2 1

      45

      41

      1 1 + 2 1 + 1 2 = 5

      Normalise

      Kernel

      Signal (1D image)

      41

      DTU Compute

      2122018Introduction to Medical Image Analysis26 DTU Compute Technical University of Denmark

      Correlation (1D)

      1 1 2 2 1 1 2 2 1 1

      1 2 1

      45

      47

      47

      45

      45

      47

      47

      45

      41

      DTU Compute

      2122018Introduction to Medical Image Analysis27 DTU Compute Technical University of Denmark

      Normalisation

      1 1 2 2 1 1 2 2 1 1

      1 2 1

      45

      41

      1 1 + 2 1 + 1 2 = 5

      Normalise41

      bull The sum of the kernel elements is used

      bull Keep the values in the same range as the input image

      Sum is 4

      DTU Compute

      2122018Introduction to Medical Image Analysis28 DTU Compute Technical University of Denmark

      Normalisation Normalisation factor

      ndash Sum of kernel coefficients

      1 2 1h(x)

      119909119909

      ℎ 119909119909 = 1 + 2 + 1

      DTU Compute

      2122018Introduction to Medical Image Analysis29 DTU Compute Technical University of Denmark

      Correlation on images The filter is now 2D 1 1 1

      1 1 1

      1 1 1

      0 2 4

      1 2 2

      1 6 3

      1 2 12 5 3

      2 1 3

      1 3 1

      2 2 2

      0 1 3

      1 2 0

      2 1 4

      1 0 1

      912

      91

      Input OutputKernel

      Kernel coefficients

      DTU Compute

      2122018Introduction to Medical Image Analysis30 DTU Compute Technical University of Denmark

      Correlation on images

      1 1 11 1 11 1 1

      0 2 4

      1 2 2

      1 6 3

      1 2 0

      2 1 4

      1 0 1

      912

      911

      91

      Input Output

      1 3 1

      2 2 2

      0 1 3

      1 2 12 5 3

      2 1 3

      DTU Compute

      2122018Introduction to Medical Image Analysis31 DTU Compute Technical University of Denmark

      Correlation on images

      Input Output

      The mask is moved row by row

      No values at the border

      0 2 4

      1 2 2

      1 6 3

      1 2 0

      2 1 4

      1 0 1

      1 3 1

      2 2 2

      0 1 3

      1 2 12 5 3

      2 1 3

      DTU Compute

      2122018Introduction to Medical Image Analysis32 DTU Compute Technical University of Denmark

      1 2 1

      1 3 1

      1 2 1

      -1 -2 -1

      0 0 0

      1 2 1

      Draw your filter

      DTU Compute

      2122018Introduction to Medical Image Analysis33 DTU Compute Technical University of Denmark

      Correlation on images ndash no normalisationA) 4B) 7C) 16D) 23E) 25

      1 2 11 3 11 2 1

      0 2 41 2 2

      1 6 3

      1 2 12 5 3

      2 1 3

      1 3 1

      2 2 2

      0 1 3

      1 2 0

      2 1 4

      1 0 11 0

      14

      0 0

      A B C D E

      Chart1

      1
      0
      14
      0
      0

      Sheet1

      DTU Compute

      2122018Introduction to Medical Image Analysis34 DTU Compute Technical University of Denmark

      Correlation on images ndash no normalisation 2A) 010B) 3 3C) 6 2D) 10 15E) 11 32

      13

      0 0 0 0

      A B C D E

      -1 -2 -10 0 01 2 1

      0 2 41 2 2

      1 6 3

      1 2 12 5 3

      2 1 3

      1 3 1

      2 2 2

      0 1 3

      1 2 0

      2 1 4

      1 0 1

      Chart1

      13
      0
      0
      0
      0

      Sheet1

      DTU Compute

      2122018Introduction to Medical Image Analysis37 DTU Compute Technical University of Denmark

      Mathematics of 2D Correlation

      h

      f

      Correlation operator

      1 2 11 3 11 2 1

      0 2 4

      1 2 2

      1 6 3

      1 2 1

      2 5 3

      2 1 3

      1 3 1

      2 2 2

      0 1 3

      1 2 0

      2 1 4

      1 0 1

      119892119892 119909119909119910119910 = 119891119891 119909119909119910119910 ∘ ℎ(119909119909119910119910)

      DTU Compute

      2122018Introduction to Medical Image Analysis38 DTU Compute Technical University of Denmark

      Mathematics of 2D Correlation

      1 2 11 3 11 2 1

      0 2 4

      1 2 2

      1 6 3

      1 2 1

      2 5 3

      2 1 3

      1 3 1

      2 2 2

      0 1 3

      1 2 0

      2 1 4

      1 0 1

      h

      fh(00)

      f(21)

      Example g(21)

      i = -1 j = -1

      i = 1 j = 0

      119892119892 119909119909119910119910 = 119895119895=minus119877119877

      119877119877

      119894119894=minus119877119877

      119877119877

      ℎ(119894119894 119895119895) 119891119891(119909119909 + 119894119894119910119910 + 119895119895)

      DTU Compute

      2122018Introduction to Medical Image Analysis39 DTU Compute Technical University of Denmark

      Mathematics of 2D Correlation

      1 2 11 3 11 2 1

      0 2 4

      1 2 2

      1 6 3

      1 2 1

      2 5 3

      2 1 3

      1 3 1

      2 2 2

      0 1 3

      1 2 0

      2 1 4

      1 0 1

      h

      f

      119892119892 119909119909119910119910 = 119895119895=minus119877119877

      119877119877

      119894119894=minus119877119877

      119877119877

      ℎ(119894119894 119895119895) 119891119891(119909119909 + 119894119894119910119910 + 119895119895)

      119892119892(119909119909119910119910 = 1 2 + 2 0 + 1 1 + 1 1 + 3 4 + 1 2 + 1 0 + 2 1 + 1 0

      DTU Compute

      2122018Introduction to Medical Image Analysis40 DTU Compute Technical University of Denmark

      119892119892 119909119909 119910119910 = 119895119895=minus119877119877

      119877119877

      119894119894=minus119877119877

      119877119877

      ℎ(119894119894 119895119895) 119891119891(119909119909 + 119894119894119910119910 + 119895119895)

      119892119892 22 =ℎ minus1minus1 sdot 119891119891 11 + ℎ 0minus1 sdot 119891119891 21 + ℎ 1minus1 sdot 119891119891 31 +ℎ minus10 sdot 119891119891 12 + ℎ 00 sdot 119891119891 22 + ℎ 10 sdot 119891119891 32 +ℎ minus11 sdot 119891119891 13 + ℎ 01 sdot 119891119891 23 + ℎ 11 sdot 119891119891 33

      DTU Compute

      2122018Introduction to Medical Image Analysis41 DTU Compute Technical University of Denmark

      2D Kernel Normalisation

      1 2 11 3 11 2 1

      h

      Normalisation factor

      1 + 2 + 1 + 1 + 3 + 1 + 1 + 2 + 1 = 13

      119909119909

      119910119910

      ℎ(119909119909119910119910)

      DTU Compute

      2122018Introduction to Medical Image Analysis42 DTU Compute Technical University of Denmark

      CorrelationA) 50122B) 123001C) 11233D) 2550E) 90454

      0 0 0 0

      13

      A B C D E

      Chart1

      0
      0
      0
      0
      13

      Sheet1

      DTU Compute

      2122018Introduction to Medical Image Analysis44 DTU Compute Technical University of Denmark

      Smoothing filters

      Also know as ndash Smoothing kernel Mean filter Low pass filter blurring

      The simplest filter ndash Spatial low pass filterndash Removes high frequencies

      Another mask ndash Gaussian filter

      1 1 1

      1 1 1

      1 1 191

      1 2 1

      2 4 2

      1 2 1161

      Why Gaussian

      DTU Compute

      2122018Introduction to Medical Image Analysis45 DTU Compute Technical University of Denmark

      Use of smoothing

      3x3 7x7 11x11 15x15

      DTU Compute

      2122018Introduction to Medical Image Analysis46 DTU Compute Technical University of Denmark

      Use of smoothing Large kernels smooth more Removes high frequency information Good at enhancing big structures

      3x3 15x15

      DTU Compute

      2122018Introduction to Medical Image Analysis47 DTU Compute Technical University of Denmark

      Mean filterA) 166B) 113C) 12D) 51E) 245

      0 0 0 0

      A B C D E

      Chart1

      12
      0
      0
      0
      0

      Sheet1

      DTU Compute

      2122018Introduction to Medical Image Analysis49 DTU Compute Technical University of Denmark

      Border handling

      0 2 41 2 2

      1 6 3

      1 2 12 5 3

      2 1 3

      1 3 1

      2 2 2

      0 1 3

      1 2 0

      2 1 4

      1 0 1

      Input Output

      No values at the border

      DTU Compute

      2122018Introduction to Medical Image Analysis50 DTU Compute Technical University of Denmark

      Border handling ndash extend the input

      0 2 41 2 2

      1 6 3

      1 2 12 5 3

      2 1 3

      1 3 1

      2 2 2

      0 1 3

      1 2 0

      2 1 4

      1 0 1

      Input

      0 0 0 0 000000

      bull Zero padding ndash what happens

      bull Zero is black ndash creates dark border around the image

      DTU Compute

      2122018Introduction to Medical Image Analysis51 DTU Compute Technical University of Denmark

      Correlation with zero paddingA) 5 8B) 12 16C) 13 3D) 15 21E) 17 12

      1 2 11 3 11 2 1

      0 2 41 2 2

      1 6 3

      1 2 12 5 3

      2 1 3

      1 3 1

      2 2 2

      0 1 3

      1 2 0

      2 1 4

      1 0 1

      0

      13

      0 0 0

      A B C D E

      Chart1

      0
      13
      0
      0
      0

      Sheet1

      DTU Compute

      2122018Introduction to Medical Image Analysis53 DTU Compute Technical University of Denmark

      Border handling ndash extend the input

      0 2 41 2 2

      1 6 3

      1 2 12 5 3

      2 1 3

      1 3 1

      2 2 2

      0 1 3

      1 2 0

      2 1 4

      1 0 1

      Input

      1 2 0 1 311211

      bull Reflection

      bull Normally better than zero padding

      DTU Compute

      2122018Introduction to Medical Image Analysis54 DTU Compute Technical University of Denmark

      Template Matching Template

      ndash Skabelon paring dansk Locates objects in images

      Input

      Template

      Output Correlation image

      DTU Compute

      2122018Introduction to Medical Image Analysis55 DTU Compute Technical University of Denmark

      Template Matching The correlation between the template and the input

      image is computed for each pixel

      Input

      Template

      Output Correlation image

      DTU Compute

      2122018Introduction to Medical Image Analysis56 DTU Compute Technical University of Denmark

      Template Matching The pixel with the highest value is found in the

      output imagendash Here is the highest correlation

      Input

      Template

      Output Correlation image

      DTU Compute

      2122018Introduction to Medical Image Analysis57 DTU Compute Technical University of Denmark

      Template Matching This corresponds to the found pattern in the input

      image

      Input

      Template

      Output Correlation image

      DTU Compute

      2122018Introduction to Medical Image Analysis58 DTU Compute Technical University of Denmark

      Problematic Correlation Correlation matching has problem with light areas ndash

      why

      Input (f)

      Template (h)

      Output Correlation imageFake max

      Real max

      Very High119892119892 119909119909119910119910 = 119895119895=minus119877119877

      119877119877

      119894119894=minus119877119877

      119877119877

      ℎ(119894119894 119895119895) 119891119891(119909119909 + 119894119894119910119910 + 119895119895)

      DTU Compute

      2122018Introduction to Medical Image Analysis59 DTU Compute Technical University of Denmark

      Normalised Cross Correlation

      Input (f)

      Template (h)

      Output Correlation image

      Real max

      NCC x y =Correlation

      Length of image patch sdot Length of template

      DTU Compute

      2122018Introduction to Medical Image Analysis60 DTU Compute Technical University of Denmark

      Length of template Vector length

      ndash Put all pixel values into a vectorndash Compute the length of this vector

      Describes the intensity of the templatendash Bright template has a large lengthndash Dark template has a small length

      Template (h)

      Length of template = 119895119895=minus119877119877

      119877119877

      119894119894=minus119877119877

      119877119877

      ℎ(119894119894 119895119895) ℎ(119894119894 119895119895)

      DTU Compute

      2122018Introduction to Medical Image Analysis61 DTU Compute Technical University of Denmark

      Length of image patch Vector length based on pixel values in image patch Describes the intensity of the image patch

      Template (h)

      Input (f) with patch

      DTU Compute

      2122018Introduction to Medical Image Analysis62 DTU Compute Technical University of Denmark

      Normalised Cross Correlation The length of the image patch and the length of

      template normalise the NCC If the image is very bright the NCC will be ldquopulled

      downrdquo

      NCC x y =Correlation

      Length of image patch sdot Length of template

      DTU Compute

      2122018Introduction to Medical Image Analysis63 DTU Compute Technical University of Denmark

      Normalised Cross Correlation NCC will be between

      ndash 0 No similarity between template and image patchndash 1 Template and image patch are identical

      Input (f)

      Template (h)

      Output Correlation image

      Real max

      NCC x y =Correlation

      Length of image patch sdot Length of template

      DTU Compute

      2122018Introduction to Medical Image Analysis64 DTU Compute Technical University of Denmark

      Normalised Cross Correlation

      A) 010B) 033C) 083D) 062E) 098

      Der udfoslashres template matching med og normalized crosscorrelation (NCC) beregnes Hvad bliver NNC i den markerede pixel

      1

      2 2

      3

      2

      A B C D E

      Chart1

      1
      2
      2
      3
      2

      Sheet1

      DTU Compute

      2122018Introduction to Medical Image Analysis66 DTU Compute Technical University of Denmark

      Edges An edge is where there is a

      high change in gray level values

      Objects are often separated from the background by edgesGray level profile

      DTU Compute

      2122018Introduction to Medical Image Analysis67 DTU Compute Technical University of Denmark

      Edges The profile as a function f(d) What value is high when there

      is an edgendash The slope of fndash The slope of the tangent at d

      f(d)

      119891119891prime(119889119889)

      DTU Compute

      2122018Introduction to Medical Image Analysis68 DTU Compute Technical University of Denmark

      Finite Difference Definition of slope

      Approximation

      Simpler approximationh = 1

      119891119891prime 119889119889 = limℎrarr0

      119891119891 119889119889 + ℎ minus 119891119891(119889119889)ℎ

      119891119891prime 119889119889 asymp119891119891 119889119889 + ℎ minus 119891119891(119889119889)

      ℎ

      119891119891prime 119889119889 asymp 119891119891 119889119889 + 1 minus 119891119891(119889119889)

      DTU Compute

      2122018Introduction to Medical Image Analysis69 DTU Compute Technical University of Denmark

      Edges Discrete approximation of frsquo(d) Can be implemented as a filter

      -1 0 1

      f(d-2) f(d-1) f(d) f(d+1) f(d+2) f(d+3)

      f(d)

      119891119891prime 119889119889 asymp 119891119891 119889119889 + 1 minus 119891119891(119889119889)

      DTU Compute

      2122018Introduction to Medical Image Analysis70 DTU Compute Technical University of Denmark

      Edges in 2D Changes in gray level values

      ndash Image gradientndash Gradient is the 2D derivative of a 2D function f(xy)ndash Equal to the slope of the imagendash A steep slope is equal to an edge

      120571120571119891119891 119909119909119910119910 = 119866(119892119892119909119909119892119892119910119910)

      DTU Compute

      2122018Introduction to Medical Image Analysis71 DTU Compute Technical University of Denmark

      Edge filter kernel The Prewitt filter is a typical

      edge filter Output image has high

      values where there are edges

      -1 0 1

      -1 0 1

      -1 0 1Vertical Prewitt filter

      DTU Compute

      2122018Introduction to Medical Image Analysis72 DTU Compute Technical University of Denmark

      Prewitt filter

      Original Prewitt Prewitt

      Hot colormapSmooth 15x15

      Smooth 15x15

      Prewitt

      DTU Compute

      2122018Introduction to Medical Image Analysis73 DTU Compute Technical University of Denmark

      Edge detection Edge filter

      ndash Prewitt for example Thresholding

      ndash Separate edges from non-edges

      Output is binary imagendash Edges are white

      DTU Compute

      2122018Introduction to Medical Image Analysis74 DTU Compute Technical University of Denmark

      Edge filtering

      A) MeanB) Horizontal SobelC) Vertical PrewittD) Horisontal PrewittE) Median

      Der udfoslashres en filtrering (correlation) med et filter paring billedet Der bruges ikke coefficient normalization Den filtrerede vaeligrdi i den markerede pixel bliver -119 Hvilket et 3x3 filter blev benyttet

      0

      8

      1 10

      A B C D E

      Chart1

      0
      8
      1
      1
      0

      Sheet1

      DTU Compute

      2122018Introduction to Medical Image Analysis76 DTU Compute Technical University of Denmark

      02511 - Niveau af dagens emne forelaeligsingA) Meget letB) LetC) PassendeD) SvaeligrtE) Meget svaeligrt

      23

      6

      10

      A B C D E

      Chart1

      2
      3
      6
      1
      0

      Sheet1

      DTU Compute

      2122018Introduction to Medical Image Analysis77 DTU Compute Technical University of Denmark

      02512 - Niveau af dagens emne forelaeligsingA) Meget letB) LetC) PassendeD) SvaeligrtE) Meget svaeligrt

      0 0

      1

      0 0

      A B C D E

      Chart1

      0
      0
      1
      0
      0

      Sheet1

      DTU Compute

      2122018Introduction to Medical Image Analysis78 DTU Compute Technical University of Denmark

      02511 - Mit eget udbytte af dagenA) Jeg har laeligrt meget lidtB) Lidt laeligringC) PassendeD) God laeligringE) Jeg har laeligrt meget

      0 0

      2

      6

      0

      A B C D E

      Chart1

      0
      0
      2
      6
      0

      Sheet1

      DTU Compute

      2122018Introduction to Medical Image Analysis79 DTU Compute Technical University of Denmark

      02512 - Mit eget udbytte af dagenA) Jeg har laeligrt meget lidtB) Lidt laeligringC) PassendeD) God laeligringE) Jeg har laeligrt meget

      2

      1

      3

      2

      0

      A B C D E

      Chart1

      2
      1
      3
      2
      0

      Sheet1

      DTU Compute

      2122018Introduction to Medical Image Analysis80 DTU Compute Technical University of Denmark

      02511 - Sidste uges oslashvelser (pixelwiseoperations)A) Meget letteB) LetteC) PassendeD) SvaeligreE) Meget svaeligre

      0 0

      1

      4

      1

      A B C D E

      Chart1

      0
      0
      1
      4
      1

      Sheet1

      DTU Compute

      2122018Introduction to Medical Image Analysis81 DTU Compute Technical University of Denmark

      02512 - Sidste uges oslashvelser (pixelwiseoperations)A) Meget letteB) LetteC) PassendeD) SvaeligreE) Meget svaeligre

      3

      0

      3

      0 0

      A B C D E

      Chart1

      3
      0
      3
      0
      0

      Sheet1

      DTU Compute

      2122018Introduction to Medical Image Analysis82 DTU Compute Technical University of Denmark

      Denne uges brug af clickersA) click click click ndash jeg bliver

      sindssygB) For meget clickC) PassendeD) Jeg vil gerne have lidt mereE) Jeg kan ikrsquo faring nok

      0 0

      5

      0

      6

      A B C D E

      Chart1

      0
      0
      5
      0
      6

      Sheet1

      DTU Compute

      2122018Introduction to Medical Image Analysis83 DTU Compute Technical University of Denmark

      What can you do after today Describe the difference between point processing and neighbourhood

      processing Compute a rank filtered image using the min max median and

      difference rank filters Compute a mean filtered image Decide if median or average filtering should be used for noise removal Choose the appropriate image border handling based on a given input

      image Implement and apply template matching Compute the normalised cross correlation and explain why it should be

      used Apply given image filter kernels to images Use edge filters on images Describe finite difference approximation of image gradients Describe the concept of edge detection

      DTU Compute

      2122018Introduction to Medical Image Analysis84 DTU Compute Technical University of Denmark

      Oslashvelsesrapport over oslashvelse 4 - 02511 Oslashvelser taeligller cirka 30 af karakteren Skal afleveres senest den 7 marts kl 2359 Kan afleveres af 1 eller 2 personer

      ndash I skal skrive jeres egen oslashvelsesrapportndash Brug mindst et af jeres egne billeder

      Afleveres som PDF Lad vaeligre med at kopiere opgaveteksten ind i jeres

      opgave Put Matlab kode i et Appendix og henvis fra teksten Eksempel rapport over oslashvelse findes paring

      hjemmesiden under eksamen

      DTU Compute

      2122018Introduction to Medical Image Analysis85 DTU Compute Technical University of Denmark

      Exercises

      • Introduction to Medical Image Analysis
      • Lecture 4 ndash Neighbourhood Processing
      • What can you do after today
      • Point processing
      • Point processing
      • Neighbourhood processing
      • Use of filtering
      • Salt and pepper noise
      • Salt and pepper noise
      • What is so special about noise
      • Noise ndash go away
      • What is the median Value
      • The median value
      • Noise away ndash the median filter
      • Noise removal ndash average filter
      • Noise removal ndash median filter
      • Image Filtering
      • Median filter
      • Rank filters
      • Median filter
      • Correlation
      • Why do we need similarity
      • Correlation (1D)
      • Correlation (1D)
      • Normalisation
      • Normalisation
      • Correlation on images
      • Correlation on images
      • Correlation on images
      • Draw your filter
      • Correlation on images ndash no normalisation
      • Correlation on images ndash no normalisation 2
      • Mathematics of 2D Correlation
      • Mathematics of 2D Correlation
      • Mathematics of 2D Correlation
      • Slide Number 40
      • 2D Kernel Normalisation
      • Correlation
      • Smoothing filters
      • Use of smoothing
      • Use of smoothing
      • Mean filter
      • Border handling
      • Border handling ndash extend the input
      • Correlation with zero padding
      • Border handling ndash extend the input
      • Template Matching
      • Template Matching
      • Template Matching
      • Template Matching
      • Problematic Correlation
      • Normalised Cross Correlation
      • Length of template
      • Length of image patch
      • Normalised Cross Correlation
      • Normalised Cross Correlation
      • Normalised Cross Correlation
      • Edges
      • Edges
      • Finite Difference
      • Edges
      • Edges in 2D
      • Edge filter kernel
      • Prewitt filter
      • Edge detection
      • Edge filtering
      • 02511 - Niveau af dagens emne forelaeligsing
      • 02512 - Niveau af dagens emne forelaeligsing
      • 02511 - Mit eget udbytte af dagen
      • 02512 - Mit eget udbytte af dagen
      • 02511 - Sidste uges oslashvelser (pixelwise operations)
      • 02512 - Sidste uges oslashvelser (pixelwise operations)
      • Denne uges brug af clickers
      • What can you do after today
      • Oslashvelsesrapport over oslashvelse 4 - 02511
      • Exercises
        A0
        B0
        C5
        D0
        E6
        A
        B
        C
        D
        E
        A3
        B0
        C3
        D0
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        E1
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        E
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        C3
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        E
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        E0
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        C
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        E
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        C1
        D0
        E0
        A
        B
        C
        D
        E
        A2
        B3
        C6
        D1
        E0
        A
        B
        C
        D
        E
        A0
        B8
        C1
        D1
        E0
        A
        B
        C
        D
        E
        A1
        B2
        C2
        D3
        E2
        A
        B
        C
        D
        E
        A0
        B13
        C0
        D0
        E0
        A
        B
        C
        D
        E
        A12
        B0
        C0
        D0
        E0
        A
        B
        C
        D
        E
        A0
        B0
        C0
        D0
        E13
        A
        B
        C
        D
        E
        A13
        B0
        C0
        D0
        E0
        A
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        C
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        A1
        B0
        C14
        D0
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        A
        B
        C
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        E
        A0
        B12
        C1
        D0
        E0
        A
        B
        C
        D
        E
        A0
        B13
        C1
        D0
        E0
        A
        B
        C
        D
        E
        A13
        B0
        C0
        D0
        E2
        A
        B
        C
        D
        E

        DTU Compute

        2122018Introduction to Medical Image Analysis4 DTU Compute Technical University of Denmark

        Point processing

        0 2

        1 2

        1 2 1

        2 5 3

        1 3

        2 2

        0 1

        1 2 0

        2 1 4

        1 0 19

        12

        Input Output

        bull The value of the output pixel is only dependent on the value of one input pixel

        bull A global operation ndash changes all pixels

        DTU Compute

        2122018Introduction to Medical Image Analysis5 DTU Compute Technical University of Denmark

        Point processing Grey level enhancement

        ndash Process one pixel at a time independent of all other pixelsndash For example used to correct Brightness and Contrast

        Too lowcontrastCorrect

        Too highcontrast

        Too high brightness

        Too low brightness

        DTU Compute

        2122018Introduction to Medical Image Analysis6 DTU Compute Technical University of Denmark

        Neighbourhood processing

        0 2

        1 2

        1 2 1

        2 5 3

        1 3

        2 2

        0 1

        1 2 0

        2 1 4

        1 0 19

        12

        Input Output

        bull Several pixels in the input has an effect on the output

        DTU Compute

        2122018Introduction to Medical Image Analysis7 DTU Compute Technical University of Denmark

        Use of filtering

        Noise removal Enhance edges Smoothing

        bull Image processing

        bull Typically done before actual image analysis

        DTU Compute

        2122018Introduction to Medical Image Analysis8 DTU Compute Technical University of Denmark

        Salt and pepper noise Pixel values that are very

        different from their neighbours

        Very bright or very dark spots

        Scratches in X-rays

        What is that

        DTU Compute

        2122018Introduction to Medical Image Analysis9 DTU Compute Technical University of Denmark

        Salt and pepper noise Fake example

        ndash Let us take a closer look at noise pixels

        They are all 0 or 255

        Should we just remove all the 0rsquos and 255rsquos from the image

        DTU Compute

        2122018Introduction to Medical Image Analysis10 DTU Compute Technical University of Denmark

        What is so special about noise What is the value of the pixel

        compared to the neighbours Average of the neighbours

        ndash 170 Can we compare to the

        averagendash Difficult ndash should we remove

        all values bigger than average+1

        It is difficult to detect noise

        172 169 171 168 0 169 172 173 168

        DTU Compute

        2122018Introduction to Medical Image Analysis11 DTU Compute Technical University of Denmark

        Noise ndash go away We can not tell what pixels

        are noise One solution

        ndash Set all pixels to the average of the neighbours (and the pixel itself)

        Oh nondash Problemsndash The noise ldquopollutesrdquo the

        good pixels

        172 169 171 168 0 169 172 173 168

        170

        169 168 0 170 172173 170 172 170

        149

        DTU Compute

        2122018Introduction to Medical Image Analysis12 DTU Compute Technical University of Denmark

        What is the median ValueA) 170B) 173C) 169D) 171E) 172

        13

        0 0 02

        A B C D E

        169 168 0 170172 173 170 172 170

        Chart1

        13
        0
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        Sheet1

        DTU Compute

        2122018Introduction to Medical Image Analysis13 DTU Compute Technical University of Denmark

        The median value The values are sorted from low to high The middle number is picked

        ndash The median value

        169 168 0 170172 173 170 172 170

        0168 169 170 170 170172 172173

        Median

        Noise has no influence on the median

        DTU Compute

        2122018Introduction to Medical Image Analysis14 DTU Compute Technical University of Denmark

        Noise away ndash the median filter All pixels are set to the

        median of its neighbourhood Noise pixels do not pollute

        good pixels

        172 169 171 168 0 169 172 173 168

        170

        169 168 0 170 172173 170 172 170

        170

        DTU Compute

        2122018Introduction to Medical Image Analysis15 DTU Compute Technical University of Denmark

        Noise removal ndash average filter

        Scanned X-ray with salt and pepper noise

        Average filter (3x3)

        DTU Compute

        2122018Introduction to Medical Image Analysis16 DTU Compute Technical University of Denmark

        Noise removal ndash median filter

        Scanned X-ray with salt and pepper noise

        Median filter (3x3)

        DTU Compute

        2122018Introduction to Medical Image Analysis17 DTU Compute Technical University of Denmark

        Image Filtering Creates a new filtered image Output pixel is computed based

        on a neighbourhood in the input image

        3 x 3 neighbourhoodndash Filter size 3 x 3ndash Kernel size 3 x 3ndash Mask size 3 x 3

        Larger filters often usedndash Size

        7 x 7ndash Number of elements

        49

        DTU Compute

        2122018Introduction to Medical Image Analysis18 DTU Compute Technical University of Denmark

        Median filterA) 25B) 90C) 198D) 86E) 103

        0

        13

        1 0 0

        A B C D E

        Chart1

        0
        13
        1
        0
        0

        Sheet1

        DTU Compute

        2122018Introduction to Medical Image Analysis20 DTU Compute Technical University of Denmark

        Rank filters Based on sorting the pixel

        values in the neighbouring region

        Minimum rank filterndash Darker image Noise problems

        Maximum rank filterndash Lighter image Noise problems

        Difference filterndash Enhances changes (edges)

        0168 169 170 170 170172 172173

        -

        DTU Compute

        2122018Introduction to Medical Image Analysis21 DTU Compute Technical University of Denmark

        Median filter

        A) 3B) 84C) 112D) 73E) 202

        0

        12

        10 0

        A B C D E

        Chart1

        0
        12
        1
        0
        0

        Sheet1

        DTU Compute

        2122018Introduction to Medical Image Analysis23 DTU Compute Technical University of Denmark

        Correlation What is it Two measurements

        ndash Low correlationndash High correlation

        High correlation means that there is a relation between the values

        They look the same Correlation is a measure of

        similarity

        Low

        High

        Muscles

        Mat

        h Ski

        lls

        Muscles

        Ben

        ch P

        ress

        DTU Compute

        2122018Introduction to Medical Image Analysis24 DTU Compute Technical University of Denmark

        Why do we need similarity Image analysis is also about recognition of patterns Often an example pattern is used We need something to tell us if there is a high match

        between our pattern and a part of the image

        Example pattern

        Image

        Find matches

        DTU Compute

        2122018Introduction to Medical Image Analysis25 DTU Compute Technical University of Denmark

        Correlation (1D)

        1 1 2 2 1 1 2 2 1 1

        1 2 1

        45

        41

        1 1 + 2 1 + 1 2 = 5

        Normalise

        Kernel

        Signal (1D image)

        41

        DTU Compute

        2122018Introduction to Medical Image Analysis26 DTU Compute Technical University of Denmark

        Correlation (1D)

        1 1 2 2 1 1 2 2 1 1

        1 2 1

        45

        47

        47

        45

        45

        47

        47

        45

        41

        DTU Compute

        2122018Introduction to Medical Image Analysis27 DTU Compute Technical University of Denmark

        Normalisation

        1 1 2 2 1 1 2 2 1 1

        1 2 1

        45

        41

        1 1 + 2 1 + 1 2 = 5

        Normalise41

        bull The sum of the kernel elements is used

        bull Keep the values in the same range as the input image

        Sum is 4

        DTU Compute

        2122018Introduction to Medical Image Analysis28 DTU Compute Technical University of Denmark

        Normalisation Normalisation factor

        ndash Sum of kernel coefficients

        1 2 1h(x)

        119909119909

        ℎ 119909119909 = 1 + 2 + 1

        DTU Compute

        2122018Introduction to Medical Image Analysis29 DTU Compute Technical University of Denmark

        Correlation on images The filter is now 2D 1 1 1

        1 1 1

        1 1 1

        0 2 4

        1 2 2

        1 6 3

        1 2 12 5 3

        2 1 3

        1 3 1

        2 2 2

        0 1 3

        1 2 0

        2 1 4

        1 0 1

        912

        91

        Input OutputKernel

        Kernel coefficients

        DTU Compute

        2122018Introduction to Medical Image Analysis30 DTU Compute Technical University of Denmark

        Correlation on images

        1 1 11 1 11 1 1

        0 2 4

        1 2 2

        1 6 3

        1 2 0

        2 1 4

        1 0 1

        912

        911

        91

        Input Output

        1 3 1

        2 2 2

        0 1 3

        1 2 12 5 3

        2 1 3

        DTU Compute

        2122018Introduction to Medical Image Analysis31 DTU Compute Technical University of Denmark

        Correlation on images

        Input Output

        The mask is moved row by row

        No values at the border

        0 2 4

        1 2 2

        1 6 3

        1 2 0

        2 1 4

        1 0 1

        1 3 1

        2 2 2

        0 1 3

        1 2 12 5 3

        2 1 3

        DTU Compute

        2122018Introduction to Medical Image Analysis32 DTU Compute Technical University of Denmark

        1 2 1

        1 3 1

        1 2 1

        -1 -2 -1

        0 0 0

        1 2 1

        Draw your filter

        DTU Compute

        2122018Introduction to Medical Image Analysis33 DTU Compute Technical University of Denmark

        Correlation on images ndash no normalisationA) 4B) 7C) 16D) 23E) 25

        1 2 11 3 11 2 1

        0 2 41 2 2

        1 6 3

        1 2 12 5 3

        2 1 3

        1 3 1

        2 2 2

        0 1 3

        1 2 0

        2 1 4

        1 0 11 0

        14

        0 0

        A B C D E

        Chart1

        1
        0
        14
        0
        0

        Sheet1

        DTU Compute

        2122018Introduction to Medical Image Analysis34 DTU Compute Technical University of Denmark

        Correlation on images ndash no normalisation 2A) 010B) 3 3C) 6 2D) 10 15E) 11 32

        13

        0 0 0 0

        A B C D E

        -1 -2 -10 0 01 2 1

        0 2 41 2 2

        1 6 3

        1 2 12 5 3

        2 1 3

        1 3 1

        2 2 2

        0 1 3

        1 2 0

        2 1 4

        1 0 1

        Chart1

        13
        0
        0
        0
        0

        Sheet1

        DTU Compute

        2122018Introduction to Medical Image Analysis37 DTU Compute Technical University of Denmark

        Mathematics of 2D Correlation

        h

        f

        Correlation operator

        1 2 11 3 11 2 1

        0 2 4

        1 2 2

        1 6 3

        1 2 1

        2 5 3

        2 1 3

        1 3 1

        2 2 2

        0 1 3

        1 2 0

        2 1 4

        1 0 1

        119892119892 119909119909119910119910 = 119891119891 119909119909119910119910 ∘ ℎ(119909119909119910119910)

        DTU Compute

        2122018Introduction to Medical Image Analysis38 DTU Compute Technical University of Denmark

        Mathematics of 2D Correlation

        1 2 11 3 11 2 1

        0 2 4

        1 2 2

        1 6 3

        1 2 1

        2 5 3

        2 1 3

        1 3 1

        2 2 2

        0 1 3

        1 2 0

        2 1 4

        1 0 1

        h

        fh(00)

        f(21)

        Example g(21)

        i = -1 j = -1

        i = 1 j = 0

        119892119892 119909119909119910119910 = 119895119895=minus119877119877

        119877119877

        119894119894=minus119877119877

        119877119877

        ℎ(119894119894 119895119895) 119891119891(119909119909 + 119894119894119910119910 + 119895119895)

        DTU Compute

        2122018Introduction to Medical Image Analysis39 DTU Compute Technical University of Denmark

        Mathematics of 2D Correlation

        1 2 11 3 11 2 1

        0 2 4

        1 2 2

        1 6 3

        1 2 1

        2 5 3

        2 1 3

        1 3 1

        2 2 2

        0 1 3

        1 2 0

        2 1 4

        1 0 1

        h

        f

        119892119892 119909119909119910119910 = 119895119895=minus119877119877

        119877119877

        119894119894=minus119877119877

        119877119877

        ℎ(119894119894 119895119895) 119891119891(119909119909 + 119894119894119910119910 + 119895119895)

        119892119892(119909119909119910119910 = 1 2 + 2 0 + 1 1 + 1 1 + 3 4 + 1 2 + 1 0 + 2 1 + 1 0

        DTU Compute

        2122018Introduction to Medical Image Analysis40 DTU Compute Technical University of Denmark

        119892119892 119909119909 119910119910 = 119895119895=minus119877119877

        119877119877

        119894119894=minus119877119877

        119877119877

        ℎ(119894119894 119895119895) 119891119891(119909119909 + 119894119894119910119910 + 119895119895)

        119892119892 22 =ℎ minus1minus1 sdot 119891119891 11 + ℎ 0minus1 sdot 119891119891 21 + ℎ 1minus1 sdot 119891119891 31 +ℎ minus10 sdot 119891119891 12 + ℎ 00 sdot 119891119891 22 + ℎ 10 sdot 119891119891 32 +ℎ minus11 sdot 119891119891 13 + ℎ 01 sdot 119891119891 23 + ℎ 11 sdot 119891119891 33

        DTU Compute

        2122018Introduction to Medical Image Analysis41 DTU Compute Technical University of Denmark

        2D Kernel Normalisation

        1 2 11 3 11 2 1

        h

        Normalisation factor

        1 + 2 + 1 + 1 + 3 + 1 + 1 + 2 + 1 = 13

        119909119909

        119910119910

        ℎ(119909119909119910119910)

        DTU Compute

        2122018Introduction to Medical Image Analysis42 DTU Compute Technical University of Denmark

        CorrelationA) 50122B) 123001C) 11233D) 2550E) 90454

        0 0 0 0

        13

        A B C D E

        Chart1

        0
        0
        0
        0
        13

        Sheet1

        DTU Compute

        2122018Introduction to Medical Image Analysis44 DTU Compute Technical University of Denmark

        Smoothing filters

        Also know as ndash Smoothing kernel Mean filter Low pass filter blurring

        The simplest filter ndash Spatial low pass filterndash Removes high frequencies

        Another mask ndash Gaussian filter

        1 1 1

        1 1 1

        1 1 191

        1 2 1

        2 4 2

        1 2 1161

        Why Gaussian

        DTU Compute

        2122018Introduction to Medical Image Analysis45 DTU Compute Technical University of Denmark

        Use of smoothing

        3x3 7x7 11x11 15x15

        DTU Compute

        2122018Introduction to Medical Image Analysis46 DTU Compute Technical University of Denmark

        Use of smoothing Large kernels smooth more Removes high frequency information Good at enhancing big structures

        3x3 15x15

        DTU Compute

        2122018Introduction to Medical Image Analysis47 DTU Compute Technical University of Denmark

        Mean filterA) 166B) 113C) 12D) 51E) 245

        0 0 0 0

        A B C D E

        Chart1

        12
        0
        0
        0
        0

        Sheet1

        DTU Compute

        2122018Introduction to Medical Image Analysis49 DTU Compute Technical University of Denmark

        Border handling

        0 2 41 2 2

        1 6 3

        1 2 12 5 3

        2 1 3

        1 3 1

        2 2 2

        0 1 3

        1 2 0

        2 1 4

        1 0 1

        Input Output

        No values at the border

        DTU Compute

        2122018Introduction to Medical Image Analysis50 DTU Compute Technical University of Denmark

        Border handling ndash extend the input

        0 2 41 2 2

        1 6 3

        1 2 12 5 3

        2 1 3

        1 3 1

        2 2 2

        0 1 3

        1 2 0

        2 1 4

        1 0 1

        Input

        0 0 0 0 000000

        bull Zero padding ndash what happens

        bull Zero is black ndash creates dark border around the image

        DTU Compute

        2122018Introduction to Medical Image Analysis51 DTU Compute Technical University of Denmark

        Correlation with zero paddingA) 5 8B) 12 16C) 13 3D) 15 21E) 17 12

        1 2 11 3 11 2 1

        0 2 41 2 2

        1 6 3

        1 2 12 5 3

        2 1 3

        1 3 1

        2 2 2

        0 1 3

        1 2 0

        2 1 4

        1 0 1

        0

        13

        0 0 0

        A B C D E

        Chart1

        0
        13
        0
        0
        0

        Sheet1

        DTU Compute

        2122018Introduction to Medical Image Analysis53 DTU Compute Technical University of Denmark

        Border handling ndash extend the input

        0 2 41 2 2

        1 6 3

        1 2 12 5 3

        2 1 3

        1 3 1

        2 2 2

        0 1 3

        1 2 0

        2 1 4

        1 0 1

        Input

        1 2 0 1 311211

        bull Reflection

        bull Normally better than zero padding

        DTU Compute

        2122018Introduction to Medical Image Analysis54 DTU Compute Technical University of Denmark

        Template Matching Template

        ndash Skabelon paring dansk Locates objects in images

        Input

        Template

        Output Correlation image

        DTU Compute

        2122018Introduction to Medical Image Analysis55 DTU Compute Technical University of Denmark

        Template Matching The correlation between the template and the input

        image is computed for each pixel

        Input

        Template

        Output Correlation image

        DTU Compute

        2122018Introduction to Medical Image Analysis56 DTU Compute Technical University of Denmark

        Template Matching The pixel with the highest value is found in the

        output imagendash Here is the highest correlation

        Input

        Template

        Output Correlation image

        DTU Compute

        2122018Introduction to Medical Image Analysis57 DTU Compute Technical University of Denmark

        Template Matching This corresponds to the found pattern in the input

        image

        Input

        Template

        Output Correlation image

        DTU Compute

        2122018Introduction to Medical Image Analysis58 DTU Compute Technical University of Denmark

        Problematic Correlation Correlation matching has problem with light areas ndash

        why

        Input (f)

        Template (h)

        Output Correlation imageFake max

        Real max

        Very High119892119892 119909119909119910119910 = 119895119895=minus119877119877

        119877119877

        119894119894=minus119877119877

        119877119877

        ℎ(119894119894 119895119895) 119891119891(119909119909 + 119894119894119910119910 + 119895119895)

        DTU Compute

        2122018Introduction to Medical Image Analysis59 DTU Compute Technical University of Denmark

        Normalised Cross Correlation

        Input (f)

        Template (h)

        Output Correlation image

        Real max

        NCC x y =Correlation

        Length of image patch sdot Length of template

        DTU Compute

        2122018Introduction to Medical Image Analysis60 DTU Compute Technical University of Denmark

        Length of template Vector length

        ndash Put all pixel values into a vectorndash Compute the length of this vector

        Describes the intensity of the templatendash Bright template has a large lengthndash Dark template has a small length

        Template (h)

        Length of template = 119895119895=minus119877119877

        119877119877

        119894119894=minus119877119877

        119877119877

        ℎ(119894119894 119895119895) ℎ(119894119894 119895119895)

        DTU Compute

        2122018Introduction to Medical Image Analysis61 DTU Compute Technical University of Denmark

        Length of image patch Vector length based on pixel values in image patch Describes the intensity of the image patch

        Template (h)

        Input (f) with patch

        DTU Compute

        2122018Introduction to Medical Image Analysis62 DTU Compute Technical University of Denmark

        Normalised Cross Correlation The length of the image patch and the length of

        template normalise the NCC If the image is very bright the NCC will be ldquopulled

        downrdquo

        NCC x y =Correlation

        Length of image patch sdot Length of template

        DTU Compute

        2122018Introduction to Medical Image Analysis63 DTU Compute Technical University of Denmark

        Normalised Cross Correlation NCC will be between

        ndash 0 No similarity between template and image patchndash 1 Template and image patch are identical

        Input (f)

        Template (h)

        Output Correlation image

        Real max

        NCC x y =Correlation

        Length of image patch sdot Length of template

        DTU Compute

        2122018Introduction to Medical Image Analysis64 DTU Compute Technical University of Denmark

        Normalised Cross Correlation

        A) 010B) 033C) 083D) 062E) 098

        Der udfoslashres template matching med og normalized crosscorrelation (NCC) beregnes Hvad bliver NNC i den markerede pixel

        1

        2 2

        3

        2

        A B C D E

        Chart1

        1
        2
        2
        3
        2

        Sheet1

        DTU Compute

        2122018Introduction to Medical Image Analysis66 DTU Compute Technical University of Denmark

        Edges An edge is where there is a

        high change in gray level values

        Objects are often separated from the background by edgesGray level profile

        DTU Compute

        2122018Introduction to Medical Image Analysis67 DTU Compute Technical University of Denmark

        Edges The profile as a function f(d) What value is high when there

        is an edgendash The slope of fndash The slope of the tangent at d

        f(d)

        119891119891prime(119889119889)

        DTU Compute

        2122018Introduction to Medical Image Analysis68 DTU Compute Technical University of Denmark

        Finite Difference Definition of slope

        Approximation

        Simpler approximationh = 1

        119891119891prime 119889119889 = limℎrarr0

        119891119891 119889119889 + ℎ minus 119891119891(119889119889)ℎ

        119891119891prime 119889119889 asymp119891119891 119889119889 + ℎ minus 119891119891(119889119889)

        ℎ

        119891119891prime 119889119889 asymp 119891119891 119889119889 + 1 minus 119891119891(119889119889)

        DTU Compute

        2122018Introduction to Medical Image Analysis69 DTU Compute Technical University of Denmark

        Edges Discrete approximation of frsquo(d) Can be implemented as a filter

        -1 0 1

        f(d-2) f(d-1) f(d) f(d+1) f(d+2) f(d+3)

        f(d)

        119891119891prime 119889119889 asymp 119891119891 119889119889 + 1 minus 119891119891(119889119889)

        DTU Compute

        2122018Introduction to Medical Image Analysis70 DTU Compute Technical University of Denmark

        Edges in 2D Changes in gray level values

        ndash Image gradientndash Gradient is the 2D derivative of a 2D function f(xy)ndash Equal to the slope of the imagendash A steep slope is equal to an edge

        120571120571119891119891 119909119909119910119910 = 119866(119892119892119909119909119892119892119910119910)

        DTU Compute

        2122018Introduction to Medical Image Analysis71 DTU Compute Technical University of Denmark

        Edge filter kernel The Prewitt filter is a typical

        edge filter Output image has high

        values where there are edges

        -1 0 1

        -1 0 1

        -1 0 1Vertical Prewitt filter

        DTU Compute

        2122018Introduction to Medical Image Analysis72 DTU Compute Technical University of Denmark

        Prewitt filter

        Original Prewitt Prewitt

        Hot colormapSmooth 15x15

        Smooth 15x15

        Prewitt

        DTU Compute

        2122018Introduction to Medical Image Analysis73 DTU Compute Technical University of Denmark

        Edge detection Edge filter

        ndash Prewitt for example Thresholding

        ndash Separate edges from non-edges

        Output is binary imagendash Edges are white

        DTU Compute

        2122018Introduction to Medical Image Analysis74 DTU Compute Technical University of Denmark

        Edge filtering

        A) MeanB) Horizontal SobelC) Vertical PrewittD) Horisontal PrewittE) Median

        Der udfoslashres en filtrering (correlation) med et filter paring billedet Der bruges ikke coefficient normalization Den filtrerede vaeligrdi i den markerede pixel bliver -119 Hvilket et 3x3 filter blev benyttet

        0

        8

        1 10

        A B C D E

        Chart1

        0
        8
        1
        1
        0

        Sheet1

        DTU Compute

        2122018Introduction to Medical Image Analysis76 DTU Compute Technical University of Denmark

        02511 - Niveau af dagens emne forelaeligsingA) Meget letB) LetC) PassendeD) SvaeligrtE) Meget svaeligrt

        23

        6

        10

        A B C D E

        Chart1

        2
        3
        6
        1
        0

        Sheet1

        DTU Compute

        2122018Introduction to Medical Image Analysis77 DTU Compute Technical University of Denmark

        02512 - Niveau af dagens emne forelaeligsingA) Meget letB) LetC) PassendeD) SvaeligrtE) Meget svaeligrt

        0 0

        1

        0 0

        A B C D E

        Chart1

        0
        0
        1
        0
        0

        Sheet1

        DTU Compute

        2122018Introduction to Medical Image Analysis78 DTU Compute Technical University of Denmark

        02511 - Mit eget udbytte af dagenA) Jeg har laeligrt meget lidtB) Lidt laeligringC) PassendeD) God laeligringE) Jeg har laeligrt meget

        0 0

        2

        6

        0

        A B C D E

        Chart1

        0
        0
        2
        6
        0

        Sheet1

        DTU Compute

        2122018Introduction to Medical Image Analysis79 DTU Compute Technical University of Denmark

        02512 - Mit eget udbytte af dagenA) Jeg har laeligrt meget lidtB) Lidt laeligringC) PassendeD) God laeligringE) Jeg har laeligrt meget

        2

        1

        3

        2

        0

        A B C D E

        Chart1

        2
        1
        3
        2
        0

        Sheet1

        DTU Compute

        2122018Introduction to Medical Image Analysis80 DTU Compute Technical University of Denmark

        02511 - Sidste uges oslashvelser (pixelwiseoperations)A) Meget letteB) LetteC) PassendeD) SvaeligreE) Meget svaeligre

        0 0

        1

        4

        1

        A B C D E

        Chart1

        0
        0
        1
        4
        1

        Sheet1

        DTU Compute

        2122018Introduction to Medical Image Analysis81 DTU Compute Technical University of Denmark

        02512 - Sidste uges oslashvelser (pixelwiseoperations)A) Meget letteB) LetteC) PassendeD) SvaeligreE) Meget svaeligre

        3

        0

        3

        0 0

        A B C D E

        Chart1

        3
        0
        3
        0
        0

        Sheet1

        DTU Compute

        2122018Introduction to Medical Image Analysis82 DTU Compute Technical University of Denmark

        Denne uges brug af clickersA) click click click ndash jeg bliver

        sindssygB) For meget clickC) PassendeD) Jeg vil gerne have lidt mereE) Jeg kan ikrsquo faring nok

        0 0

        5

        0

        6

        A B C D E

        Chart1

        0
        0
        5
        0
        6

        Sheet1

        DTU Compute

        2122018Introduction to Medical Image Analysis83 DTU Compute Technical University of Denmark

        What can you do after today Describe the difference between point processing and neighbourhood

        processing Compute a rank filtered image using the min max median and

        difference rank filters Compute a mean filtered image Decide if median or average filtering should be used for noise removal Choose the appropriate image border handling based on a given input

        image Implement and apply template matching Compute the normalised cross correlation and explain why it should be

        used Apply given image filter kernels to images Use edge filters on images Describe finite difference approximation of image gradients Describe the concept of edge detection

        DTU Compute

        2122018Introduction to Medical Image Analysis84 DTU Compute Technical University of Denmark

        Oslashvelsesrapport over oslashvelse 4 - 02511 Oslashvelser taeligller cirka 30 af karakteren Skal afleveres senest den 7 marts kl 2359 Kan afleveres af 1 eller 2 personer

        ndash I skal skrive jeres egen oslashvelsesrapportndash Brug mindst et af jeres egne billeder

        Afleveres som PDF Lad vaeligre med at kopiere opgaveteksten ind i jeres

        opgave Put Matlab kode i et Appendix og henvis fra teksten Eksempel rapport over oslashvelse findes paring

        hjemmesiden under eksamen

        DTU Compute

        2122018Introduction to Medical Image Analysis85 DTU Compute Technical University of Denmark

        Exercises

        • Introduction to Medical Image Analysis
        • Lecture 4 ndash Neighbourhood Processing
        • What can you do after today
        • Point processing
        • Point processing
        • Neighbourhood processing
        • Use of filtering
        • Salt and pepper noise
        • Salt and pepper noise
        • What is so special about noise
        • Noise ndash go away
        • What is the median Value
        • The median value
        • Noise away ndash the median filter
        • Noise removal ndash average filter
        • Noise removal ndash median filter
        • Image Filtering
        • Median filter
        • Rank filters
        • Median filter
        • Correlation
        • Why do we need similarity
        • Correlation (1D)
        • Correlation (1D)
        • Normalisation
        • Normalisation
        • Correlation on images
        • Correlation on images
        • Correlation on images
        • Draw your filter
        • Correlation on images ndash no normalisation
        • Correlation on images ndash no normalisation 2
        • Mathematics of 2D Correlation
        • Mathematics of 2D Correlation
        • Mathematics of 2D Correlation
        • Slide Number 40
        • 2D Kernel Normalisation
        • Correlation
        • Smoothing filters
        • Use of smoothing
        • Use of smoothing
        • Mean filter
        • Border handling
        • Border handling ndash extend the input
        • Correlation with zero padding
        • Border handling ndash extend the input
        • Template Matching
        • Template Matching
        • Template Matching
        • Template Matching
        • Problematic Correlation
        • Normalised Cross Correlation
        • Length of template
        • Length of image patch
        • Normalised Cross Correlation
        • Normalised Cross Correlation
        • Normalised Cross Correlation
        • Edges
        • Edges
        • Finite Difference
        • Edges
        • Edges in 2D
        • Edge filter kernel
        • Prewitt filter
        • Edge detection
        • Edge filtering
        • 02511 - Niveau af dagens emne forelaeligsing
        • 02512 - Niveau af dagens emne forelaeligsing
        • 02511 - Mit eget udbytte af dagen
        • 02512 - Mit eget udbytte af dagen
        • 02511 - Sidste uges oslashvelser (pixelwise operations)
        • 02512 - Sidste uges oslashvelser (pixelwise operations)
        • Denne uges brug af clickers
        • What can you do after today
        • Oslashvelsesrapport over oslashvelse 4 - 02511
        • Exercises
          A0
          B0
          C5
          D0
          E6
          A
          B
          C
          D
          E
          A3
          B0
          C3
          D0
          E0
          A
          B
          C
          D
          E
          A0
          B0
          C1
          D4
          E1
          A
          B
          C
          D
          E
          A2
          B1
          C3
          D2
          E0
          A
          B
          C
          D
          E
          A0
          B0
          C2
          D6
          E0
          A
          B
          C
          D
          E
          A0
          B0
          C1
          D0
          E0
          A
          B
          C
          D
          E
          A2
          B3
          C6
          D1
          E0
          A
          B
          C
          D
          E
          A0
          B8
          C1
          D1
          E0
          A
          B
          C
          D
          E
          A1
          B2
          C2
          D3
          E2
          A
          B
          C
          D
          E
          A0
          B13
          C0
          D0
          E0
          A
          B
          C
          D
          E
          A12
          B0
          C0
          D0
          E0
          A
          B
          C
          D
          E
          A0
          B0
          C0
          D0
          E13
          A
          B
          C
          D
          E
          A13
          B0
          C0
          D0
          E0
          A
          B
          C
          D
          E
          A1
          B0
          C14
          D0
          E0
          A
          B
          C
          D
          E
          A0
          B12
          C1
          D0
          E0
          A
          B
          C
          D
          E
          A0
          B13
          C1
          D0
          E0
          A
          B
          C
          D
          E
          A13
          B0
          C0
          D0
          E2
          A
          B
          C
          D
          E

          DTU Compute

          2122018Introduction to Medical Image Analysis5 DTU Compute Technical University of Denmark

          Point processing Grey level enhancement

          ndash Process one pixel at a time independent of all other pixelsndash For example used to correct Brightness and Contrast

          Too lowcontrastCorrect

          Too highcontrast

          Too high brightness

          Too low brightness

          DTU Compute

          2122018Introduction to Medical Image Analysis6 DTU Compute Technical University of Denmark

          Neighbourhood processing

          0 2

          1 2

          1 2 1

          2 5 3

          1 3

          2 2

          0 1

          1 2 0

          2 1 4

          1 0 19

          12

          Input Output

          bull Several pixels in the input has an effect on the output

          DTU Compute

          2122018Introduction to Medical Image Analysis7 DTU Compute Technical University of Denmark

          Use of filtering

          Noise removal Enhance edges Smoothing

          bull Image processing

          bull Typically done before actual image analysis

          DTU Compute

          2122018Introduction to Medical Image Analysis8 DTU Compute Technical University of Denmark

          Salt and pepper noise Pixel values that are very

          different from their neighbours

          Very bright or very dark spots

          Scratches in X-rays

          What is that

          DTU Compute

          2122018Introduction to Medical Image Analysis9 DTU Compute Technical University of Denmark

          Salt and pepper noise Fake example

          ndash Let us take a closer look at noise pixels

          They are all 0 or 255

          Should we just remove all the 0rsquos and 255rsquos from the image

          DTU Compute

          2122018Introduction to Medical Image Analysis10 DTU Compute Technical University of Denmark

          What is so special about noise What is the value of the pixel

          compared to the neighbours Average of the neighbours

          ndash 170 Can we compare to the

          averagendash Difficult ndash should we remove

          all values bigger than average+1

          It is difficult to detect noise

          172 169 171 168 0 169 172 173 168

          DTU Compute

          2122018Introduction to Medical Image Analysis11 DTU Compute Technical University of Denmark

          Noise ndash go away We can not tell what pixels

          are noise One solution

          ndash Set all pixels to the average of the neighbours (and the pixel itself)

          Oh nondash Problemsndash The noise ldquopollutesrdquo the

          good pixels

          172 169 171 168 0 169 172 173 168

          170

          169 168 0 170 172173 170 172 170

          149

          DTU Compute

          2122018Introduction to Medical Image Analysis12 DTU Compute Technical University of Denmark

          What is the median ValueA) 170B) 173C) 169D) 171E) 172

          13

          0 0 02

          A B C D E

          169 168 0 170172 173 170 172 170

          Chart1

          13
          0
          0
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          2

          Sheet1

          DTU Compute

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          The median value The values are sorted from low to high The middle number is picked

          ndash The median value

          169 168 0 170172 173 170 172 170

          0168 169 170 170 170172 172173

          Median

          Noise has no influence on the median

          DTU Compute

          2122018Introduction to Medical Image Analysis14 DTU Compute Technical University of Denmark

          Noise away ndash the median filter All pixels are set to the

          median of its neighbourhood Noise pixels do not pollute

          good pixels

          172 169 171 168 0 169 172 173 168

          170

          169 168 0 170 172173 170 172 170

          170

          DTU Compute

          2122018Introduction to Medical Image Analysis15 DTU Compute Technical University of Denmark

          Noise removal ndash average filter

          Scanned X-ray with salt and pepper noise

          Average filter (3x3)

          DTU Compute

          2122018Introduction to Medical Image Analysis16 DTU Compute Technical University of Denmark

          Noise removal ndash median filter

          Scanned X-ray with salt and pepper noise

          Median filter (3x3)

          DTU Compute

          2122018Introduction to Medical Image Analysis17 DTU Compute Technical University of Denmark

          Image Filtering Creates a new filtered image Output pixel is computed based

          on a neighbourhood in the input image

          3 x 3 neighbourhoodndash Filter size 3 x 3ndash Kernel size 3 x 3ndash Mask size 3 x 3

          Larger filters often usedndash Size

          7 x 7ndash Number of elements

          49

          DTU Compute

          2122018Introduction to Medical Image Analysis18 DTU Compute Technical University of Denmark

          Median filterA) 25B) 90C) 198D) 86E) 103

          0

          13

          1 0 0

          A B C D E

          Chart1

          0
          13
          1
          0
          0

          Sheet1

          DTU Compute

          2122018Introduction to Medical Image Analysis20 DTU Compute Technical University of Denmark

          Rank filters Based on sorting the pixel

          values in the neighbouring region

          Minimum rank filterndash Darker image Noise problems

          Maximum rank filterndash Lighter image Noise problems

          Difference filterndash Enhances changes (edges)

          0168 169 170 170 170172 172173

          -

          DTU Compute

          2122018Introduction to Medical Image Analysis21 DTU Compute Technical University of Denmark

          Median filter

          A) 3B) 84C) 112D) 73E) 202

          0

          12

          10 0

          A B C D E

          Chart1

          0
          12
          1
          0
          0

          Sheet1

          DTU Compute

          2122018Introduction to Medical Image Analysis23 DTU Compute Technical University of Denmark

          Correlation What is it Two measurements

          ndash Low correlationndash High correlation

          High correlation means that there is a relation between the values

          They look the same Correlation is a measure of

          similarity

          Low

          High

          Muscles

          Mat

          h Ski

          lls

          Muscles

          Ben

          ch P

          ress

          DTU Compute

          2122018Introduction to Medical Image Analysis24 DTU Compute Technical University of Denmark

          Why do we need similarity Image analysis is also about recognition of patterns Often an example pattern is used We need something to tell us if there is a high match

          between our pattern and a part of the image

          Example pattern

          Image

          Find matches

          DTU Compute

          2122018Introduction to Medical Image Analysis25 DTU Compute Technical University of Denmark

          Correlation (1D)

          1 1 2 2 1 1 2 2 1 1

          1 2 1

          45

          41

          1 1 + 2 1 + 1 2 = 5

          Normalise

          Kernel

          Signal (1D image)

          41

          DTU Compute

          2122018Introduction to Medical Image Analysis26 DTU Compute Technical University of Denmark

          Correlation (1D)

          1 1 2 2 1 1 2 2 1 1

          1 2 1

          45

          47

          47

          45

          45

          47

          47

          45

          41

          DTU Compute

          2122018Introduction to Medical Image Analysis27 DTU Compute Technical University of Denmark

          Normalisation

          1 1 2 2 1 1 2 2 1 1

          1 2 1

          45

          41

          1 1 + 2 1 + 1 2 = 5

          Normalise41

          bull The sum of the kernel elements is used

          bull Keep the values in the same range as the input image

          Sum is 4

          DTU Compute

          2122018Introduction to Medical Image Analysis28 DTU Compute Technical University of Denmark

          Normalisation Normalisation factor

          ndash Sum of kernel coefficients

          1 2 1h(x)

          119909119909

          ℎ 119909119909 = 1 + 2 + 1

          DTU Compute

          2122018Introduction to Medical Image Analysis29 DTU Compute Technical University of Denmark

          Correlation on images The filter is now 2D 1 1 1

          1 1 1

          1 1 1

          0 2 4

          1 2 2

          1 6 3

          1 2 12 5 3

          2 1 3

          1 3 1

          2 2 2

          0 1 3

          1 2 0

          2 1 4

          1 0 1

          912

          91

          Input OutputKernel

          Kernel coefficients

          DTU Compute

          2122018Introduction to Medical Image Analysis30 DTU Compute Technical University of Denmark

          Correlation on images

          1 1 11 1 11 1 1

          0 2 4

          1 2 2

          1 6 3

          1 2 0

          2 1 4

          1 0 1

          912

          911

          91

          Input Output

          1 3 1

          2 2 2

          0 1 3

          1 2 12 5 3

          2 1 3

          DTU Compute

          2122018Introduction to Medical Image Analysis31 DTU Compute Technical University of Denmark

          Correlation on images

          Input Output

          The mask is moved row by row

          No values at the border

          0 2 4

          1 2 2

          1 6 3

          1 2 0

          2 1 4

          1 0 1

          1 3 1

          2 2 2

          0 1 3

          1 2 12 5 3

          2 1 3

          DTU Compute

          2122018Introduction to Medical Image Analysis32 DTU Compute Technical University of Denmark

          1 2 1

          1 3 1

          1 2 1

          -1 -2 -1

          0 0 0

          1 2 1

          Draw your filter

          DTU Compute

          2122018Introduction to Medical Image Analysis33 DTU Compute Technical University of Denmark

          Correlation on images ndash no normalisationA) 4B) 7C) 16D) 23E) 25

          1 2 11 3 11 2 1

          0 2 41 2 2

          1 6 3

          1 2 12 5 3

          2 1 3

          1 3 1

          2 2 2

          0 1 3

          1 2 0

          2 1 4

          1 0 11 0

          14

          0 0

          A B C D E

          Chart1

          1
          0
          14
          0
          0

          Sheet1

          DTU Compute

          2122018Introduction to Medical Image Analysis34 DTU Compute Technical University of Denmark

          Correlation on images ndash no normalisation 2A) 010B) 3 3C) 6 2D) 10 15E) 11 32

          13

          0 0 0 0

          A B C D E

          -1 -2 -10 0 01 2 1

          0 2 41 2 2

          1 6 3

          1 2 12 5 3

          2 1 3

          1 3 1

          2 2 2

          0 1 3

          1 2 0

          2 1 4

          1 0 1

          Chart1

          13
          0
          0
          0
          0

          Sheet1

          DTU Compute

          2122018Introduction to Medical Image Analysis37 DTU Compute Technical University of Denmark

          Mathematics of 2D Correlation

          h

          f

          Correlation operator

          1 2 11 3 11 2 1

          0 2 4

          1 2 2

          1 6 3

          1 2 1

          2 5 3

          2 1 3

          1 3 1

          2 2 2

          0 1 3

          1 2 0

          2 1 4

          1 0 1

          119892119892 119909119909119910119910 = 119891119891 119909119909119910119910 ∘ ℎ(119909119909119910119910)

          DTU Compute

          2122018Introduction to Medical Image Analysis38 DTU Compute Technical University of Denmark

          Mathematics of 2D Correlation

          1 2 11 3 11 2 1

          0 2 4

          1 2 2

          1 6 3

          1 2 1

          2 5 3

          2 1 3

          1 3 1

          2 2 2

          0 1 3

          1 2 0

          2 1 4

          1 0 1

          h

          fh(00)

          f(21)

          Example g(21)

          i = -1 j = -1

          i = 1 j = 0

          119892119892 119909119909119910119910 = 119895119895=minus119877119877

          119877119877

          119894119894=minus119877119877

          119877119877

          ℎ(119894119894 119895119895) 119891119891(119909119909 + 119894119894119910119910 + 119895119895)

          DTU Compute

          2122018Introduction to Medical Image Analysis39 DTU Compute Technical University of Denmark

          Mathematics of 2D Correlation

          1 2 11 3 11 2 1

          0 2 4

          1 2 2

          1 6 3

          1 2 1

          2 5 3

          2 1 3

          1 3 1

          2 2 2

          0 1 3

          1 2 0

          2 1 4

          1 0 1

          h

          f

          119892119892 119909119909119910119910 = 119895119895=minus119877119877

          119877119877

          119894119894=minus119877119877

          119877119877

          ℎ(119894119894 119895119895) 119891119891(119909119909 + 119894119894119910119910 + 119895119895)

          119892119892(119909119909119910119910 = 1 2 + 2 0 + 1 1 + 1 1 + 3 4 + 1 2 + 1 0 + 2 1 + 1 0

          DTU Compute

          2122018Introduction to Medical Image Analysis40 DTU Compute Technical University of Denmark

          119892119892 119909119909 119910119910 = 119895119895=minus119877119877

          119877119877

          119894119894=minus119877119877

          119877119877

          ℎ(119894119894 119895119895) 119891119891(119909119909 + 119894119894119910119910 + 119895119895)

          119892119892 22 =ℎ minus1minus1 sdot 119891119891 11 + ℎ 0minus1 sdot 119891119891 21 + ℎ 1minus1 sdot 119891119891 31 +ℎ minus10 sdot 119891119891 12 + ℎ 00 sdot 119891119891 22 + ℎ 10 sdot 119891119891 32 +ℎ minus11 sdot 119891119891 13 + ℎ 01 sdot 119891119891 23 + ℎ 11 sdot 119891119891 33

          DTU Compute

          2122018Introduction to Medical Image Analysis41 DTU Compute Technical University of Denmark

          2D Kernel Normalisation

          1 2 11 3 11 2 1

          h

          Normalisation factor

          1 + 2 + 1 + 1 + 3 + 1 + 1 + 2 + 1 = 13

          119909119909

          119910119910

          ℎ(119909119909119910119910)

          DTU Compute

          2122018Introduction to Medical Image Analysis42 DTU Compute Technical University of Denmark

          CorrelationA) 50122B) 123001C) 11233D) 2550E) 90454

          0 0 0 0

          13

          A B C D E

          Chart1

          0
          0
          0
          0
          13

          Sheet1

          DTU Compute

          2122018Introduction to Medical Image Analysis44 DTU Compute Technical University of Denmark

          Smoothing filters

          Also know as ndash Smoothing kernel Mean filter Low pass filter blurring

          The simplest filter ndash Spatial low pass filterndash Removes high frequencies

          Another mask ndash Gaussian filter

          1 1 1

          1 1 1

          1 1 191

          1 2 1

          2 4 2

          1 2 1161

          Why Gaussian

          DTU Compute

          2122018Introduction to Medical Image Analysis45 DTU Compute Technical University of Denmark

          Use of smoothing

          3x3 7x7 11x11 15x15

          DTU Compute

          2122018Introduction to Medical Image Analysis46 DTU Compute Technical University of Denmark

          Use of smoothing Large kernels smooth more Removes high frequency information Good at enhancing big structures

          3x3 15x15

          DTU Compute

          2122018Introduction to Medical Image Analysis47 DTU Compute Technical University of Denmark

          Mean filterA) 166B) 113C) 12D) 51E) 245

          0 0 0 0

          A B C D E

          Chart1

          12
          0
          0
          0
          0

          Sheet1

          DTU Compute

          2122018Introduction to Medical Image Analysis49 DTU Compute Technical University of Denmark

          Border handling

          0 2 41 2 2

          1 6 3

          1 2 12 5 3

          2 1 3

          1 3 1

          2 2 2

          0 1 3

          1 2 0

          2 1 4

          1 0 1

          Input Output

          No values at the border

          DTU Compute

          2122018Introduction to Medical Image Analysis50 DTU Compute Technical University of Denmark

          Border handling ndash extend the input

          0 2 41 2 2

          1 6 3

          1 2 12 5 3

          2 1 3

          1 3 1

          2 2 2

          0 1 3

          1 2 0

          2 1 4

          1 0 1

          Input

          0 0 0 0 000000

          bull Zero padding ndash what happens

          bull Zero is black ndash creates dark border around the image

          DTU Compute

          2122018Introduction to Medical Image Analysis51 DTU Compute Technical University of Denmark

          Correlation with zero paddingA) 5 8B) 12 16C) 13 3D) 15 21E) 17 12

          1 2 11 3 11 2 1

          0 2 41 2 2

          1 6 3

          1 2 12 5 3

          2 1 3

          1 3 1

          2 2 2

          0 1 3

          1 2 0

          2 1 4

          1 0 1

          0

          13

          0 0 0

          A B C D E

          Chart1

          0
          13
          0
          0
          0

          Sheet1

          DTU Compute

          2122018Introduction to Medical Image Analysis53 DTU Compute Technical University of Denmark

          Border handling ndash extend the input

          0 2 41 2 2

          1 6 3

          1 2 12 5 3

          2 1 3

          1 3 1

          2 2 2

          0 1 3

          1 2 0

          2 1 4

          1 0 1

          Input

          1 2 0 1 311211

          bull Reflection

          bull Normally better than zero padding

          DTU Compute

          2122018Introduction to Medical Image Analysis54 DTU Compute Technical University of Denmark

          Template Matching Template

          ndash Skabelon paring dansk Locates objects in images

          Input

          Template

          Output Correlation image

          DTU Compute

          2122018Introduction to Medical Image Analysis55 DTU Compute Technical University of Denmark

          Template Matching The correlation between the template and the input

          image is computed for each pixel

          Input

          Template

          Output Correlation image

          DTU Compute

          2122018Introduction to Medical Image Analysis56 DTU Compute Technical University of Denmark

          Template Matching The pixel with the highest value is found in the

          output imagendash Here is the highest correlation

          Input

          Template

          Output Correlation image

          DTU Compute

          2122018Introduction to Medical Image Analysis57 DTU Compute Technical University of Denmark

          Template Matching This corresponds to the found pattern in the input

          image

          Input

          Template

          Output Correlation image

          DTU Compute

          2122018Introduction to Medical Image Analysis58 DTU Compute Technical University of Denmark

          Problematic Correlation Correlation matching has problem with light areas ndash

          why

          Input (f)

          Template (h)

          Output Correlation imageFake max

          Real max

          Very High119892119892 119909119909119910119910 = 119895119895=minus119877119877

          119877119877

          119894119894=minus119877119877

          119877119877

          ℎ(119894119894 119895119895) 119891119891(119909119909 + 119894119894119910119910 + 119895119895)

          DTU Compute

          2122018Introduction to Medical Image Analysis59 DTU Compute Technical University of Denmark

          Normalised Cross Correlation

          Input (f)

          Template (h)

          Output Correlation image

          Real max

          NCC x y =Correlation

          Length of image patch sdot Length of template

          DTU Compute

          2122018Introduction to Medical Image Analysis60 DTU Compute Technical University of Denmark

          Length of template Vector length

          ndash Put all pixel values into a vectorndash Compute the length of this vector

          Describes the intensity of the templatendash Bright template has a large lengthndash Dark template has a small length

          Template (h)

          Length of template = 119895119895=minus119877119877

          119877119877

          119894119894=minus119877119877

          119877119877

          ℎ(119894119894 119895119895) ℎ(119894119894 119895119895)

          DTU Compute

          2122018Introduction to Medical Image Analysis61 DTU Compute Technical University of Denmark

          Length of image patch Vector length based on pixel values in image patch Describes the intensity of the image patch

          Template (h)

          Input (f) with patch

          DTU Compute

          2122018Introduction to Medical Image Analysis62 DTU Compute Technical University of Denmark

          Normalised Cross Correlation The length of the image patch and the length of

          template normalise the NCC If the image is very bright the NCC will be ldquopulled

          downrdquo

          NCC x y =Correlation

          Length of image patch sdot Length of template

          DTU Compute

          2122018Introduction to Medical Image Analysis63 DTU Compute Technical University of Denmark

          Normalised Cross Correlation NCC will be between

          ndash 0 No similarity between template and image patchndash 1 Template and image patch are identical

          Input (f)

          Template (h)

          Output Correlation image

          Real max

          NCC x y =Correlation

          Length of image patch sdot Length of template

          DTU Compute

          2122018Introduction to Medical Image Analysis64 DTU Compute Technical University of Denmark

          Normalised Cross Correlation

          A) 010B) 033C) 083D) 062E) 098

          Der udfoslashres template matching med og normalized crosscorrelation (NCC) beregnes Hvad bliver NNC i den markerede pixel

          1

          2 2

          3

          2

          A B C D E

          Chart1

          1
          2
          2
          3
          2

          Sheet1

          DTU Compute

          2122018Introduction to Medical Image Analysis66 DTU Compute Technical University of Denmark

          Edges An edge is where there is a

          high change in gray level values

          Objects are often separated from the background by edgesGray level profile

          DTU Compute

          2122018Introduction to Medical Image Analysis67 DTU Compute Technical University of Denmark

          Edges The profile as a function f(d) What value is high when there

          is an edgendash The slope of fndash The slope of the tangent at d

          f(d)

          119891119891prime(119889119889)

          DTU Compute

          2122018Introduction to Medical Image Analysis68 DTU Compute Technical University of Denmark

          Finite Difference Definition of slope

          Approximation

          Simpler approximationh = 1

          119891119891prime 119889119889 = limℎrarr0

          119891119891 119889119889 + ℎ minus 119891119891(119889119889)ℎ

          119891119891prime 119889119889 asymp119891119891 119889119889 + ℎ minus 119891119891(119889119889)

          ℎ

          119891119891prime 119889119889 asymp 119891119891 119889119889 + 1 minus 119891119891(119889119889)

          DTU Compute

          2122018Introduction to Medical Image Analysis69 DTU Compute Technical University of Denmark

          Edges Discrete approximation of frsquo(d) Can be implemented as a filter

          -1 0 1

          f(d-2) f(d-1) f(d) f(d+1) f(d+2) f(d+3)

          f(d)

          119891119891prime 119889119889 asymp 119891119891 119889119889 + 1 minus 119891119891(119889119889)

          DTU Compute

          2122018Introduction to Medical Image Analysis70 DTU Compute Technical University of Denmark

          Edges in 2D Changes in gray level values

          ndash Image gradientndash Gradient is the 2D derivative of a 2D function f(xy)ndash Equal to the slope of the imagendash A steep slope is equal to an edge

          120571120571119891119891 119909119909119910119910 = 119866(119892119892119909119909119892119892119910119910)

          DTU Compute

          2122018Introduction to Medical Image Analysis71 DTU Compute Technical University of Denmark

          Edge filter kernel The Prewitt filter is a typical

          edge filter Output image has high

          values where there are edges

          -1 0 1

          -1 0 1

          -1 0 1Vertical Prewitt filter

          DTU Compute

          2122018Introduction to Medical Image Analysis72 DTU Compute Technical University of Denmark

          Prewitt filter

          Original Prewitt Prewitt

          Hot colormapSmooth 15x15

          Smooth 15x15

          Prewitt

          DTU Compute

          2122018Introduction to Medical Image Analysis73 DTU Compute Technical University of Denmark

          Edge detection Edge filter

          ndash Prewitt for example Thresholding

          ndash Separate edges from non-edges

          Output is binary imagendash Edges are white

          DTU Compute

          2122018Introduction to Medical Image Analysis74 DTU Compute Technical University of Denmark

          Edge filtering

          A) MeanB) Horizontal SobelC) Vertical PrewittD) Horisontal PrewittE) Median

          Der udfoslashres en filtrering (correlation) med et filter paring billedet Der bruges ikke coefficient normalization Den filtrerede vaeligrdi i den markerede pixel bliver -119 Hvilket et 3x3 filter blev benyttet

          0

          8

          1 10

          A B C D E

          Chart1

          0
          8
          1
          1
          0

          Sheet1

          DTU Compute

          2122018Introduction to Medical Image Analysis76 DTU Compute Technical University of Denmark

          02511 - Niveau af dagens emne forelaeligsingA) Meget letB) LetC) PassendeD) SvaeligrtE) Meget svaeligrt

          23

          6

          10

          A B C D E

          Chart1

          2
          3
          6
          1
          0

          Sheet1

          DTU Compute

          2122018Introduction to Medical Image Analysis77 DTU Compute Technical University of Denmark

          02512 - Niveau af dagens emne forelaeligsingA) Meget letB) LetC) PassendeD) SvaeligrtE) Meget svaeligrt

          0 0

          1

          0 0

          A B C D E

          Chart1

          0
          0
          1
          0
          0

          Sheet1

          DTU Compute

          2122018Introduction to Medical Image Analysis78 DTU Compute Technical University of Denmark

          02511 - Mit eget udbytte af dagenA) Jeg har laeligrt meget lidtB) Lidt laeligringC) PassendeD) God laeligringE) Jeg har laeligrt meget

          0 0

          2

          6

          0

          A B C D E

          Chart1

          0
          0
          2
          6
          0

          Sheet1

          DTU Compute

          2122018Introduction to Medical Image Analysis79 DTU Compute Technical University of Denmark

          02512 - Mit eget udbytte af dagenA) Jeg har laeligrt meget lidtB) Lidt laeligringC) PassendeD) God laeligringE) Jeg har laeligrt meget

          2

          1

          3

          2

          0

          A B C D E

          Chart1

          2
          1
          3
          2
          0

          Sheet1

          DTU Compute

          2122018Introduction to Medical Image Analysis80 DTU Compute Technical University of Denmark

          02511 - Sidste uges oslashvelser (pixelwiseoperations)A) Meget letteB) LetteC) PassendeD) SvaeligreE) Meget svaeligre

          0 0

          1

          4

          1

          A B C D E

          Chart1

          0
          0
          1
          4
          1

          Sheet1

          DTU Compute

          2122018Introduction to Medical Image Analysis81 DTU Compute Technical University of Denmark

          02512 - Sidste uges oslashvelser (pixelwiseoperations)A) Meget letteB) LetteC) PassendeD) SvaeligreE) Meget svaeligre

          3

          0

          3

          0 0

          A B C D E

          Chart1

          3
          0
          3
          0
          0

          Sheet1

          DTU Compute

          2122018Introduction to Medical Image Analysis82 DTU Compute Technical University of Denmark

          Denne uges brug af clickersA) click click click ndash jeg bliver

          sindssygB) For meget clickC) PassendeD) Jeg vil gerne have lidt mereE) Jeg kan ikrsquo faring nok

          0 0

          5

          0

          6

          A B C D E

          Chart1

          0
          0
          5
          0
          6

          Sheet1

          DTU Compute

          2122018Introduction to Medical Image Analysis83 DTU Compute Technical University of Denmark

          What can you do after today Describe the difference between point processing and neighbourhood

          processing Compute a rank filtered image using the min max median and

          difference rank filters Compute a mean filtered image Decide if median or average filtering should be used for noise removal Choose the appropriate image border handling based on a given input

          image Implement and apply template matching Compute the normalised cross correlation and explain why it should be

          used Apply given image filter kernels to images Use edge filters on images Describe finite difference approximation of image gradients Describe the concept of edge detection

          DTU Compute

          2122018Introduction to Medical Image Analysis84 DTU Compute Technical University of Denmark

          Oslashvelsesrapport over oslashvelse 4 - 02511 Oslashvelser taeligller cirka 30 af karakteren Skal afleveres senest den 7 marts kl 2359 Kan afleveres af 1 eller 2 personer

          ndash I skal skrive jeres egen oslashvelsesrapportndash Brug mindst et af jeres egne billeder

          Afleveres som PDF Lad vaeligre med at kopiere opgaveteksten ind i jeres

          opgave Put Matlab kode i et Appendix og henvis fra teksten Eksempel rapport over oslashvelse findes paring

          hjemmesiden under eksamen

          DTU Compute

          2122018Introduction to Medical Image Analysis85 DTU Compute Technical University of Denmark

          Exercises

          • Introduction to Medical Image Analysis
          • Lecture 4 ndash Neighbourhood Processing
          • What can you do after today
          • Point processing
          • Point processing
          • Neighbourhood processing
          • Use of filtering
          • Salt and pepper noise
          • Salt and pepper noise
          • What is so special about noise
          • Noise ndash go away
          • What is the median Value
          • The median value
          • Noise away ndash the median filter
          • Noise removal ndash average filter
          • Noise removal ndash median filter
          • Image Filtering
          • Median filter
          • Rank filters
          • Median filter
          • Correlation
          • Why do we need similarity
          • Correlation (1D)
          • Correlation (1D)
          • Normalisation
          • Normalisation
          • Correlation on images
          • Correlation on images
          • Correlation on images
          • Draw your filter
          • Correlation on images ndash no normalisation
          • Correlation on images ndash no normalisation 2
          • Mathematics of 2D Correlation
          • Mathematics of 2D Correlation
          • Mathematics of 2D Correlation
          • Slide Number 40
          • 2D Kernel Normalisation
          • Correlation
          • Smoothing filters
          • Use of smoothing
          • Use of smoothing
          • Mean filter
          • Border handling
          • Border handling ndash extend the input
          • Correlation with zero padding
          • Border handling ndash extend the input
          • Template Matching
          • Template Matching
          • Template Matching
          • Template Matching
          • Problematic Correlation
          • Normalised Cross Correlation
          • Length of template
          • Length of image patch
          • Normalised Cross Correlation
          • Normalised Cross Correlation
          • Normalised Cross Correlation
          • Edges
          • Edges
          • Finite Difference
          • Edges
          • Edges in 2D
          • Edge filter kernel
          • Prewitt filter
          • Edge detection
          • Edge filtering
          • 02511 - Niveau af dagens emne forelaeligsing
          • 02512 - Niveau af dagens emne forelaeligsing
          • 02511 - Mit eget udbytte af dagen
          • 02512 - Mit eget udbytte af dagen
          • 02511 - Sidste uges oslashvelser (pixelwise operations)
          • 02512 - Sidste uges oslashvelser (pixelwise operations)
          • Denne uges brug af clickers
          • What can you do after today
          • Oslashvelsesrapport over oslashvelse 4 - 02511
          • Exercises
            A0
            B0
            C5
            D0
            E6
            A
            B
            C
            D
            E
            A3
            B0
            C3
            D0
            E0
            A
            B
            C
            D
            E
            A0
            B0
            C1
            D4
            E1
            A
            B
            C
            D
            E
            A2
            B1
            C3
            D2
            E0
            A
            B
            C
            D
            E
            A0
            B0
            C2
            D6
            E0
            A
            B
            C
            D
            E
            A0
            B0
            C1
            D0
            E0
            A
            B
            C
            D
            E
            A2
            B3
            C6
            D1
            E0
            A
            B
            C
            D
            E
            A0
            B8
            C1
            D1
            E0
            A
            B
            C
            D
            E
            A1
            B2
            C2
            D3
            E2
            A
            B
            C
            D
            E
            A0
            B13
            C0
            D0
            E0
            A
            B
            C
            D
            E
            A12
            B0
            C0
            D0
            E0
            A
            B
            C
            D
            E
            A0
            B0
            C0
            D0
            E13
            A
            B
            C
            D
            E
            A13
            B0
            C0
            D0
            E0
            A
            B
            C
            D
            E
            A1
            B0
            C14
            D0
            E0
            A
            B
            C
            D
            E
            A0
            B12
            C1
            D0
            E0
            A
            B
            C
            D
            E
            A0
            B13
            C1
            D0
            E0
            A
            B
            C
            D
            E
            A13
            B0
            C0
            D0
            E2
            A
            B
            C
            D
            E

            DTU Compute

            2122018Introduction to Medical Image Analysis6 DTU Compute Technical University of Denmark

            Neighbourhood processing

            0 2

            1 2

            1 2 1

            2 5 3

            1 3

            2 2

            0 1

            1 2 0

            2 1 4

            1 0 19

            12

            Input Output

            bull Several pixels in the input has an effect on the output

            DTU Compute

            2122018Introduction to Medical Image Analysis7 DTU Compute Technical University of Denmark

            Use of filtering

            Noise removal Enhance edges Smoothing

            bull Image processing

            bull Typically done before actual image analysis

            DTU Compute

            2122018Introduction to Medical Image Analysis8 DTU Compute Technical University of Denmark

            Salt and pepper noise Pixel values that are very

            different from their neighbours

            Very bright or very dark spots

            Scratches in X-rays

            What is that

            DTU Compute

            2122018Introduction to Medical Image Analysis9 DTU Compute Technical University of Denmark

            Salt and pepper noise Fake example

            ndash Let us take a closer look at noise pixels

            They are all 0 or 255

            Should we just remove all the 0rsquos and 255rsquos from the image

            DTU Compute

            2122018Introduction to Medical Image Analysis10 DTU Compute Technical University of Denmark

            What is so special about noise What is the value of the pixel

            compared to the neighbours Average of the neighbours

            ndash 170 Can we compare to the

            averagendash Difficult ndash should we remove

            all values bigger than average+1

            It is difficult to detect noise

            172 169 171 168 0 169 172 173 168

            DTU Compute

            2122018Introduction to Medical Image Analysis11 DTU Compute Technical University of Denmark

            Noise ndash go away We can not tell what pixels

            are noise One solution

            ndash Set all pixels to the average of the neighbours (and the pixel itself)

            Oh nondash Problemsndash The noise ldquopollutesrdquo the

            good pixels

            172 169 171 168 0 169 172 173 168

            170

            169 168 0 170 172173 170 172 170

            149

            DTU Compute

            2122018Introduction to Medical Image Analysis12 DTU Compute Technical University of Denmark

            What is the median ValueA) 170B) 173C) 169D) 171E) 172

            13

            0 0 02

            A B C D E

            169 168 0 170172 173 170 172 170

            Chart1

            13
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            DTU Compute

            2122018Introduction to Medical Image Analysis13 DTU Compute Technical University of Denmark

            The median value The values are sorted from low to high The middle number is picked

            ndash The median value

            169 168 0 170172 173 170 172 170

            0168 169 170 170 170172 172173

            Median

            Noise has no influence on the median

            DTU Compute

            2122018Introduction to Medical Image Analysis14 DTU Compute Technical University of Denmark

            Noise away ndash the median filter All pixels are set to the

            median of its neighbourhood Noise pixels do not pollute

            good pixels

            172 169 171 168 0 169 172 173 168

            170

            169 168 0 170 172173 170 172 170

            170

            DTU Compute

            2122018Introduction to Medical Image Analysis15 DTU Compute Technical University of Denmark

            Noise removal ndash average filter

            Scanned X-ray with salt and pepper noise

            Average filter (3x3)

            DTU Compute

            2122018Introduction to Medical Image Analysis16 DTU Compute Technical University of Denmark

            Noise removal ndash median filter

            Scanned X-ray with salt and pepper noise

            Median filter (3x3)

            DTU Compute

            2122018Introduction to Medical Image Analysis17 DTU Compute Technical University of Denmark

            Image Filtering Creates a new filtered image Output pixel is computed based

            on a neighbourhood in the input image

            3 x 3 neighbourhoodndash Filter size 3 x 3ndash Kernel size 3 x 3ndash Mask size 3 x 3

            Larger filters often usedndash Size

            7 x 7ndash Number of elements

            49

            DTU Compute

            2122018Introduction to Medical Image Analysis18 DTU Compute Technical University of Denmark

            Median filterA) 25B) 90C) 198D) 86E) 103

            0

            13

            1 0 0

            A B C D E

            Chart1

            0
            13
            1
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            Sheet1

            DTU Compute

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            Rank filters Based on sorting the pixel

            values in the neighbouring region

            Minimum rank filterndash Darker image Noise problems

            Maximum rank filterndash Lighter image Noise problems

            Difference filterndash Enhances changes (edges)

            0168 169 170 170 170172 172173

            -

            DTU Compute

            2122018Introduction to Medical Image Analysis21 DTU Compute Technical University of Denmark

            Median filter

            A) 3B) 84C) 112D) 73E) 202

            0

            12

            10 0

            A B C D E

            Chart1

            0
            12
            1
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            0

            Sheet1

            DTU Compute

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            Correlation What is it Two measurements

            ndash Low correlationndash High correlation

            High correlation means that there is a relation between the values

            They look the same Correlation is a measure of

            similarity

            Low

            High

            Muscles

            Mat

            h Ski

            lls

            Muscles

            Ben

            ch P

            ress

            DTU Compute

            2122018Introduction to Medical Image Analysis24 DTU Compute Technical University of Denmark

            Why do we need similarity Image analysis is also about recognition of patterns Often an example pattern is used We need something to tell us if there is a high match

            between our pattern and a part of the image

            Example pattern

            Image

            Find matches

            DTU Compute

            2122018Introduction to Medical Image Analysis25 DTU Compute Technical University of Denmark

            Correlation (1D)

            1 1 2 2 1 1 2 2 1 1

            1 2 1

            45

            41

            1 1 + 2 1 + 1 2 = 5

            Normalise

            Kernel

            Signal (1D image)

            41

            DTU Compute

            2122018Introduction to Medical Image Analysis26 DTU Compute Technical University of Denmark

            Correlation (1D)

            1 1 2 2 1 1 2 2 1 1

            1 2 1

            45

            47

            47

            45

            45

            47

            47

            45

            41

            DTU Compute

            2122018Introduction to Medical Image Analysis27 DTU Compute Technical University of Denmark

            Normalisation

            1 1 2 2 1 1 2 2 1 1

            1 2 1

            45

            41

            1 1 + 2 1 + 1 2 = 5

            Normalise41

            bull The sum of the kernel elements is used

            bull Keep the values in the same range as the input image

            Sum is 4

            DTU Compute

            2122018Introduction to Medical Image Analysis28 DTU Compute Technical University of Denmark

            Normalisation Normalisation factor

            ndash Sum of kernel coefficients

            1 2 1h(x)

            119909119909

            ℎ 119909119909 = 1 + 2 + 1

            DTU Compute

            2122018Introduction to Medical Image Analysis29 DTU Compute Technical University of Denmark

            Correlation on images The filter is now 2D 1 1 1

            1 1 1

            1 1 1

            0 2 4

            1 2 2

            1 6 3

            1 2 12 5 3

            2 1 3

            1 3 1

            2 2 2

            0 1 3

            1 2 0

            2 1 4

            1 0 1

            912

            91

            Input OutputKernel

            Kernel coefficients

            DTU Compute

            2122018Introduction to Medical Image Analysis30 DTU Compute Technical University of Denmark

            Correlation on images

            1 1 11 1 11 1 1

            0 2 4

            1 2 2

            1 6 3

            1 2 0

            2 1 4

            1 0 1

            912

            911

            91

            Input Output

            1 3 1

            2 2 2

            0 1 3

            1 2 12 5 3

            2 1 3

            DTU Compute

            2122018Introduction to Medical Image Analysis31 DTU Compute Technical University of Denmark

            Correlation on images

            Input Output

            The mask is moved row by row

            No values at the border

            0 2 4

            1 2 2

            1 6 3

            1 2 0

            2 1 4

            1 0 1

            1 3 1

            2 2 2

            0 1 3

            1 2 12 5 3

            2 1 3

            DTU Compute

            2122018Introduction to Medical Image Analysis32 DTU Compute Technical University of Denmark

            1 2 1

            1 3 1

            1 2 1

            -1 -2 -1

            0 0 0

            1 2 1

            Draw your filter

            DTU Compute

            2122018Introduction to Medical Image Analysis33 DTU Compute Technical University of Denmark

            Correlation on images ndash no normalisationA) 4B) 7C) 16D) 23E) 25

            1 2 11 3 11 2 1

            0 2 41 2 2

            1 6 3

            1 2 12 5 3

            2 1 3

            1 3 1

            2 2 2

            0 1 3

            1 2 0

            2 1 4

            1 0 11 0

            14

            0 0

            A B C D E

            Chart1

            1
            0
            14
            0
            0

            Sheet1

            DTU Compute

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            Correlation on images ndash no normalisation 2A) 010B) 3 3C) 6 2D) 10 15E) 11 32

            13

            0 0 0 0

            A B C D E

            -1 -2 -10 0 01 2 1

            0 2 41 2 2

            1 6 3

            1 2 12 5 3

            2 1 3

            1 3 1

            2 2 2

            0 1 3

            1 2 0

            2 1 4

            1 0 1

            Chart1

            13
            0
            0
            0
            0

            Sheet1

            DTU Compute

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            Mathematics of 2D Correlation

            h

            f

            Correlation operator

            1 2 11 3 11 2 1

            0 2 4

            1 2 2

            1 6 3

            1 2 1

            2 5 3

            2 1 3

            1 3 1

            2 2 2

            0 1 3

            1 2 0

            2 1 4

            1 0 1

            119892119892 119909119909119910119910 = 119891119891 119909119909119910119910 ∘ ℎ(119909119909119910119910)

            DTU Compute

            2122018Introduction to Medical Image Analysis38 DTU Compute Technical University of Denmark

            Mathematics of 2D Correlation

            1 2 11 3 11 2 1

            0 2 4

            1 2 2

            1 6 3

            1 2 1

            2 5 3

            2 1 3

            1 3 1

            2 2 2

            0 1 3

            1 2 0

            2 1 4

            1 0 1

            h

            fh(00)

            f(21)

            Example g(21)

            i = -1 j = -1

            i = 1 j = 0

            119892119892 119909119909119910119910 = 119895119895=minus119877119877

            119877119877

            119894119894=minus119877119877

            119877119877

            ℎ(119894119894 119895119895) 119891119891(119909119909 + 119894119894119910119910 + 119895119895)

            DTU Compute

            2122018Introduction to Medical Image Analysis39 DTU Compute Technical University of Denmark

            Mathematics of 2D Correlation

            1 2 11 3 11 2 1

            0 2 4

            1 2 2

            1 6 3

            1 2 1

            2 5 3

            2 1 3

            1 3 1

            2 2 2

            0 1 3

            1 2 0

            2 1 4

            1 0 1

            h

            f

            119892119892 119909119909119910119910 = 119895119895=minus119877119877

            119877119877

            119894119894=minus119877119877

            119877119877

            ℎ(119894119894 119895119895) 119891119891(119909119909 + 119894119894119910119910 + 119895119895)

            119892119892(119909119909119910119910 = 1 2 + 2 0 + 1 1 + 1 1 + 3 4 + 1 2 + 1 0 + 2 1 + 1 0

            DTU Compute

            2122018Introduction to Medical Image Analysis40 DTU Compute Technical University of Denmark

            119892119892 119909119909 119910119910 = 119895119895=minus119877119877

            119877119877

            119894119894=minus119877119877

            119877119877

            ℎ(119894119894 119895119895) 119891119891(119909119909 + 119894119894119910119910 + 119895119895)

            119892119892 22 =ℎ minus1minus1 sdot 119891119891 11 + ℎ 0minus1 sdot 119891119891 21 + ℎ 1minus1 sdot 119891119891 31 +ℎ minus10 sdot 119891119891 12 + ℎ 00 sdot 119891119891 22 + ℎ 10 sdot 119891119891 32 +ℎ minus11 sdot 119891119891 13 + ℎ 01 sdot 119891119891 23 + ℎ 11 sdot 119891119891 33

            DTU Compute

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            2D Kernel Normalisation

            1 2 11 3 11 2 1

            h

            Normalisation factor

            1 + 2 + 1 + 1 + 3 + 1 + 1 + 2 + 1 = 13

            119909119909

            119910119910

            ℎ(119909119909119910119910)

            DTU Compute

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            CorrelationA) 50122B) 123001C) 11233D) 2550E) 90454

            0 0 0 0

            13

            A B C D E

            Chart1

            0
            0
            0
            0
            13

            Sheet1

            DTU Compute

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            Smoothing filters

            Also know as ndash Smoothing kernel Mean filter Low pass filter blurring

            The simplest filter ndash Spatial low pass filterndash Removes high frequencies

            Another mask ndash Gaussian filter

            1 1 1

            1 1 1

            1 1 191

            1 2 1

            2 4 2

            1 2 1161

            Why Gaussian

            DTU Compute

            2122018Introduction to Medical Image Analysis45 DTU Compute Technical University of Denmark

            Use of smoothing

            3x3 7x7 11x11 15x15

            DTU Compute

            2122018Introduction to Medical Image Analysis46 DTU Compute Technical University of Denmark

            Use of smoothing Large kernels smooth more Removes high frequency information Good at enhancing big structures

            3x3 15x15

            DTU Compute

            2122018Introduction to Medical Image Analysis47 DTU Compute Technical University of Denmark

            Mean filterA) 166B) 113C) 12D) 51E) 245

            0 0 0 0

            A B C D E

            Chart1

            12
            0
            0
            0
            0

            Sheet1

            DTU Compute

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            Border handling

            0 2 41 2 2

            1 6 3

            1 2 12 5 3

            2 1 3

            1 3 1

            2 2 2

            0 1 3

            1 2 0

            2 1 4

            1 0 1

            Input Output

            No values at the border

            DTU Compute

            2122018Introduction to Medical Image Analysis50 DTU Compute Technical University of Denmark

            Border handling ndash extend the input

            0 2 41 2 2

            1 6 3

            1 2 12 5 3

            2 1 3

            1 3 1

            2 2 2

            0 1 3

            1 2 0

            2 1 4

            1 0 1

            Input

            0 0 0 0 000000

            bull Zero padding ndash what happens

            bull Zero is black ndash creates dark border around the image

            DTU Compute

            2122018Introduction to Medical Image Analysis51 DTU Compute Technical University of Denmark

            Correlation with zero paddingA) 5 8B) 12 16C) 13 3D) 15 21E) 17 12

            1 2 11 3 11 2 1

            0 2 41 2 2

            1 6 3

            1 2 12 5 3

            2 1 3

            1 3 1

            2 2 2

            0 1 3

            1 2 0

            2 1 4

            1 0 1

            0

            13

            0 0 0

            A B C D E

            Chart1

            0
            13
            0
            0
            0

            Sheet1

            DTU Compute

            2122018Introduction to Medical Image Analysis53 DTU Compute Technical University of Denmark

            Border handling ndash extend the input

            0 2 41 2 2

            1 6 3

            1 2 12 5 3

            2 1 3

            1 3 1

            2 2 2

            0 1 3

            1 2 0

            2 1 4

            1 0 1

            Input

            1 2 0 1 311211

            bull Reflection

            bull Normally better than zero padding

            DTU Compute

            2122018Introduction to Medical Image Analysis54 DTU Compute Technical University of Denmark

            Template Matching Template

            ndash Skabelon paring dansk Locates objects in images

            Input

            Template

            Output Correlation image

            DTU Compute

            2122018Introduction to Medical Image Analysis55 DTU Compute Technical University of Denmark

            Template Matching The correlation between the template and the input

            image is computed for each pixel

            Input

            Template

            Output Correlation image

            DTU Compute

            2122018Introduction to Medical Image Analysis56 DTU Compute Technical University of Denmark

            Template Matching The pixel with the highest value is found in the

            output imagendash Here is the highest correlation

            Input

            Template

            Output Correlation image

            DTU Compute

            2122018Introduction to Medical Image Analysis57 DTU Compute Technical University of Denmark

            Template Matching This corresponds to the found pattern in the input

            image

            Input

            Template

            Output Correlation image

            DTU Compute

            2122018Introduction to Medical Image Analysis58 DTU Compute Technical University of Denmark

            Problematic Correlation Correlation matching has problem with light areas ndash

            why

            Input (f)

            Template (h)

            Output Correlation imageFake max

            Real max

            Very High119892119892 119909119909119910119910 = 119895119895=minus119877119877

            119877119877

            119894119894=minus119877119877

            119877119877

            ℎ(119894119894 119895119895) 119891119891(119909119909 + 119894119894119910119910 + 119895119895)

            DTU Compute

            2122018Introduction to Medical Image Analysis59 DTU Compute Technical University of Denmark

            Normalised Cross Correlation

            Input (f)

            Template (h)

            Output Correlation image

            Real max

            NCC x y =Correlation

            Length of image patch sdot Length of template

            DTU Compute

            2122018Introduction to Medical Image Analysis60 DTU Compute Technical University of Denmark

            Length of template Vector length

            ndash Put all pixel values into a vectorndash Compute the length of this vector

            Describes the intensity of the templatendash Bright template has a large lengthndash Dark template has a small length

            Template (h)

            Length of template = 119895119895=minus119877119877

            119877119877

            119894119894=minus119877119877

            119877119877

            ℎ(119894119894 119895119895) ℎ(119894119894 119895119895)

            DTU Compute

            2122018Introduction to Medical Image Analysis61 DTU Compute Technical University of Denmark

            Length of image patch Vector length based on pixel values in image patch Describes the intensity of the image patch

            Template (h)

            Input (f) with patch

            DTU Compute

            2122018Introduction to Medical Image Analysis62 DTU Compute Technical University of Denmark

            Normalised Cross Correlation The length of the image patch and the length of

            template normalise the NCC If the image is very bright the NCC will be ldquopulled

            downrdquo

            NCC x y =Correlation

            Length of image patch sdot Length of template

            DTU Compute

            2122018Introduction to Medical Image Analysis63 DTU Compute Technical University of Denmark

            Normalised Cross Correlation NCC will be between

            ndash 0 No similarity between template and image patchndash 1 Template and image patch are identical

            Input (f)

            Template (h)

            Output Correlation image

            Real max

            NCC x y =Correlation

            Length of image patch sdot Length of template

            DTU Compute

            2122018Introduction to Medical Image Analysis64 DTU Compute Technical University of Denmark

            Normalised Cross Correlation

            A) 010B) 033C) 083D) 062E) 098

            Der udfoslashres template matching med og normalized crosscorrelation (NCC) beregnes Hvad bliver NNC i den markerede pixel

            1

            2 2

            3

            2

            A B C D E

            Chart1

            1
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            3
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            Sheet1

            DTU Compute

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            Edges An edge is where there is a

            high change in gray level values

            Objects are often separated from the background by edgesGray level profile

            DTU Compute

            2122018Introduction to Medical Image Analysis67 DTU Compute Technical University of Denmark

            Edges The profile as a function f(d) What value is high when there

            is an edgendash The slope of fndash The slope of the tangent at d

            f(d)

            119891119891prime(119889119889)

            DTU Compute

            2122018Introduction to Medical Image Analysis68 DTU Compute Technical University of Denmark

            Finite Difference Definition of slope

            Approximation

            Simpler approximationh = 1

            119891119891prime 119889119889 = limℎrarr0

            119891119891 119889119889 + ℎ minus 119891119891(119889119889)ℎ

            119891119891prime 119889119889 asymp119891119891 119889119889 + ℎ minus 119891119891(119889119889)

            ℎ

            119891119891prime 119889119889 asymp 119891119891 119889119889 + 1 minus 119891119891(119889119889)

            DTU Compute

            2122018Introduction to Medical Image Analysis69 DTU Compute Technical University of Denmark

            Edges Discrete approximation of frsquo(d) Can be implemented as a filter

            -1 0 1

            f(d-2) f(d-1) f(d) f(d+1) f(d+2) f(d+3)

            f(d)

            119891119891prime 119889119889 asymp 119891119891 119889119889 + 1 minus 119891119891(119889119889)

            DTU Compute

            2122018Introduction to Medical Image Analysis70 DTU Compute Technical University of Denmark

            Edges in 2D Changes in gray level values

            ndash Image gradientndash Gradient is the 2D derivative of a 2D function f(xy)ndash Equal to the slope of the imagendash A steep slope is equal to an edge

            120571120571119891119891 119909119909119910119910 = 119866(119892119892119909119909119892119892119910119910)

            DTU Compute

            2122018Introduction to Medical Image Analysis71 DTU Compute Technical University of Denmark

            Edge filter kernel The Prewitt filter is a typical

            edge filter Output image has high

            values where there are edges

            -1 0 1

            -1 0 1

            -1 0 1Vertical Prewitt filter

            DTU Compute

            2122018Introduction to Medical Image Analysis72 DTU Compute Technical University of Denmark

            Prewitt filter

            Original Prewitt Prewitt

            Hot colormapSmooth 15x15

            Smooth 15x15

            Prewitt

            DTU Compute

            2122018Introduction to Medical Image Analysis73 DTU Compute Technical University of Denmark

            Edge detection Edge filter

            ndash Prewitt for example Thresholding

            ndash Separate edges from non-edges

            Output is binary imagendash Edges are white

            DTU Compute

            2122018Introduction to Medical Image Analysis74 DTU Compute Technical University of Denmark

            Edge filtering

            A) MeanB) Horizontal SobelC) Vertical PrewittD) Horisontal PrewittE) Median

            Der udfoslashres en filtrering (correlation) med et filter paring billedet Der bruges ikke coefficient normalization Den filtrerede vaeligrdi i den markerede pixel bliver -119 Hvilket et 3x3 filter blev benyttet

            0

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            A B C D E

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            02511 - Niveau af dagens emne forelaeligsingA) Meget letB) LetC) PassendeD) SvaeligrtE) Meget svaeligrt

            23

            6

            10

            A B C D E

            Chart1

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            02512 - Niveau af dagens emne forelaeligsingA) Meget letB) LetC) PassendeD) SvaeligrtE) Meget svaeligrt

            0 0

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            02511 - Mit eget udbytte af dagenA) Jeg har laeligrt meget lidtB) Lidt laeligringC) PassendeD) God laeligringE) Jeg har laeligrt meget

            0 0

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            0

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            02512 - Mit eget udbytte af dagenA) Jeg har laeligrt meget lidtB) Lidt laeligringC) PassendeD) God laeligringE) Jeg har laeligrt meget

            2

            1

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            2

            0

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            2
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            02511 - Sidste uges oslashvelser (pixelwiseoperations)A) Meget letteB) LetteC) PassendeD) SvaeligreE) Meget svaeligre

            0 0

            1

            4

            1

            A B C D E

            Chart1

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            1
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            Sheet1

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            02512 - Sidste uges oslashvelser (pixelwiseoperations)A) Meget letteB) LetteC) PassendeD) SvaeligreE) Meget svaeligre

            3

            0

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            0 0

            A B C D E

            Chart1

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            Sheet1

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            Denne uges brug af clickersA) click click click ndash jeg bliver

            sindssygB) For meget clickC) PassendeD) Jeg vil gerne have lidt mereE) Jeg kan ikrsquo faring nok

            0 0

            5

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            6

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            DTU Compute

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            What can you do after today Describe the difference between point processing and neighbourhood

            processing Compute a rank filtered image using the min max median and

            difference rank filters Compute a mean filtered image Decide if median or average filtering should be used for noise removal Choose the appropriate image border handling based on a given input

            image Implement and apply template matching Compute the normalised cross correlation and explain why it should be

            used Apply given image filter kernels to images Use edge filters on images Describe finite difference approximation of image gradients Describe the concept of edge detection

            DTU Compute

            2122018Introduction to Medical Image Analysis84 DTU Compute Technical University of Denmark

            Oslashvelsesrapport over oslashvelse 4 - 02511 Oslashvelser taeligller cirka 30 af karakteren Skal afleveres senest den 7 marts kl 2359 Kan afleveres af 1 eller 2 personer

            ndash I skal skrive jeres egen oslashvelsesrapportndash Brug mindst et af jeres egne billeder

            Afleveres som PDF Lad vaeligre med at kopiere opgaveteksten ind i jeres

            opgave Put Matlab kode i et Appendix og henvis fra teksten Eksempel rapport over oslashvelse findes paring

            hjemmesiden under eksamen

            DTU Compute

            2122018Introduction to Medical Image Analysis85 DTU Compute Technical University of Denmark

            Exercises

            • Introduction to Medical Image Analysis
            • Lecture 4 ndash Neighbourhood Processing
            • What can you do after today
            • Point processing
            • Point processing
            • Neighbourhood processing
            • Use of filtering
            • Salt and pepper noise
            • Salt and pepper noise
            • What is so special about noise
            • Noise ndash go away
            • What is the median Value
            • The median value
            • Noise away ndash the median filter
            • Noise removal ndash average filter
            • Noise removal ndash median filter
            • Image Filtering
            • Median filter
            • Rank filters
            • Median filter
            • Correlation
            • Why do we need similarity
            • Correlation (1D)
            • Correlation (1D)
            • Normalisation
            • Normalisation
            • Correlation on images
            • Correlation on images
            • Correlation on images
            • Draw your filter
            • Correlation on images ndash no normalisation
            • Correlation on images ndash no normalisation 2
            • Mathematics of 2D Correlation
            • Mathematics of 2D Correlation
            • Mathematics of 2D Correlation
            • Slide Number 40
            • 2D Kernel Normalisation
            • Correlation
            • Smoothing filters
            • Use of smoothing
            • Use of smoothing
            • Mean filter
            • Border handling
            • Border handling ndash extend the input
            • Correlation with zero padding
            • Border handling ndash extend the input
            • Template Matching
            • Template Matching
            • Template Matching
            • Template Matching
            • Problematic Correlation
            • Normalised Cross Correlation
            • Length of template
            • Length of image patch
            • Normalised Cross Correlation
            • Normalised Cross Correlation
            • Normalised Cross Correlation
            • Edges
            • Edges
            • Finite Difference
            • Edges
            • Edges in 2D
            • Edge filter kernel
            • Prewitt filter
            • Edge detection
            • Edge filtering
            • 02511 - Niveau af dagens emne forelaeligsing
            • 02512 - Niveau af dagens emne forelaeligsing
            • 02511 - Mit eget udbytte af dagen
            • 02512 - Mit eget udbytte af dagen
            • 02511 - Sidste uges oslashvelser (pixelwise operations)
            • 02512 - Sidste uges oslashvelser (pixelwise operations)
            • Denne uges brug af clickers
            • What can you do after today
            • Oslashvelsesrapport over oslashvelse 4 - 02511
            • Exercises
              A0
              B0
              C5
              D0
              E6
              A
              B
              C
              D
              E
              A3
              B0
              C3
              D0
              E0
              A
              B
              C
              D
              E
              A0
              B0
              C1
              D4
              E1
              A
              B
              C
              D
              E
              A2
              B1
              C3
              D2
              E0
              A
              B
              C
              D
              E
              A0
              B0
              C2
              D6
              E0
              A
              B
              C
              D
              E
              A0
              B0
              C1
              D0
              E0
              A
              B
              C
              D
              E
              A2
              B3
              C6
              D1
              E0
              A
              B
              C
              D
              E
              A0
              B8
              C1
              D1
              E0
              A
              B
              C
              D
              E
              A1
              B2
              C2
              D3
              E2
              A
              B
              C
              D
              E
              A0
              B13
              C0
              D0
              E0
              A
              B
              C
              D
              E
              A12
              B0
              C0
              D0
              E0
              A
              B
              C
              D
              E
              A0
              B0
              C0
              D0
              E13
              A
              B
              C
              D
              E
              A13
              B0
              C0
              D0
              E0
              A
              B
              C
              D
              E
              A1
              B0
              C14
              D0
              E0
              A
              B
              C
              D
              E
              A0
              B12
              C1
              D0
              E0
              A
              B
              C
              D
              E
              A0
              B13
              C1
              D0
              E0
              A
              B
              C
              D
              E
              A13
              B0
              C0
              D0
              E2
              A
              B
              C
              D
              E

              DTU Compute

              2122018Introduction to Medical Image Analysis7 DTU Compute Technical University of Denmark

              Use of filtering

              Noise removal Enhance edges Smoothing

              bull Image processing

              bull Typically done before actual image analysis

              DTU Compute

              2122018Introduction to Medical Image Analysis8 DTU Compute Technical University of Denmark

              Salt and pepper noise Pixel values that are very

              different from their neighbours

              Very bright or very dark spots

              Scratches in X-rays

              What is that

              DTU Compute

              2122018Introduction to Medical Image Analysis9 DTU Compute Technical University of Denmark

              Salt and pepper noise Fake example

              ndash Let us take a closer look at noise pixels

              They are all 0 or 255

              Should we just remove all the 0rsquos and 255rsquos from the image

              DTU Compute

              2122018Introduction to Medical Image Analysis10 DTU Compute Technical University of Denmark

              What is so special about noise What is the value of the pixel

              compared to the neighbours Average of the neighbours

              ndash 170 Can we compare to the

              averagendash Difficult ndash should we remove

              all values bigger than average+1

              It is difficult to detect noise

              172 169 171 168 0 169 172 173 168

              DTU Compute

              2122018Introduction to Medical Image Analysis11 DTU Compute Technical University of Denmark

              Noise ndash go away We can not tell what pixels

              are noise One solution

              ndash Set all pixels to the average of the neighbours (and the pixel itself)

              Oh nondash Problemsndash The noise ldquopollutesrdquo the

              good pixels

              172 169 171 168 0 169 172 173 168

              170

              169 168 0 170 172173 170 172 170

              149

              DTU Compute

              2122018Introduction to Medical Image Analysis12 DTU Compute Technical University of Denmark

              What is the median ValueA) 170B) 173C) 169D) 171E) 172

              13

              0 0 02

              A B C D E

              169 168 0 170172 173 170 172 170

              Chart1

              13
              0
              0
              0
              2

              Sheet1

              DTU Compute

              2122018Introduction to Medical Image Analysis13 DTU Compute Technical University of Denmark

              The median value The values are sorted from low to high The middle number is picked

              ndash The median value

              169 168 0 170172 173 170 172 170

              0168 169 170 170 170172 172173

              Median

              Noise has no influence on the median

              DTU Compute

              2122018Introduction to Medical Image Analysis14 DTU Compute Technical University of Denmark

              Noise away ndash the median filter All pixels are set to the

              median of its neighbourhood Noise pixels do not pollute

              good pixels

              172 169 171 168 0 169 172 173 168

              170

              169 168 0 170 172173 170 172 170

              170

              DTU Compute

              2122018Introduction to Medical Image Analysis15 DTU Compute Technical University of Denmark

              Noise removal ndash average filter

              Scanned X-ray with salt and pepper noise

              Average filter (3x3)

              DTU Compute

              2122018Introduction to Medical Image Analysis16 DTU Compute Technical University of Denmark

              Noise removal ndash median filter

              Scanned X-ray with salt and pepper noise

              Median filter (3x3)

              DTU Compute

              2122018Introduction to Medical Image Analysis17 DTU Compute Technical University of Denmark

              Image Filtering Creates a new filtered image Output pixel is computed based

              on a neighbourhood in the input image

              3 x 3 neighbourhoodndash Filter size 3 x 3ndash Kernel size 3 x 3ndash Mask size 3 x 3

              Larger filters often usedndash Size

              7 x 7ndash Number of elements

              49

              DTU Compute

              2122018Introduction to Medical Image Analysis18 DTU Compute Technical University of Denmark

              Median filterA) 25B) 90C) 198D) 86E) 103

              0

              13

              1 0 0

              A B C D E

              Chart1

              0
              13
              1
              0
              0

              Sheet1

              DTU Compute

              2122018Introduction to Medical Image Analysis20 DTU Compute Technical University of Denmark

              Rank filters Based on sorting the pixel

              values in the neighbouring region

              Minimum rank filterndash Darker image Noise problems

              Maximum rank filterndash Lighter image Noise problems

              Difference filterndash Enhances changes (edges)

              0168 169 170 170 170172 172173

              -

              DTU Compute

              2122018Introduction to Medical Image Analysis21 DTU Compute Technical University of Denmark

              Median filter

              A) 3B) 84C) 112D) 73E) 202

              0

              12

              10 0

              A B C D E

              Chart1

              0
              12
              1
              0
              0

              Sheet1

              DTU Compute

              2122018Introduction to Medical Image Analysis23 DTU Compute Technical University of Denmark

              Correlation What is it Two measurements

              ndash Low correlationndash High correlation

              High correlation means that there is a relation between the values

              They look the same Correlation is a measure of

              similarity

              Low

              High

              Muscles

              Mat

              h Ski

              lls

              Muscles

              Ben

              ch P

              ress

              DTU Compute

              2122018Introduction to Medical Image Analysis24 DTU Compute Technical University of Denmark

              Why do we need similarity Image analysis is also about recognition of patterns Often an example pattern is used We need something to tell us if there is a high match

              between our pattern and a part of the image

              Example pattern

              Image

              Find matches

              DTU Compute

              2122018Introduction to Medical Image Analysis25 DTU Compute Technical University of Denmark

              Correlation (1D)

              1 1 2 2 1 1 2 2 1 1

              1 2 1

              45

              41

              1 1 + 2 1 + 1 2 = 5

              Normalise

              Kernel

              Signal (1D image)

              41

              DTU Compute

              2122018Introduction to Medical Image Analysis26 DTU Compute Technical University of Denmark

              Correlation (1D)

              1 1 2 2 1 1 2 2 1 1

              1 2 1

              45

              47

              47

              45

              45

              47

              47

              45

              41

              DTU Compute

              2122018Introduction to Medical Image Analysis27 DTU Compute Technical University of Denmark

              Normalisation

              1 1 2 2 1 1 2 2 1 1

              1 2 1

              45

              41

              1 1 + 2 1 + 1 2 = 5

              Normalise41

              bull The sum of the kernel elements is used

              bull Keep the values in the same range as the input image

              Sum is 4

              DTU Compute

              2122018Introduction to Medical Image Analysis28 DTU Compute Technical University of Denmark

              Normalisation Normalisation factor

              ndash Sum of kernel coefficients

              1 2 1h(x)

              119909119909

              ℎ 119909119909 = 1 + 2 + 1

              DTU Compute

              2122018Introduction to Medical Image Analysis29 DTU Compute Technical University of Denmark

              Correlation on images The filter is now 2D 1 1 1

              1 1 1

              1 1 1

              0 2 4

              1 2 2

              1 6 3

              1 2 12 5 3

              2 1 3

              1 3 1

              2 2 2

              0 1 3

              1 2 0

              2 1 4

              1 0 1

              912

              91

              Input OutputKernel

              Kernel coefficients

              DTU Compute

              2122018Introduction to Medical Image Analysis30 DTU Compute Technical University of Denmark

              Correlation on images

              1 1 11 1 11 1 1

              0 2 4

              1 2 2

              1 6 3

              1 2 0

              2 1 4

              1 0 1

              912

              911

              91

              Input Output

              1 3 1

              2 2 2

              0 1 3

              1 2 12 5 3

              2 1 3

              DTU Compute

              2122018Introduction to Medical Image Analysis31 DTU Compute Technical University of Denmark

              Correlation on images

              Input Output

              The mask is moved row by row

              No values at the border

              0 2 4

              1 2 2

              1 6 3

              1 2 0

              2 1 4

              1 0 1

              1 3 1

              2 2 2

              0 1 3

              1 2 12 5 3

              2 1 3

              DTU Compute

              2122018Introduction to Medical Image Analysis32 DTU Compute Technical University of Denmark

              1 2 1

              1 3 1

              1 2 1

              -1 -2 -1

              0 0 0

              1 2 1

              Draw your filter

              DTU Compute

              2122018Introduction to Medical Image Analysis33 DTU Compute Technical University of Denmark

              Correlation on images ndash no normalisationA) 4B) 7C) 16D) 23E) 25

              1 2 11 3 11 2 1

              0 2 41 2 2

              1 6 3

              1 2 12 5 3

              2 1 3

              1 3 1

              2 2 2

              0 1 3

              1 2 0

              2 1 4

              1 0 11 0

              14

              0 0

              A B C D E

              Chart1

              1
              0
              14
              0
              0

              Sheet1

              DTU Compute

              2122018Introduction to Medical Image Analysis34 DTU Compute Technical University of Denmark

              Correlation on images ndash no normalisation 2A) 010B) 3 3C) 6 2D) 10 15E) 11 32

              13

              0 0 0 0

              A B C D E

              -1 -2 -10 0 01 2 1

              0 2 41 2 2

              1 6 3

              1 2 12 5 3

              2 1 3

              1 3 1

              2 2 2

              0 1 3

              1 2 0

              2 1 4

              1 0 1

              Chart1

              13
              0
              0
              0
              0

              Sheet1

              DTU Compute

              2122018Introduction to Medical Image Analysis37 DTU Compute Technical University of Denmark

              Mathematics of 2D Correlation

              h

              f

              Correlation operator

              1 2 11 3 11 2 1

              0 2 4

              1 2 2

              1 6 3

              1 2 1

              2 5 3

              2 1 3

              1 3 1

              2 2 2

              0 1 3

              1 2 0

              2 1 4

              1 0 1

              119892119892 119909119909119910119910 = 119891119891 119909119909119910119910 ∘ ℎ(119909119909119910119910)

              DTU Compute

              2122018Introduction to Medical Image Analysis38 DTU Compute Technical University of Denmark

              Mathematics of 2D Correlation

              1 2 11 3 11 2 1

              0 2 4

              1 2 2

              1 6 3

              1 2 1

              2 5 3

              2 1 3

              1 3 1

              2 2 2

              0 1 3

              1 2 0

              2 1 4

              1 0 1

              h

              fh(00)

              f(21)

              Example g(21)

              i = -1 j = -1

              i = 1 j = 0

              119892119892 119909119909119910119910 = 119895119895=minus119877119877

              119877119877

              119894119894=minus119877119877

              119877119877

              ℎ(119894119894 119895119895) 119891119891(119909119909 + 119894119894119910119910 + 119895119895)

              DTU Compute

              2122018Introduction to Medical Image Analysis39 DTU Compute Technical University of Denmark

              Mathematics of 2D Correlation

              1 2 11 3 11 2 1

              0 2 4

              1 2 2

              1 6 3

              1 2 1

              2 5 3

              2 1 3

              1 3 1

              2 2 2

              0 1 3

              1 2 0

              2 1 4

              1 0 1

              h

              f

              119892119892 119909119909119910119910 = 119895119895=minus119877119877

              119877119877

              119894119894=minus119877119877

              119877119877

              ℎ(119894119894 119895119895) 119891119891(119909119909 + 119894119894119910119910 + 119895119895)

              119892119892(119909119909119910119910 = 1 2 + 2 0 + 1 1 + 1 1 + 3 4 + 1 2 + 1 0 + 2 1 + 1 0

              DTU Compute

              2122018Introduction to Medical Image Analysis40 DTU Compute Technical University of Denmark

              119892119892 119909119909 119910119910 = 119895119895=minus119877119877

              119877119877

              119894119894=minus119877119877

              119877119877

              ℎ(119894119894 119895119895) 119891119891(119909119909 + 119894119894119910119910 + 119895119895)

              119892119892 22 =ℎ minus1minus1 sdot 119891119891 11 + ℎ 0minus1 sdot 119891119891 21 + ℎ 1minus1 sdot 119891119891 31 +ℎ minus10 sdot 119891119891 12 + ℎ 00 sdot 119891119891 22 + ℎ 10 sdot 119891119891 32 +ℎ minus11 sdot 119891119891 13 + ℎ 01 sdot 119891119891 23 + ℎ 11 sdot 119891119891 33

              DTU Compute

              2122018Introduction to Medical Image Analysis41 DTU Compute Technical University of Denmark

              2D Kernel Normalisation

              1 2 11 3 11 2 1

              h

              Normalisation factor

              1 + 2 + 1 + 1 + 3 + 1 + 1 + 2 + 1 = 13

              119909119909

              119910119910

              ℎ(119909119909119910119910)

              DTU Compute

              2122018Introduction to Medical Image Analysis42 DTU Compute Technical University of Denmark

              CorrelationA) 50122B) 123001C) 11233D) 2550E) 90454

              0 0 0 0

              13

              A B C D E

              Chart1

              0
              0
              0
              0
              13

              Sheet1

              DTU Compute

              2122018Introduction to Medical Image Analysis44 DTU Compute Technical University of Denmark

              Smoothing filters

              Also know as ndash Smoothing kernel Mean filter Low pass filter blurring

              The simplest filter ndash Spatial low pass filterndash Removes high frequencies

              Another mask ndash Gaussian filter

              1 1 1

              1 1 1

              1 1 191

              1 2 1

              2 4 2

              1 2 1161

              Why Gaussian

              DTU Compute

              2122018Introduction to Medical Image Analysis45 DTU Compute Technical University of Denmark

              Use of smoothing

              3x3 7x7 11x11 15x15

              DTU Compute

              2122018Introduction to Medical Image Analysis46 DTU Compute Technical University of Denmark

              Use of smoothing Large kernels smooth more Removes high frequency information Good at enhancing big structures

              3x3 15x15

              DTU Compute

              2122018Introduction to Medical Image Analysis47 DTU Compute Technical University of Denmark

              Mean filterA) 166B) 113C) 12D) 51E) 245

              0 0 0 0

              A B C D E

              Chart1

              12
              0
              0
              0
              0

              Sheet1

              DTU Compute

              2122018Introduction to Medical Image Analysis49 DTU Compute Technical University of Denmark

              Border handling

              0 2 41 2 2

              1 6 3

              1 2 12 5 3

              2 1 3

              1 3 1

              2 2 2

              0 1 3

              1 2 0

              2 1 4

              1 0 1

              Input Output

              No values at the border

              DTU Compute

              2122018Introduction to Medical Image Analysis50 DTU Compute Technical University of Denmark

              Border handling ndash extend the input

              0 2 41 2 2

              1 6 3

              1 2 12 5 3

              2 1 3

              1 3 1

              2 2 2

              0 1 3

              1 2 0

              2 1 4

              1 0 1

              Input

              0 0 0 0 000000

              bull Zero padding ndash what happens

              bull Zero is black ndash creates dark border around the image

              DTU Compute

              2122018Introduction to Medical Image Analysis51 DTU Compute Technical University of Denmark

              Correlation with zero paddingA) 5 8B) 12 16C) 13 3D) 15 21E) 17 12

              1 2 11 3 11 2 1

              0 2 41 2 2

              1 6 3

              1 2 12 5 3

              2 1 3

              1 3 1

              2 2 2

              0 1 3

              1 2 0

              2 1 4

              1 0 1

              0

              13

              0 0 0

              A B C D E

              Chart1

              0
              13
              0
              0
              0

              Sheet1

              DTU Compute

              2122018Introduction to Medical Image Analysis53 DTU Compute Technical University of Denmark

              Border handling ndash extend the input

              0 2 41 2 2

              1 6 3

              1 2 12 5 3

              2 1 3

              1 3 1

              2 2 2

              0 1 3

              1 2 0

              2 1 4

              1 0 1

              Input

              1 2 0 1 311211

              bull Reflection

              bull Normally better than zero padding

              DTU Compute

              2122018Introduction to Medical Image Analysis54 DTU Compute Technical University of Denmark

              Template Matching Template

              ndash Skabelon paring dansk Locates objects in images

              Input

              Template

              Output Correlation image

              DTU Compute

              2122018Introduction to Medical Image Analysis55 DTU Compute Technical University of Denmark

              Template Matching The correlation between the template and the input

              image is computed for each pixel

              Input

              Template

              Output Correlation image

              DTU Compute

              2122018Introduction to Medical Image Analysis56 DTU Compute Technical University of Denmark

              Template Matching The pixel with the highest value is found in the

              output imagendash Here is the highest correlation

              Input

              Template

              Output Correlation image

              DTU Compute

              2122018Introduction to Medical Image Analysis57 DTU Compute Technical University of Denmark

              Template Matching This corresponds to the found pattern in the input

              image

              Input

              Template

              Output Correlation image

              DTU Compute

              2122018Introduction to Medical Image Analysis58 DTU Compute Technical University of Denmark

              Problematic Correlation Correlation matching has problem with light areas ndash

              why

              Input (f)

              Template (h)

              Output Correlation imageFake max

              Real max

              Very High119892119892 119909119909119910119910 = 119895119895=minus119877119877

              119877119877

              119894119894=minus119877119877

              119877119877

              ℎ(119894119894 119895119895) 119891119891(119909119909 + 119894119894119910119910 + 119895119895)

              DTU Compute

              2122018Introduction to Medical Image Analysis59 DTU Compute Technical University of Denmark

              Normalised Cross Correlation

              Input (f)

              Template (h)

              Output Correlation image

              Real max

              NCC x y =Correlation

              Length of image patch sdot Length of template

              DTU Compute

              2122018Introduction to Medical Image Analysis60 DTU Compute Technical University of Denmark

              Length of template Vector length

              ndash Put all pixel values into a vectorndash Compute the length of this vector

              Describes the intensity of the templatendash Bright template has a large lengthndash Dark template has a small length

              Template (h)

              Length of template = 119895119895=minus119877119877

              119877119877

              119894119894=minus119877119877

              119877119877

              ℎ(119894119894 119895119895) ℎ(119894119894 119895119895)

              DTU Compute

              2122018Introduction to Medical Image Analysis61 DTU Compute Technical University of Denmark

              Length of image patch Vector length based on pixel values in image patch Describes the intensity of the image patch

              Template (h)

              Input (f) with patch

              DTU Compute

              2122018Introduction to Medical Image Analysis62 DTU Compute Technical University of Denmark

              Normalised Cross Correlation The length of the image patch and the length of

              template normalise the NCC If the image is very bright the NCC will be ldquopulled

              downrdquo

              NCC x y =Correlation

              Length of image patch sdot Length of template

              DTU Compute

              2122018Introduction to Medical Image Analysis63 DTU Compute Technical University of Denmark

              Normalised Cross Correlation NCC will be between

              ndash 0 No similarity between template and image patchndash 1 Template and image patch are identical

              Input (f)

              Template (h)

              Output Correlation image

              Real max

              NCC x y =Correlation

              Length of image patch sdot Length of template

              DTU Compute

              2122018Introduction to Medical Image Analysis64 DTU Compute Technical University of Denmark

              Normalised Cross Correlation

              A) 010B) 033C) 083D) 062E) 098

              Der udfoslashres template matching med og normalized crosscorrelation (NCC) beregnes Hvad bliver NNC i den markerede pixel

              1

              2 2

              3

              2

              A B C D E

              Chart1

              1
              2
              2
              3
              2

              Sheet1

              DTU Compute

              2122018Introduction to Medical Image Analysis66 DTU Compute Technical University of Denmark

              Edges An edge is where there is a

              high change in gray level values

              Objects are often separated from the background by edgesGray level profile

              DTU Compute

              2122018Introduction to Medical Image Analysis67 DTU Compute Technical University of Denmark

              Edges The profile as a function f(d) What value is high when there

              is an edgendash The slope of fndash The slope of the tangent at d

              f(d)

              119891119891prime(119889119889)

              DTU Compute

              2122018Introduction to Medical Image Analysis68 DTU Compute Technical University of Denmark

              Finite Difference Definition of slope

              Approximation

              Simpler approximationh = 1

              119891119891prime 119889119889 = limℎrarr0

              119891119891 119889119889 + ℎ minus 119891119891(119889119889)ℎ

              119891119891prime 119889119889 asymp119891119891 119889119889 + ℎ minus 119891119891(119889119889)

              ℎ

              119891119891prime 119889119889 asymp 119891119891 119889119889 + 1 minus 119891119891(119889119889)

              DTU Compute

              2122018Introduction to Medical Image Analysis69 DTU Compute Technical University of Denmark

              Edges Discrete approximation of frsquo(d) Can be implemented as a filter

              -1 0 1

              f(d-2) f(d-1) f(d) f(d+1) f(d+2) f(d+3)

              f(d)

              119891119891prime 119889119889 asymp 119891119891 119889119889 + 1 minus 119891119891(119889119889)

              DTU Compute

              2122018Introduction to Medical Image Analysis70 DTU Compute Technical University of Denmark

              Edges in 2D Changes in gray level values

              ndash Image gradientndash Gradient is the 2D derivative of a 2D function f(xy)ndash Equal to the slope of the imagendash A steep slope is equal to an edge

              120571120571119891119891 119909119909119910119910 = 119866(119892119892119909119909119892119892119910119910)

              DTU Compute

              2122018Introduction to Medical Image Analysis71 DTU Compute Technical University of Denmark

              Edge filter kernel The Prewitt filter is a typical

              edge filter Output image has high

              values where there are edges

              -1 0 1

              -1 0 1

              -1 0 1Vertical Prewitt filter

              DTU Compute

              2122018Introduction to Medical Image Analysis72 DTU Compute Technical University of Denmark

              Prewitt filter

              Original Prewitt Prewitt

              Hot colormapSmooth 15x15

              Smooth 15x15

              Prewitt

              DTU Compute

              2122018Introduction to Medical Image Analysis73 DTU Compute Technical University of Denmark

              Edge detection Edge filter

              ndash Prewitt for example Thresholding

              ndash Separate edges from non-edges

              Output is binary imagendash Edges are white

              DTU Compute

              2122018Introduction to Medical Image Analysis74 DTU Compute Technical University of Denmark

              Edge filtering

              A) MeanB) Horizontal SobelC) Vertical PrewittD) Horisontal PrewittE) Median

              Der udfoslashres en filtrering (correlation) med et filter paring billedet Der bruges ikke coefficient normalization Den filtrerede vaeligrdi i den markerede pixel bliver -119 Hvilket et 3x3 filter blev benyttet

              0

              8

              1 10

              A B C D E

              Chart1

              0
              8
              1
              1
              0

              Sheet1

              DTU Compute

              2122018Introduction to Medical Image Analysis76 DTU Compute Technical University of Denmark

              02511 - Niveau af dagens emne forelaeligsingA) Meget letB) LetC) PassendeD) SvaeligrtE) Meget svaeligrt

              23

              6

              10

              A B C D E

              Chart1

              2
              3
              6
              1
              0

              Sheet1

              DTU Compute

              2122018Introduction to Medical Image Analysis77 DTU Compute Technical University of Denmark

              02512 - Niveau af dagens emne forelaeligsingA) Meget letB) LetC) PassendeD) SvaeligrtE) Meget svaeligrt

              0 0

              1

              0 0

              A B C D E

              Chart1

              0
              0
              1
              0
              0

              Sheet1

              DTU Compute

              2122018Introduction to Medical Image Analysis78 DTU Compute Technical University of Denmark

              02511 - Mit eget udbytte af dagenA) Jeg har laeligrt meget lidtB) Lidt laeligringC) PassendeD) God laeligringE) Jeg har laeligrt meget

              0 0

              2

              6

              0

              A B C D E

              Chart1

              0
              0
              2
              6
              0

              Sheet1

              DTU Compute

              2122018Introduction to Medical Image Analysis79 DTU Compute Technical University of Denmark

              02512 - Mit eget udbytte af dagenA) Jeg har laeligrt meget lidtB) Lidt laeligringC) PassendeD) God laeligringE) Jeg har laeligrt meget

              2

              1

              3

              2

              0

              A B C D E

              Chart1

              2
              1
              3
              2
              0

              Sheet1

              DTU Compute

              2122018Introduction to Medical Image Analysis80 DTU Compute Technical University of Denmark

              02511 - Sidste uges oslashvelser (pixelwiseoperations)A) Meget letteB) LetteC) PassendeD) SvaeligreE) Meget svaeligre

              0 0

              1

              4

              1

              A B C D E

              Chart1

              0
              0
              1
              4
              1

              Sheet1

              DTU Compute

              2122018Introduction to Medical Image Analysis81 DTU Compute Technical University of Denmark

              02512 - Sidste uges oslashvelser (pixelwiseoperations)A) Meget letteB) LetteC) PassendeD) SvaeligreE) Meget svaeligre

              3

              0

              3

              0 0

              A B C D E

              Chart1

              3
              0
              3
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              0

              Sheet1

              DTU Compute

              2122018Introduction to Medical Image Analysis82 DTU Compute Technical University of Denmark

              Denne uges brug af clickersA) click click click ndash jeg bliver

              sindssygB) For meget clickC) PassendeD) Jeg vil gerne have lidt mereE) Jeg kan ikrsquo faring nok

              0 0

              5

              0

              6

              A B C D E

              Chart1

              0
              0
              5
              0
              6

              Sheet1

              DTU Compute

              2122018Introduction to Medical Image Analysis83 DTU Compute Technical University of Denmark

              What can you do after today Describe the difference between point processing and neighbourhood

              processing Compute a rank filtered image using the min max median and

              difference rank filters Compute a mean filtered image Decide if median or average filtering should be used for noise removal Choose the appropriate image border handling based on a given input

              image Implement and apply template matching Compute the normalised cross correlation and explain why it should be

              used Apply given image filter kernels to images Use edge filters on images Describe finite difference approximation of image gradients Describe the concept of edge detection

              DTU Compute

              2122018Introduction to Medical Image Analysis84 DTU Compute Technical University of Denmark

              Oslashvelsesrapport over oslashvelse 4 - 02511 Oslashvelser taeligller cirka 30 af karakteren Skal afleveres senest den 7 marts kl 2359 Kan afleveres af 1 eller 2 personer

              ndash I skal skrive jeres egen oslashvelsesrapportndash Brug mindst et af jeres egne billeder

              Afleveres som PDF Lad vaeligre med at kopiere opgaveteksten ind i jeres

              opgave Put Matlab kode i et Appendix og henvis fra teksten Eksempel rapport over oslashvelse findes paring

              hjemmesiden under eksamen

              DTU Compute

              2122018Introduction to Medical Image Analysis85 DTU Compute Technical University of Denmark

              Exercises

              • Introduction to Medical Image Analysis
              • Lecture 4 ndash Neighbourhood Processing
              • What can you do after today
              • Point processing
              • Point processing
              • Neighbourhood processing
              • Use of filtering
              • Salt and pepper noise
              • Salt and pepper noise
              • What is so special about noise
              • Noise ndash go away
              • What is the median Value
              • The median value
              • Noise away ndash the median filter
              • Noise removal ndash average filter
              • Noise removal ndash median filter
              • Image Filtering
              • Median filter
              • Rank filters
              • Median filter
              • Correlation
              • Why do we need similarity
              • Correlation (1D)
              • Correlation (1D)
              • Normalisation
              • Normalisation
              • Correlation on images
              • Correlation on images
              • Correlation on images
              • Draw your filter
              • Correlation on images ndash no normalisation
              • Correlation on images ndash no normalisation 2
              • Mathematics of 2D Correlation
              • Mathematics of 2D Correlation
              • Mathematics of 2D Correlation
              • Slide Number 40
              • 2D Kernel Normalisation
              • Correlation
              • Smoothing filters
              • Use of smoothing
              • Use of smoothing
              • Mean filter
              • Border handling
              • Border handling ndash extend the input
              • Correlation with zero padding
              • Border handling ndash extend the input
              • Template Matching
              • Template Matching
              • Template Matching
              • Template Matching
              • Problematic Correlation
              • Normalised Cross Correlation
              • Length of template
              • Length of image patch
              • Normalised Cross Correlation
              • Normalised Cross Correlation
              • Normalised Cross Correlation
              • Edges
              • Edges
              • Finite Difference
              • Edges
              • Edges in 2D
              • Edge filter kernel
              • Prewitt filter
              • Edge detection
              • Edge filtering
              • 02511 - Niveau af dagens emne forelaeligsing
              • 02512 - Niveau af dagens emne forelaeligsing
              • 02511 - Mit eget udbytte af dagen
              • 02512 - Mit eget udbytte af dagen
              • 02511 - Sidste uges oslashvelser (pixelwise operations)
              • 02512 - Sidste uges oslashvelser (pixelwise operations)
              • Denne uges brug af clickers
              • What can you do after today
              • Oslashvelsesrapport over oslashvelse 4 - 02511
              • Exercises
                A0
                B0
                C5
                D0
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                E
                A1
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                C2
                D3
                E2
                A
                B
                C
                D
                E
                A0
                B13
                C0
                D0
                E0
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                B
                C
                D
                E
                A12
                B0
                C0
                D0
                E0
                A
                B
                C
                D
                E
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                E13
                A
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                E
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                B0
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                E
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                E
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                C1
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                E
                A13
                B0
                C0
                D0
                E2
                A
                B
                C
                D
                E

                DTU Compute

                2122018Introduction to Medical Image Analysis8 DTU Compute Technical University of Denmark

                Salt and pepper noise Pixel values that are very

                different from their neighbours

                Very bright or very dark spots

                Scratches in X-rays

                What is that

                DTU Compute

                2122018Introduction to Medical Image Analysis9 DTU Compute Technical University of Denmark

                Salt and pepper noise Fake example

                ndash Let us take a closer look at noise pixels

                They are all 0 or 255

                Should we just remove all the 0rsquos and 255rsquos from the image

                DTU Compute

                2122018Introduction to Medical Image Analysis10 DTU Compute Technical University of Denmark

                What is so special about noise What is the value of the pixel

                compared to the neighbours Average of the neighbours

                ndash 170 Can we compare to the

                averagendash Difficult ndash should we remove

                all values bigger than average+1

                It is difficult to detect noise

                172 169 171 168 0 169 172 173 168

                DTU Compute

                2122018Introduction to Medical Image Analysis11 DTU Compute Technical University of Denmark

                Noise ndash go away We can not tell what pixels

                are noise One solution

                ndash Set all pixels to the average of the neighbours (and the pixel itself)

                Oh nondash Problemsndash The noise ldquopollutesrdquo the

                good pixels

                172 169 171 168 0 169 172 173 168

                170

                169 168 0 170 172173 170 172 170

                149

                DTU Compute

                2122018Introduction to Medical Image Analysis12 DTU Compute Technical University of Denmark

                What is the median ValueA) 170B) 173C) 169D) 171E) 172

                13

                0 0 02

                A B C D E

                169 168 0 170172 173 170 172 170

                Chart1

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                DTU Compute

                2122018Introduction to Medical Image Analysis13 DTU Compute Technical University of Denmark

                The median value The values are sorted from low to high The middle number is picked

                ndash The median value

                169 168 0 170172 173 170 172 170

                0168 169 170 170 170172 172173

                Median

                Noise has no influence on the median

                DTU Compute

                2122018Introduction to Medical Image Analysis14 DTU Compute Technical University of Denmark

                Noise away ndash the median filter All pixels are set to the

                median of its neighbourhood Noise pixels do not pollute

                good pixels

                172 169 171 168 0 169 172 173 168

                170

                169 168 0 170 172173 170 172 170

                170

                DTU Compute

                2122018Introduction to Medical Image Analysis15 DTU Compute Technical University of Denmark

                Noise removal ndash average filter

                Scanned X-ray with salt and pepper noise

                Average filter (3x3)

                DTU Compute

                2122018Introduction to Medical Image Analysis16 DTU Compute Technical University of Denmark

                Noise removal ndash median filter

                Scanned X-ray with salt and pepper noise

                Median filter (3x3)

                DTU Compute

                2122018Introduction to Medical Image Analysis17 DTU Compute Technical University of Denmark

                Image Filtering Creates a new filtered image Output pixel is computed based

                on a neighbourhood in the input image

                3 x 3 neighbourhoodndash Filter size 3 x 3ndash Kernel size 3 x 3ndash Mask size 3 x 3

                Larger filters often usedndash Size

                7 x 7ndash Number of elements

                49

                DTU Compute

                2122018Introduction to Medical Image Analysis18 DTU Compute Technical University of Denmark

                Median filterA) 25B) 90C) 198D) 86E) 103

                0

                13

                1 0 0

                A B C D E

                Chart1

                0
                13
                1
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                0

                Sheet1

                DTU Compute

                2122018Introduction to Medical Image Analysis20 DTU Compute Technical University of Denmark

                Rank filters Based on sorting the pixel

                values in the neighbouring region

                Minimum rank filterndash Darker image Noise problems

                Maximum rank filterndash Lighter image Noise problems

                Difference filterndash Enhances changes (edges)

                0168 169 170 170 170172 172173

                -

                DTU Compute

                2122018Introduction to Medical Image Analysis21 DTU Compute Technical University of Denmark

                Median filter

                A) 3B) 84C) 112D) 73E) 202

                0

                12

                10 0

                A B C D E

                Chart1

                0
                12
                1
                0
                0

                Sheet1

                DTU Compute

                2122018Introduction to Medical Image Analysis23 DTU Compute Technical University of Denmark

                Correlation What is it Two measurements

                ndash Low correlationndash High correlation

                High correlation means that there is a relation between the values

                They look the same Correlation is a measure of

                similarity

                Low

                High

                Muscles

                Mat

                h Ski

                lls

                Muscles

                Ben

                ch P

                ress

                DTU Compute

                2122018Introduction to Medical Image Analysis24 DTU Compute Technical University of Denmark

                Why do we need similarity Image analysis is also about recognition of patterns Often an example pattern is used We need something to tell us if there is a high match

                between our pattern and a part of the image

                Example pattern

                Image

                Find matches

                DTU Compute

                2122018Introduction to Medical Image Analysis25 DTU Compute Technical University of Denmark

                Correlation (1D)

                1 1 2 2 1 1 2 2 1 1

                1 2 1

                45

                41

                1 1 + 2 1 + 1 2 = 5

                Normalise

                Kernel

                Signal (1D image)

                41

                DTU Compute

                2122018Introduction to Medical Image Analysis26 DTU Compute Technical University of Denmark

                Correlation (1D)

                1 1 2 2 1 1 2 2 1 1

                1 2 1

                45

                47

                47

                45

                45

                47

                47

                45

                41

                DTU Compute

                2122018Introduction to Medical Image Analysis27 DTU Compute Technical University of Denmark

                Normalisation

                1 1 2 2 1 1 2 2 1 1

                1 2 1

                45

                41

                1 1 + 2 1 + 1 2 = 5

                Normalise41

                bull The sum of the kernel elements is used

                bull Keep the values in the same range as the input image

                Sum is 4

                DTU Compute

                2122018Introduction to Medical Image Analysis28 DTU Compute Technical University of Denmark

                Normalisation Normalisation factor

                ndash Sum of kernel coefficients

                1 2 1h(x)

                119909119909

                ℎ 119909119909 = 1 + 2 + 1

                DTU Compute

                2122018Introduction to Medical Image Analysis29 DTU Compute Technical University of Denmark

                Correlation on images The filter is now 2D 1 1 1

                1 1 1

                1 1 1

                0 2 4

                1 2 2

                1 6 3

                1 2 12 5 3

                2 1 3

                1 3 1

                2 2 2

                0 1 3

                1 2 0

                2 1 4

                1 0 1

                912

                91

                Input OutputKernel

                Kernel coefficients

                DTU Compute

                2122018Introduction to Medical Image Analysis30 DTU Compute Technical University of Denmark

                Correlation on images

                1 1 11 1 11 1 1

                0 2 4

                1 2 2

                1 6 3

                1 2 0

                2 1 4

                1 0 1

                912

                911

                91

                Input Output

                1 3 1

                2 2 2

                0 1 3

                1 2 12 5 3

                2 1 3

                DTU Compute

                2122018Introduction to Medical Image Analysis31 DTU Compute Technical University of Denmark

                Correlation on images

                Input Output

                The mask is moved row by row

                No values at the border

                0 2 4

                1 2 2

                1 6 3

                1 2 0

                2 1 4

                1 0 1

                1 3 1

                2 2 2

                0 1 3

                1 2 12 5 3

                2 1 3

                DTU Compute

                2122018Introduction to Medical Image Analysis32 DTU Compute Technical University of Denmark

                1 2 1

                1 3 1

                1 2 1

                -1 -2 -1

                0 0 0

                1 2 1

                Draw your filter

                DTU Compute

                2122018Introduction to Medical Image Analysis33 DTU Compute Technical University of Denmark

                Correlation on images ndash no normalisationA) 4B) 7C) 16D) 23E) 25

                1 2 11 3 11 2 1

                0 2 41 2 2

                1 6 3

                1 2 12 5 3

                2 1 3

                1 3 1

                2 2 2

                0 1 3

                1 2 0

                2 1 4

                1 0 11 0

                14

                0 0

                A B C D E

                Chart1

                1
                0
                14
                0
                0

                Sheet1

                DTU Compute

                2122018Introduction to Medical Image Analysis34 DTU Compute Technical University of Denmark

                Correlation on images ndash no normalisation 2A) 010B) 3 3C) 6 2D) 10 15E) 11 32

                13

                0 0 0 0

                A B C D E

                -1 -2 -10 0 01 2 1

                0 2 41 2 2

                1 6 3

                1 2 12 5 3

                2 1 3

                1 3 1

                2 2 2

                0 1 3

                1 2 0

                2 1 4

                1 0 1

                Chart1

                13
                0
                0
                0
                0

                Sheet1

                DTU Compute

                2122018Introduction to Medical Image Analysis37 DTU Compute Technical University of Denmark

                Mathematics of 2D Correlation

                h

                f

                Correlation operator

                1 2 11 3 11 2 1

                0 2 4

                1 2 2

                1 6 3

                1 2 1

                2 5 3

                2 1 3

                1 3 1

                2 2 2

                0 1 3

                1 2 0

                2 1 4

                1 0 1

                119892119892 119909119909119910119910 = 119891119891 119909119909119910119910 ∘ ℎ(119909119909119910119910)

                DTU Compute

                2122018Introduction to Medical Image Analysis38 DTU Compute Technical University of Denmark

                Mathematics of 2D Correlation

                1 2 11 3 11 2 1

                0 2 4

                1 2 2

                1 6 3

                1 2 1

                2 5 3

                2 1 3

                1 3 1

                2 2 2

                0 1 3

                1 2 0

                2 1 4

                1 0 1

                h

                fh(00)

                f(21)

                Example g(21)

                i = -1 j = -1

                i = 1 j = 0

                119892119892 119909119909119910119910 = 119895119895=minus119877119877

                119877119877

                119894119894=minus119877119877

                119877119877

                ℎ(119894119894 119895119895) 119891119891(119909119909 + 119894119894119910119910 + 119895119895)

                DTU Compute

                2122018Introduction to Medical Image Analysis39 DTU Compute Technical University of Denmark

                Mathematics of 2D Correlation

                1 2 11 3 11 2 1

                0 2 4

                1 2 2

                1 6 3

                1 2 1

                2 5 3

                2 1 3

                1 3 1

                2 2 2

                0 1 3

                1 2 0

                2 1 4

                1 0 1

                h

                f

                119892119892 119909119909119910119910 = 119895119895=minus119877119877

                119877119877

                119894119894=minus119877119877

                119877119877

                ℎ(119894119894 119895119895) 119891119891(119909119909 + 119894119894119910119910 + 119895119895)

                119892119892(119909119909119910119910 = 1 2 + 2 0 + 1 1 + 1 1 + 3 4 + 1 2 + 1 0 + 2 1 + 1 0

                DTU Compute

                2122018Introduction to Medical Image Analysis40 DTU Compute Technical University of Denmark

                119892119892 119909119909 119910119910 = 119895119895=minus119877119877

                119877119877

                119894119894=minus119877119877

                119877119877

                ℎ(119894119894 119895119895) 119891119891(119909119909 + 119894119894119910119910 + 119895119895)

                119892119892 22 =ℎ minus1minus1 sdot 119891119891 11 + ℎ 0minus1 sdot 119891119891 21 + ℎ 1minus1 sdot 119891119891 31 +ℎ minus10 sdot 119891119891 12 + ℎ 00 sdot 119891119891 22 + ℎ 10 sdot 119891119891 32 +ℎ minus11 sdot 119891119891 13 + ℎ 01 sdot 119891119891 23 + ℎ 11 sdot 119891119891 33

                DTU Compute

                2122018Introduction to Medical Image Analysis41 DTU Compute Technical University of Denmark

                2D Kernel Normalisation

                1 2 11 3 11 2 1

                h

                Normalisation factor

                1 + 2 + 1 + 1 + 3 + 1 + 1 + 2 + 1 = 13

                119909119909

                119910119910

                ℎ(119909119909119910119910)

                DTU Compute

                2122018Introduction to Medical Image Analysis42 DTU Compute Technical University of Denmark

                CorrelationA) 50122B) 123001C) 11233D) 2550E) 90454

                0 0 0 0

                13

                A B C D E

                Chart1

                0
                0
                0
                0
                13

                Sheet1

                DTU Compute

                2122018Introduction to Medical Image Analysis44 DTU Compute Technical University of Denmark

                Smoothing filters

                Also know as ndash Smoothing kernel Mean filter Low pass filter blurring

                The simplest filter ndash Spatial low pass filterndash Removes high frequencies

                Another mask ndash Gaussian filter

                1 1 1

                1 1 1

                1 1 191

                1 2 1

                2 4 2

                1 2 1161

                Why Gaussian

                DTU Compute

                2122018Introduction to Medical Image Analysis45 DTU Compute Technical University of Denmark

                Use of smoothing

                3x3 7x7 11x11 15x15

                DTU Compute

                2122018Introduction to Medical Image Analysis46 DTU Compute Technical University of Denmark

                Use of smoothing Large kernels smooth more Removes high frequency information Good at enhancing big structures

                3x3 15x15

                DTU Compute

                2122018Introduction to Medical Image Analysis47 DTU Compute Technical University of Denmark

                Mean filterA) 166B) 113C) 12D) 51E) 245

                0 0 0 0

                A B C D E

                Chart1

                12
                0
                0
                0
                0

                Sheet1

                DTU Compute

                2122018Introduction to Medical Image Analysis49 DTU Compute Technical University of Denmark

                Border handling

                0 2 41 2 2

                1 6 3

                1 2 12 5 3

                2 1 3

                1 3 1

                2 2 2

                0 1 3

                1 2 0

                2 1 4

                1 0 1

                Input Output

                No values at the border

                DTU Compute

                2122018Introduction to Medical Image Analysis50 DTU Compute Technical University of Denmark

                Border handling ndash extend the input

                0 2 41 2 2

                1 6 3

                1 2 12 5 3

                2 1 3

                1 3 1

                2 2 2

                0 1 3

                1 2 0

                2 1 4

                1 0 1

                Input

                0 0 0 0 000000

                bull Zero padding ndash what happens

                bull Zero is black ndash creates dark border around the image

                DTU Compute

                2122018Introduction to Medical Image Analysis51 DTU Compute Technical University of Denmark

                Correlation with zero paddingA) 5 8B) 12 16C) 13 3D) 15 21E) 17 12

                1 2 11 3 11 2 1

                0 2 41 2 2

                1 6 3

                1 2 12 5 3

                2 1 3

                1 3 1

                2 2 2

                0 1 3

                1 2 0

                2 1 4

                1 0 1

                0

                13

                0 0 0

                A B C D E

                Chart1

                0
                13
                0
                0
                0

                Sheet1

                DTU Compute

                2122018Introduction to Medical Image Analysis53 DTU Compute Technical University of Denmark

                Border handling ndash extend the input

                0 2 41 2 2

                1 6 3

                1 2 12 5 3

                2 1 3

                1 3 1

                2 2 2

                0 1 3

                1 2 0

                2 1 4

                1 0 1

                Input

                1 2 0 1 311211

                bull Reflection

                bull Normally better than zero padding

                DTU Compute

                2122018Introduction to Medical Image Analysis54 DTU Compute Technical University of Denmark

                Template Matching Template

                ndash Skabelon paring dansk Locates objects in images

                Input

                Template

                Output Correlation image

                DTU Compute

                2122018Introduction to Medical Image Analysis55 DTU Compute Technical University of Denmark

                Template Matching The correlation between the template and the input

                image is computed for each pixel

                Input

                Template

                Output Correlation image

                DTU Compute

                2122018Introduction to Medical Image Analysis56 DTU Compute Technical University of Denmark

                Template Matching The pixel with the highest value is found in the

                output imagendash Here is the highest correlation

                Input

                Template

                Output Correlation image

                DTU Compute

                2122018Introduction to Medical Image Analysis57 DTU Compute Technical University of Denmark

                Template Matching This corresponds to the found pattern in the input

                image

                Input

                Template

                Output Correlation image

                DTU Compute

                2122018Introduction to Medical Image Analysis58 DTU Compute Technical University of Denmark

                Problematic Correlation Correlation matching has problem with light areas ndash

                why

                Input (f)

                Template (h)

                Output Correlation imageFake max

                Real max

                Very High119892119892 119909119909119910119910 = 119895119895=minus119877119877

                119877119877

                119894119894=minus119877119877

                119877119877

                ℎ(119894119894 119895119895) 119891119891(119909119909 + 119894119894119910119910 + 119895119895)

                DTU Compute

                2122018Introduction to Medical Image Analysis59 DTU Compute Technical University of Denmark

                Normalised Cross Correlation

                Input (f)

                Template (h)

                Output Correlation image

                Real max

                NCC x y =Correlation

                Length of image patch sdot Length of template

                DTU Compute

                2122018Introduction to Medical Image Analysis60 DTU Compute Technical University of Denmark

                Length of template Vector length

                ndash Put all pixel values into a vectorndash Compute the length of this vector

                Describes the intensity of the templatendash Bright template has a large lengthndash Dark template has a small length

                Template (h)

                Length of template = 119895119895=minus119877119877

                119877119877

                119894119894=minus119877119877

                119877119877

                ℎ(119894119894 119895119895) ℎ(119894119894 119895119895)

                DTU Compute

                2122018Introduction to Medical Image Analysis61 DTU Compute Technical University of Denmark

                Length of image patch Vector length based on pixel values in image patch Describes the intensity of the image patch

                Template (h)

                Input (f) with patch

                DTU Compute

                2122018Introduction to Medical Image Analysis62 DTU Compute Technical University of Denmark

                Normalised Cross Correlation The length of the image patch and the length of

                template normalise the NCC If the image is very bright the NCC will be ldquopulled

                downrdquo

                NCC x y =Correlation

                Length of image patch sdot Length of template

                DTU Compute

                2122018Introduction to Medical Image Analysis63 DTU Compute Technical University of Denmark

                Normalised Cross Correlation NCC will be between

                ndash 0 No similarity between template and image patchndash 1 Template and image patch are identical

                Input (f)

                Template (h)

                Output Correlation image

                Real max

                NCC x y =Correlation

                Length of image patch sdot Length of template

                DTU Compute

                2122018Introduction to Medical Image Analysis64 DTU Compute Technical University of Denmark

                Normalised Cross Correlation

                A) 010B) 033C) 083D) 062E) 098

                Der udfoslashres template matching med og normalized crosscorrelation (NCC) beregnes Hvad bliver NNC i den markerede pixel

                1

                2 2

                3

                2

                A B C D E

                Chart1

                1
                2
                2
                3
                2

                Sheet1

                DTU Compute

                2122018Introduction to Medical Image Analysis66 DTU Compute Technical University of Denmark

                Edges An edge is where there is a

                high change in gray level values

                Objects are often separated from the background by edgesGray level profile

                DTU Compute

                2122018Introduction to Medical Image Analysis67 DTU Compute Technical University of Denmark

                Edges The profile as a function f(d) What value is high when there

                is an edgendash The slope of fndash The slope of the tangent at d

                f(d)

                119891119891prime(119889119889)

                DTU Compute

                2122018Introduction to Medical Image Analysis68 DTU Compute Technical University of Denmark

                Finite Difference Definition of slope

                Approximation

                Simpler approximationh = 1

                119891119891prime 119889119889 = limℎrarr0

                119891119891 119889119889 + ℎ minus 119891119891(119889119889)ℎ

                119891119891prime 119889119889 asymp119891119891 119889119889 + ℎ minus 119891119891(119889119889)

                ℎ

                119891119891prime 119889119889 asymp 119891119891 119889119889 + 1 minus 119891119891(119889119889)

                DTU Compute

                2122018Introduction to Medical Image Analysis69 DTU Compute Technical University of Denmark

                Edges Discrete approximation of frsquo(d) Can be implemented as a filter

                -1 0 1

                f(d-2) f(d-1) f(d) f(d+1) f(d+2) f(d+3)

                f(d)

                119891119891prime 119889119889 asymp 119891119891 119889119889 + 1 minus 119891119891(119889119889)

                DTU Compute

                2122018Introduction to Medical Image Analysis70 DTU Compute Technical University of Denmark

                Edges in 2D Changes in gray level values

                ndash Image gradientndash Gradient is the 2D derivative of a 2D function f(xy)ndash Equal to the slope of the imagendash A steep slope is equal to an edge

                120571120571119891119891 119909119909119910119910 = 119866(119892119892119909119909119892119892119910119910)

                DTU Compute

                2122018Introduction to Medical Image Analysis71 DTU Compute Technical University of Denmark

                Edge filter kernel The Prewitt filter is a typical

                edge filter Output image has high

                values where there are edges

                -1 0 1

                -1 0 1

                -1 0 1Vertical Prewitt filter

                DTU Compute

                2122018Introduction to Medical Image Analysis72 DTU Compute Technical University of Denmark

                Prewitt filter

                Original Prewitt Prewitt

                Hot colormapSmooth 15x15

                Smooth 15x15

                Prewitt

                DTU Compute

                2122018Introduction to Medical Image Analysis73 DTU Compute Technical University of Denmark

                Edge detection Edge filter

                ndash Prewitt for example Thresholding

                ndash Separate edges from non-edges

                Output is binary imagendash Edges are white

                DTU Compute

                2122018Introduction to Medical Image Analysis74 DTU Compute Technical University of Denmark

                Edge filtering

                A) MeanB) Horizontal SobelC) Vertical PrewittD) Horisontal PrewittE) Median

                Der udfoslashres en filtrering (correlation) med et filter paring billedet Der bruges ikke coefficient normalization Den filtrerede vaeligrdi i den markerede pixel bliver -119 Hvilket et 3x3 filter blev benyttet

                0

                8

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                A B C D E

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                2122018Introduction to Medical Image Analysis76 DTU Compute Technical University of Denmark

                02511 - Niveau af dagens emne forelaeligsingA) Meget letB) LetC) PassendeD) SvaeligrtE) Meget svaeligrt

                23

                6

                10

                A B C D E

                Chart1

                2
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                2122018Introduction to Medical Image Analysis77 DTU Compute Technical University of Denmark

                02512 - Niveau af dagens emne forelaeligsingA) Meget letB) LetC) PassendeD) SvaeligrtE) Meget svaeligrt

                0 0

                1

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                A B C D E

                Chart1

                0
                0
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                DTU Compute

                2122018Introduction to Medical Image Analysis78 DTU Compute Technical University of Denmark

                02511 - Mit eget udbytte af dagenA) Jeg har laeligrt meget lidtB) Lidt laeligringC) PassendeD) God laeligringE) Jeg har laeligrt meget

                0 0

                2

                6

                0

                A B C D E

                Chart1

                0
                0
                2
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                Sheet1

                DTU Compute

                2122018Introduction to Medical Image Analysis79 DTU Compute Technical University of Denmark

                02512 - Mit eget udbytte af dagenA) Jeg har laeligrt meget lidtB) Lidt laeligringC) PassendeD) God laeligringE) Jeg har laeligrt meget

                2

                1

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                Chart1

                2
                1
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                DTU Compute

                2122018Introduction to Medical Image Analysis80 DTU Compute Technical University of Denmark

                02511 - Sidste uges oslashvelser (pixelwiseoperations)A) Meget letteB) LetteC) PassendeD) SvaeligreE) Meget svaeligre

                0 0

                1

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                1

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                2122018Introduction to Medical Image Analysis81 DTU Compute Technical University of Denmark

                02512 - Sidste uges oslashvelser (pixelwiseoperations)A) Meget letteB) LetteC) PassendeD) SvaeligreE) Meget svaeligre

                3

                0

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                0 0

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                Chart1

                3
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                DTU Compute

                2122018Introduction to Medical Image Analysis82 DTU Compute Technical University of Denmark

                Denne uges brug af clickersA) click click click ndash jeg bliver

                sindssygB) For meget clickC) PassendeD) Jeg vil gerne have lidt mereE) Jeg kan ikrsquo faring nok

                0 0

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                Chart1

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                DTU Compute

                2122018Introduction to Medical Image Analysis83 DTU Compute Technical University of Denmark

                What can you do after today Describe the difference between point processing and neighbourhood

                processing Compute a rank filtered image using the min max median and

                difference rank filters Compute a mean filtered image Decide if median or average filtering should be used for noise removal Choose the appropriate image border handling based on a given input

                image Implement and apply template matching Compute the normalised cross correlation and explain why it should be

                used Apply given image filter kernels to images Use edge filters on images Describe finite difference approximation of image gradients Describe the concept of edge detection

                DTU Compute

                2122018Introduction to Medical Image Analysis84 DTU Compute Technical University of Denmark

                Oslashvelsesrapport over oslashvelse 4 - 02511 Oslashvelser taeligller cirka 30 af karakteren Skal afleveres senest den 7 marts kl 2359 Kan afleveres af 1 eller 2 personer

                ndash I skal skrive jeres egen oslashvelsesrapportndash Brug mindst et af jeres egne billeder

                Afleveres som PDF Lad vaeligre med at kopiere opgaveteksten ind i jeres

                opgave Put Matlab kode i et Appendix og henvis fra teksten Eksempel rapport over oslashvelse findes paring

                hjemmesiden under eksamen

                DTU Compute

                2122018Introduction to Medical Image Analysis85 DTU Compute Technical University of Denmark

                Exercises

                • Introduction to Medical Image Analysis
                • Lecture 4 ndash Neighbourhood Processing
                • What can you do after today
                • Point processing
                • Point processing
                • Neighbourhood processing
                • Use of filtering
                • Salt and pepper noise
                • Salt and pepper noise
                • What is so special about noise
                • Noise ndash go away
                • What is the median Value
                • The median value
                • Noise away ndash the median filter
                • Noise removal ndash average filter
                • Noise removal ndash median filter
                • Image Filtering
                • Median filter
                • Rank filters
                • Median filter
                • Correlation
                • Why do we need similarity
                • Correlation (1D)
                • Correlation (1D)
                • Normalisation
                • Normalisation
                • Correlation on images
                • Correlation on images
                • Correlation on images
                • Draw your filter
                • Correlation on images ndash no normalisation
                • Correlation on images ndash no normalisation 2
                • Mathematics of 2D Correlation
                • Mathematics of 2D Correlation
                • Mathematics of 2D Correlation
                • Slide Number 40
                • 2D Kernel Normalisation
                • Correlation
                • Smoothing filters
                • Use of smoothing
                • Use of smoothing
                • Mean filter
                • Border handling
                • Border handling ndash extend the input
                • Correlation with zero padding
                • Border handling ndash extend the input
                • Template Matching
                • Template Matching
                • Template Matching
                • Template Matching
                • Problematic Correlation
                • Normalised Cross Correlation
                • Length of template
                • Length of image patch
                • Normalised Cross Correlation
                • Normalised Cross Correlation
                • Normalised Cross Correlation
                • Edges
                • Edges
                • Finite Difference
                • Edges
                • Edges in 2D
                • Edge filter kernel
                • Prewitt filter
                • Edge detection
                • Edge filtering
                • 02511 - Niveau af dagens emne forelaeligsing
                • 02512 - Niveau af dagens emne forelaeligsing
                • 02511 - Mit eget udbytte af dagen
                • 02512 - Mit eget udbytte af dagen
                • 02511 - Sidste uges oslashvelser (pixelwise operations)
                • 02512 - Sidste uges oslashvelser (pixelwise operations)
                • Denne uges brug af clickers
                • What can you do after today
                • Oslashvelsesrapport over oslashvelse 4 - 02511
                • Exercises
                  A0
                  B0
                  C5
                  D0
                  E6
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                  B0
                  C3
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                  E
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                  E
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                  C6
                  D1
                  E0
                  A
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                  C
                  D
                  E
                  A0
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                  C1
                  D1
                  E0
                  A
                  B
                  C
                  D
                  E
                  A1
                  B2
                  C2
                  D3
                  E2
                  A
                  B
                  C
                  D
                  E
                  A0
                  B13
                  C0
                  D0
                  E0
                  A
                  B
                  C
                  D
                  E
                  A12
                  B0
                  C0
                  D0
                  E0
                  A
                  B
                  C
                  D
                  E
                  A0
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                  C0
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                  E13
                  A
                  B
                  C
                  D
                  E
                  A13
                  B0
                  C0
                  D0
                  E0
                  A
                  B
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                  D
                  E
                  A1
                  B0
                  C14
                  D0
                  E0
                  A
                  B
                  C
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                  E
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                  C1
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                  E
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                  C1
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                  A
                  B
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                  E
                  A13
                  B0
                  C0
                  D0
                  E2
                  A
                  B
                  C
                  D
                  E

                  DTU Compute

                  2122018Introduction to Medical Image Analysis9 DTU Compute Technical University of Denmark

                  Salt and pepper noise Fake example

                  ndash Let us take a closer look at noise pixels

                  They are all 0 or 255

                  Should we just remove all the 0rsquos and 255rsquos from the image

                  DTU Compute

                  2122018Introduction to Medical Image Analysis10 DTU Compute Technical University of Denmark

                  What is so special about noise What is the value of the pixel

                  compared to the neighbours Average of the neighbours

                  ndash 170 Can we compare to the

                  averagendash Difficult ndash should we remove

                  all values bigger than average+1

                  It is difficult to detect noise

                  172 169 171 168 0 169 172 173 168

                  DTU Compute

                  2122018Introduction to Medical Image Analysis11 DTU Compute Technical University of Denmark

                  Noise ndash go away We can not tell what pixels

                  are noise One solution

                  ndash Set all pixels to the average of the neighbours (and the pixel itself)

                  Oh nondash Problemsndash The noise ldquopollutesrdquo the

                  good pixels

                  172 169 171 168 0 169 172 173 168

                  170

                  169 168 0 170 172173 170 172 170

                  149

                  DTU Compute

                  2122018Introduction to Medical Image Analysis12 DTU Compute Technical University of Denmark

                  What is the median ValueA) 170B) 173C) 169D) 171E) 172

                  13

                  0 0 02

                  A B C D E

                  169 168 0 170172 173 170 172 170

                  Chart1

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                  2122018Introduction to Medical Image Analysis13 DTU Compute Technical University of Denmark

                  The median value The values are sorted from low to high The middle number is picked

                  ndash The median value

                  169 168 0 170172 173 170 172 170

                  0168 169 170 170 170172 172173

                  Median

                  Noise has no influence on the median

                  DTU Compute

                  2122018Introduction to Medical Image Analysis14 DTU Compute Technical University of Denmark

                  Noise away ndash the median filter All pixels are set to the

                  median of its neighbourhood Noise pixels do not pollute

                  good pixels

                  172 169 171 168 0 169 172 173 168

                  170

                  169 168 0 170 172173 170 172 170

                  170

                  DTU Compute

                  2122018Introduction to Medical Image Analysis15 DTU Compute Technical University of Denmark

                  Noise removal ndash average filter

                  Scanned X-ray with salt and pepper noise

                  Average filter (3x3)

                  DTU Compute

                  2122018Introduction to Medical Image Analysis16 DTU Compute Technical University of Denmark

                  Noise removal ndash median filter

                  Scanned X-ray with salt and pepper noise

                  Median filter (3x3)

                  DTU Compute

                  2122018Introduction to Medical Image Analysis17 DTU Compute Technical University of Denmark

                  Image Filtering Creates a new filtered image Output pixel is computed based

                  on a neighbourhood in the input image

                  3 x 3 neighbourhoodndash Filter size 3 x 3ndash Kernel size 3 x 3ndash Mask size 3 x 3

                  Larger filters often usedndash Size

                  7 x 7ndash Number of elements

                  49

                  DTU Compute

                  2122018Introduction to Medical Image Analysis18 DTU Compute Technical University of Denmark

                  Median filterA) 25B) 90C) 198D) 86E) 103

                  0

                  13

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                  Chart1

                  0
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                  DTU Compute

                  2122018Introduction to Medical Image Analysis20 DTU Compute Technical University of Denmark

                  Rank filters Based on sorting the pixel

                  values in the neighbouring region

                  Minimum rank filterndash Darker image Noise problems

                  Maximum rank filterndash Lighter image Noise problems

                  Difference filterndash Enhances changes (edges)

                  0168 169 170 170 170172 172173

                  -

                  DTU Compute

                  2122018Introduction to Medical Image Analysis21 DTU Compute Technical University of Denmark

                  Median filter

                  A) 3B) 84C) 112D) 73E) 202

                  0

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                  Chart1

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                  DTU Compute

                  2122018Introduction to Medical Image Analysis23 DTU Compute Technical University of Denmark

                  Correlation What is it Two measurements

                  ndash Low correlationndash High correlation

                  High correlation means that there is a relation between the values

                  They look the same Correlation is a measure of

                  similarity

                  Low

                  High

                  Muscles

                  Mat

                  h Ski

                  lls

                  Muscles

                  Ben

                  ch P

                  ress

                  DTU Compute

                  2122018Introduction to Medical Image Analysis24 DTU Compute Technical University of Denmark

                  Why do we need similarity Image analysis is also about recognition of patterns Often an example pattern is used We need something to tell us if there is a high match

                  between our pattern and a part of the image

                  Example pattern

                  Image

                  Find matches

                  DTU Compute

                  2122018Introduction to Medical Image Analysis25 DTU Compute Technical University of Denmark

                  Correlation (1D)

                  1 1 2 2 1 1 2 2 1 1

                  1 2 1

                  45

                  41

                  1 1 + 2 1 + 1 2 = 5

                  Normalise

                  Kernel

                  Signal (1D image)

                  41

                  DTU Compute

                  2122018Introduction to Medical Image Analysis26 DTU Compute Technical University of Denmark

                  Correlation (1D)

                  1 1 2 2 1 1 2 2 1 1

                  1 2 1

                  45

                  47

                  47

                  45

                  45

                  47

                  47

                  45

                  41

                  DTU Compute

                  2122018Introduction to Medical Image Analysis27 DTU Compute Technical University of Denmark

                  Normalisation

                  1 1 2 2 1 1 2 2 1 1

                  1 2 1

                  45

                  41

                  1 1 + 2 1 + 1 2 = 5

                  Normalise41

                  bull The sum of the kernel elements is used

                  bull Keep the values in the same range as the input image

                  Sum is 4

                  DTU Compute

                  2122018Introduction to Medical Image Analysis28 DTU Compute Technical University of Denmark

                  Normalisation Normalisation factor

                  ndash Sum of kernel coefficients

                  1 2 1h(x)

                  119909119909

                  ℎ 119909119909 = 1 + 2 + 1

                  DTU Compute

                  2122018Introduction to Medical Image Analysis29 DTU Compute Technical University of Denmark

                  Correlation on images The filter is now 2D 1 1 1

                  1 1 1

                  1 1 1

                  0 2 4

                  1 2 2

                  1 6 3

                  1 2 12 5 3

                  2 1 3

                  1 3 1

                  2 2 2

                  0 1 3

                  1 2 0

                  2 1 4

                  1 0 1

                  912

                  91

                  Input OutputKernel

                  Kernel coefficients

                  DTU Compute

                  2122018Introduction to Medical Image Analysis30 DTU Compute Technical University of Denmark

                  Correlation on images

                  1 1 11 1 11 1 1

                  0 2 4

                  1 2 2

                  1 6 3

                  1 2 0

                  2 1 4

                  1 0 1

                  912

                  911

                  91

                  Input Output

                  1 3 1

                  2 2 2

                  0 1 3

                  1 2 12 5 3

                  2 1 3

                  DTU Compute

                  2122018Introduction to Medical Image Analysis31 DTU Compute Technical University of Denmark

                  Correlation on images

                  Input Output

                  The mask is moved row by row

                  No values at the border

                  0 2 4

                  1 2 2

                  1 6 3

                  1 2 0

                  2 1 4

                  1 0 1

                  1 3 1

                  2 2 2

                  0 1 3

                  1 2 12 5 3

                  2 1 3

                  DTU Compute

                  2122018Introduction to Medical Image Analysis32 DTU Compute Technical University of Denmark

                  1 2 1

                  1 3 1

                  1 2 1

                  -1 -2 -1

                  0 0 0

                  1 2 1

                  Draw your filter

                  DTU Compute

                  2122018Introduction to Medical Image Analysis33 DTU Compute Technical University of Denmark

                  Correlation on images ndash no normalisationA) 4B) 7C) 16D) 23E) 25

                  1 2 11 3 11 2 1

                  0 2 41 2 2

                  1 6 3

                  1 2 12 5 3

                  2 1 3

                  1 3 1

                  2 2 2

                  0 1 3

                  1 2 0

                  2 1 4

                  1 0 11 0

                  14

                  0 0

                  A B C D E

                  Chart1

                  1
                  0
                  14
                  0
                  0

                  Sheet1

                  DTU Compute

                  2122018Introduction to Medical Image Analysis34 DTU Compute Technical University of Denmark

                  Correlation on images ndash no normalisation 2A) 010B) 3 3C) 6 2D) 10 15E) 11 32

                  13

                  0 0 0 0

                  A B C D E

                  -1 -2 -10 0 01 2 1

                  0 2 41 2 2

                  1 6 3

                  1 2 12 5 3

                  2 1 3

                  1 3 1

                  2 2 2

                  0 1 3

                  1 2 0

                  2 1 4

                  1 0 1

                  Chart1

                  13
                  0
                  0
                  0
                  0

                  Sheet1

                  DTU Compute

                  2122018Introduction to Medical Image Analysis37 DTU Compute Technical University of Denmark

                  Mathematics of 2D Correlation

                  h

                  f

                  Correlation operator

                  1 2 11 3 11 2 1

                  0 2 4

                  1 2 2

                  1 6 3

                  1 2 1

                  2 5 3

                  2 1 3

                  1 3 1

                  2 2 2

                  0 1 3

                  1 2 0

                  2 1 4

                  1 0 1

                  119892119892 119909119909119910119910 = 119891119891 119909119909119910119910 ∘ ℎ(119909119909119910119910)

                  DTU Compute

                  2122018Introduction to Medical Image Analysis38 DTU Compute Technical University of Denmark

                  Mathematics of 2D Correlation

                  1 2 11 3 11 2 1

                  0 2 4

                  1 2 2

                  1 6 3

                  1 2 1

                  2 5 3

                  2 1 3

                  1 3 1

                  2 2 2

                  0 1 3

                  1 2 0

                  2 1 4

                  1 0 1

                  h

                  fh(00)

                  f(21)

                  Example g(21)

                  i = -1 j = -1

                  i = 1 j = 0

                  119892119892 119909119909119910119910 = 119895119895=minus119877119877

                  119877119877

                  119894119894=minus119877119877

                  119877119877

                  ℎ(119894119894 119895119895) 119891119891(119909119909 + 119894119894119910119910 + 119895119895)

                  DTU Compute

                  2122018Introduction to Medical Image Analysis39 DTU Compute Technical University of Denmark

                  Mathematics of 2D Correlation

                  1 2 11 3 11 2 1

                  0 2 4

                  1 2 2

                  1 6 3

                  1 2 1

                  2 5 3

                  2 1 3

                  1 3 1

                  2 2 2

                  0 1 3

                  1 2 0

                  2 1 4

                  1 0 1

                  h

                  f

                  119892119892 119909119909119910119910 = 119895119895=minus119877119877

                  119877119877

                  119894119894=minus119877119877

                  119877119877

                  ℎ(119894119894 119895119895) 119891119891(119909119909 + 119894119894119910119910 + 119895119895)

                  119892119892(119909119909119910119910 = 1 2 + 2 0 + 1 1 + 1 1 + 3 4 + 1 2 + 1 0 + 2 1 + 1 0

                  DTU Compute

                  2122018Introduction to Medical Image Analysis40 DTU Compute Technical University of Denmark

                  119892119892 119909119909 119910119910 = 119895119895=minus119877119877

                  119877119877

                  119894119894=minus119877119877

                  119877119877

                  ℎ(119894119894 119895119895) 119891119891(119909119909 + 119894119894119910119910 + 119895119895)

                  119892119892 22 =ℎ minus1minus1 sdot 119891119891 11 + ℎ 0minus1 sdot 119891119891 21 + ℎ 1minus1 sdot 119891119891 31 +ℎ minus10 sdot 119891119891 12 + ℎ 00 sdot 119891119891 22 + ℎ 10 sdot 119891119891 32 +ℎ minus11 sdot 119891119891 13 + ℎ 01 sdot 119891119891 23 + ℎ 11 sdot 119891119891 33

                  DTU Compute

                  2122018Introduction to Medical Image Analysis41 DTU Compute Technical University of Denmark

                  2D Kernel Normalisation

                  1 2 11 3 11 2 1

                  h

                  Normalisation factor

                  1 + 2 + 1 + 1 + 3 + 1 + 1 + 2 + 1 = 13

                  119909119909

                  119910119910

                  ℎ(119909119909119910119910)

                  DTU Compute

                  2122018Introduction to Medical Image Analysis42 DTU Compute Technical University of Denmark

                  CorrelationA) 50122B) 123001C) 11233D) 2550E) 90454

                  0 0 0 0

                  13

                  A B C D E

                  Chart1

                  0
                  0
                  0
                  0
                  13

                  Sheet1

                  DTU Compute

                  2122018Introduction to Medical Image Analysis44 DTU Compute Technical University of Denmark

                  Smoothing filters

                  Also know as ndash Smoothing kernel Mean filter Low pass filter blurring

                  The simplest filter ndash Spatial low pass filterndash Removes high frequencies

                  Another mask ndash Gaussian filter

                  1 1 1

                  1 1 1

                  1 1 191

                  1 2 1

                  2 4 2

                  1 2 1161

                  Why Gaussian

                  DTU Compute

                  2122018Introduction to Medical Image Analysis45 DTU Compute Technical University of Denmark

                  Use of smoothing

                  3x3 7x7 11x11 15x15

                  DTU Compute

                  2122018Introduction to Medical Image Analysis46 DTU Compute Technical University of Denmark

                  Use of smoothing Large kernels smooth more Removes high frequency information Good at enhancing big structures

                  3x3 15x15

                  DTU Compute

                  2122018Introduction to Medical Image Analysis47 DTU Compute Technical University of Denmark

                  Mean filterA) 166B) 113C) 12D) 51E) 245

                  0 0 0 0

                  A B C D E

                  Chart1

                  12
                  0
                  0
                  0
                  0

                  Sheet1

                  DTU Compute

                  2122018Introduction to Medical Image Analysis49 DTU Compute Technical University of Denmark

                  Border handling

                  0 2 41 2 2

                  1 6 3

                  1 2 12 5 3

                  2 1 3

                  1 3 1

                  2 2 2

                  0 1 3

                  1 2 0

                  2 1 4

                  1 0 1

                  Input Output

                  No values at the border

                  DTU Compute

                  2122018Introduction to Medical Image Analysis50 DTU Compute Technical University of Denmark

                  Border handling ndash extend the input

                  0 2 41 2 2

                  1 6 3

                  1 2 12 5 3

                  2 1 3

                  1 3 1

                  2 2 2

                  0 1 3

                  1 2 0

                  2 1 4

                  1 0 1

                  Input

                  0 0 0 0 000000

                  bull Zero padding ndash what happens

                  bull Zero is black ndash creates dark border around the image

                  DTU Compute

                  2122018Introduction to Medical Image Analysis51 DTU Compute Technical University of Denmark

                  Correlation with zero paddingA) 5 8B) 12 16C) 13 3D) 15 21E) 17 12

                  1 2 11 3 11 2 1

                  0 2 41 2 2

                  1 6 3

                  1 2 12 5 3

                  2 1 3

                  1 3 1

                  2 2 2

                  0 1 3

                  1 2 0

                  2 1 4

                  1 0 1

                  0

                  13

                  0 0 0

                  A B C D E

                  Chart1

                  0
                  13
                  0
                  0
                  0

                  Sheet1

                  DTU Compute

                  2122018Introduction to Medical Image Analysis53 DTU Compute Technical University of Denmark

                  Border handling ndash extend the input

                  0 2 41 2 2

                  1 6 3

                  1 2 12 5 3

                  2 1 3

                  1 3 1

                  2 2 2

                  0 1 3

                  1 2 0

                  2 1 4

                  1 0 1

                  Input

                  1 2 0 1 311211

                  bull Reflection

                  bull Normally better than zero padding

                  DTU Compute

                  2122018Introduction to Medical Image Analysis54 DTU Compute Technical University of Denmark

                  Template Matching Template

                  ndash Skabelon paring dansk Locates objects in images

                  Input

                  Template

                  Output Correlation image

                  DTU Compute

                  2122018Introduction to Medical Image Analysis55 DTU Compute Technical University of Denmark

                  Template Matching The correlation between the template and the input

                  image is computed for each pixel

                  Input

                  Template

                  Output Correlation image

                  DTU Compute

                  2122018Introduction to Medical Image Analysis56 DTU Compute Technical University of Denmark

                  Template Matching The pixel with the highest value is found in the

                  output imagendash Here is the highest correlation

                  Input

                  Template

                  Output Correlation image

                  DTU Compute

                  2122018Introduction to Medical Image Analysis57 DTU Compute Technical University of Denmark

                  Template Matching This corresponds to the found pattern in the input

                  image

                  Input

                  Template

                  Output Correlation image

                  DTU Compute

                  2122018Introduction to Medical Image Analysis58 DTU Compute Technical University of Denmark

                  Problematic Correlation Correlation matching has problem with light areas ndash

                  why

                  Input (f)

                  Template (h)

                  Output Correlation imageFake max

                  Real max

                  Very High119892119892 119909119909119910119910 = 119895119895=minus119877119877

                  119877119877

                  119894119894=minus119877119877

                  119877119877

                  ℎ(119894119894 119895119895) 119891119891(119909119909 + 119894119894119910119910 + 119895119895)

                  DTU Compute

                  2122018Introduction to Medical Image Analysis59 DTU Compute Technical University of Denmark

                  Normalised Cross Correlation

                  Input (f)

                  Template (h)

                  Output Correlation image

                  Real max

                  NCC x y =Correlation

                  Length of image patch sdot Length of template

                  DTU Compute

                  2122018Introduction to Medical Image Analysis60 DTU Compute Technical University of Denmark

                  Length of template Vector length

                  ndash Put all pixel values into a vectorndash Compute the length of this vector

                  Describes the intensity of the templatendash Bright template has a large lengthndash Dark template has a small length

                  Template (h)

                  Length of template = 119895119895=minus119877119877

                  119877119877

                  119894119894=minus119877119877

                  119877119877

                  ℎ(119894119894 119895119895) ℎ(119894119894 119895119895)

                  DTU Compute

                  2122018Introduction to Medical Image Analysis61 DTU Compute Technical University of Denmark

                  Length of image patch Vector length based on pixel values in image patch Describes the intensity of the image patch

                  Template (h)

                  Input (f) with patch

                  DTU Compute

                  2122018Introduction to Medical Image Analysis62 DTU Compute Technical University of Denmark

                  Normalised Cross Correlation The length of the image patch and the length of

                  template normalise the NCC If the image is very bright the NCC will be ldquopulled

                  downrdquo

                  NCC x y =Correlation

                  Length of image patch sdot Length of template

                  DTU Compute

                  2122018Introduction to Medical Image Analysis63 DTU Compute Technical University of Denmark

                  Normalised Cross Correlation NCC will be between

                  ndash 0 No similarity between template and image patchndash 1 Template and image patch are identical

                  Input (f)

                  Template (h)

                  Output Correlation image

                  Real max

                  NCC x y =Correlation

                  Length of image patch sdot Length of template

                  DTU Compute

                  2122018Introduction to Medical Image Analysis64 DTU Compute Technical University of Denmark

                  Normalised Cross Correlation

                  A) 010B) 033C) 083D) 062E) 098

                  Der udfoslashres template matching med og normalized crosscorrelation (NCC) beregnes Hvad bliver NNC i den markerede pixel

                  1

                  2 2

                  3

                  2

                  A B C D E

                  Chart1

                  1
                  2
                  2
                  3
                  2

                  Sheet1

                  DTU Compute

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                  Edges An edge is where there is a

                  high change in gray level values

                  Objects are often separated from the background by edgesGray level profile

                  DTU Compute

                  2122018Introduction to Medical Image Analysis67 DTU Compute Technical University of Denmark

                  Edges The profile as a function f(d) What value is high when there

                  is an edgendash The slope of fndash The slope of the tangent at d

                  f(d)

                  119891119891prime(119889119889)

                  DTU Compute

                  2122018Introduction to Medical Image Analysis68 DTU Compute Technical University of Denmark

                  Finite Difference Definition of slope

                  Approximation

                  Simpler approximationh = 1

                  119891119891prime 119889119889 = limℎrarr0

                  119891119891 119889119889 + ℎ minus 119891119891(119889119889)ℎ

                  119891119891prime 119889119889 asymp119891119891 119889119889 + ℎ minus 119891119891(119889119889)

                  ℎ

                  119891119891prime 119889119889 asymp 119891119891 119889119889 + 1 minus 119891119891(119889119889)

                  DTU Compute

                  2122018Introduction to Medical Image Analysis69 DTU Compute Technical University of Denmark

                  Edges Discrete approximation of frsquo(d) Can be implemented as a filter

                  -1 0 1

                  f(d-2) f(d-1) f(d) f(d+1) f(d+2) f(d+3)

                  f(d)

                  119891119891prime 119889119889 asymp 119891119891 119889119889 + 1 minus 119891119891(119889119889)

                  DTU Compute

                  2122018Introduction to Medical Image Analysis70 DTU Compute Technical University of Denmark

                  Edges in 2D Changes in gray level values

                  ndash Image gradientndash Gradient is the 2D derivative of a 2D function f(xy)ndash Equal to the slope of the imagendash A steep slope is equal to an edge

                  120571120571119891119891 119909119909119910119910 = 119866(119892119892119909119909119892119892119910119910)

                  DTU Compute

                  2122018Introduction to Medical Image Analysis71 DTU Compute Technical University of Denmark

                  Edge filter kernel The Prewitt filter is a typical

                  edge filter Output image has high

                  values where there are edges

                  -1 0 1

                  -1 0 1

                  -1 0 1Vertical Prewitt filter

                  DTU Compute

                  2122018Introduction to Medical Image Analysis72 DTU Compute Technical University of Denmark

                  Prewitt filter

                  Original Prewitt Prewitt

                  Hot colormapSmooth 15x15

                  Smooth 15x15

                  Prewitt

                  DTU Compute

                  2122018Introduction to Medical Image Analysis73 DTU Compute Technical University of Denmark

                  Edge detection Edge filter

                  ndash Prewitt for example Thresholding

                  ndash Separate edges from non-edges

                  Output is binary imagendash Edges are white

                  DTU Compute

                  2122018Introduction to Medical Image Analysis74 DTU Compute Technical University of Denmark

                  Edge filtering

                  A) MeanB) Horizontal SobelC) Vertical PrewittD) Horisontal PrewittE) Median

                  Der udfoslashres en filtrering (correlation) med et filter paring billedet Der bruges ikke coefficient normalization Den filtrerede vaeligrdi i den markerede pixel bliver -119 Hvilket et 3x3 filter blev benyttet

                  0

                  8

                  1 10

                  A B C D E

                  Chart1

                  0
                  8
                  1
                  1
                  0

                  Sheet1

                  DTU Compute

                  2122018Introduction to Medical Image Analysis76 DTU Compute Technical University of Denmark

                  02511 - Niveau af dagens emne forelaeligsingA) Meget letB) LetC) PassendeD) SvaeligrtE) Meget svaeligrt

                  23

                  6

                  10

                  A B C D E

                  Chart1

                  2
                  3
                  6
                  1
                  0

                  Sheet1

                  DTU Compute

                  2122018Introduction to Medical Image Analysis77 DTU Compute Technical University of Denmark

                  02512 - Niveau af dagens emne forelaeligsingA) Meget letB) LetC) PassendeD) SvaeligrtE) Meget svaeligrt

                  0 0

                  1

                  0 0

                  A B C D E

                  Chart1

                  0
                  0
                  1
                  0
                  0

                  Sheet1

                  DTU Compute

                  2122018Introduction to Medical Image Analysis78 DTU Compute Technical University of Denmark

                  02511 - Mit eget udbytte af dagenA) Jeg har laeligrt meget lidtB) Lidt laeligringC) PassendeD) God laeligringE) Jeg har laeligrt meget

                  0 0

                  2

                  6

                  0

                  A B C D E

                  Chart1

                  0
                  0
                  2
                  6
                  0

                  Sheet1

                  DTU Compute

                  2122018Introduction to Medical Image Analysis79 DTU Compute Technical University of Denmark

                  02512 - Mit eget udbytte af dagenA) Jeg har laeligrt meget lidtB) Lidt laeligringC) PassendeD) God laeligringE) Jeg har laeligrt meget

                  2

                  1

                  3

                  2

                  0

                  A B C D E

                  Chart1

                  2
                  1
                  3
                  2
                  0

                  Sheet1

                  DTU Compute

                  2122018Introduction to Medical Image Analysis80 DTU Compute Technical University of Denmark

                  02511 - Sidste uges oslashvelser (pixelwiseoperations)A) Meget letteB) LetteC) PassendeD) SvaeligreE) Meget svaeligre

                  0 0

                  1

                  4

                  1

                  A B C D E

                  Chart1

                  0
                  0
                  1
                  4
                  1

                  Sheet1

                  DTU Compute

                  2122018Introduction to Medical Image Analysis81 DTU Compute Technical University of Denmark

                  02512 - Sidste uges oslashvelser (pixelwiseoperations)A) Meget letteB) LetteC) PassendeD) SvaeligreE) Meget svaeligre

                  3

                  0

                  3

                  0 0

                  A B C D E

                  Chart1

                  3
                  0
                  3
                  0
                  0

                  Sheet1

                  DTU Compute

                  2122018Introduction to Medical Image Analysis82 DTU Compute Technical University of Denmark

                  Denne uges brug af clickersA) click click click ndash jeg bliver

                  sindssygB) For meget clickC) PassendeD) Jeg vil gerne have lidt mereE) Jeg kan ikrsquo faring nok

                  0 0

                  5

                  0

                  6

                  A B C D E

                  Chart1

                  0
                  0
                  5
                  0
                  6

                  Sheet1

                  DTU Compute

                  2122018Introduction to Medical Image Analysis83 DTU Compute Technical University of Denmark

                  What can you do after today Describe the difference between point processing and neighbourhood

                  processing Compute a rank filtered image using the min max median and

                  difference rank filters Compute a mean filtered image Decide if median or average filtering should be used for noise removal Choose the appropriate image border handling based on a given input

                  image Implement and apply template matching Compute the normalised cross correlation and explain why it should be

                  used Apply given image filter kernels to images Use edge filters on images Describe finite difference approximation of image gradients Describe the concept of edge detection

                  DTU Compute

                  2122018Introduction to Medical Image Analysis84 DTU Compute Technical University of Denmark

                  Oslashvelsesrapport over oslashvelse 4 - 02511 Oslashvelser taeligller cirka 30 af karakteren Skal afleveres senest den 7 marts kl 2359 Kan afleveres af 1 eller 2 personer

                  ndash I skal skrive jeres egen oslashvelsesrapportndash Brug mindst et af jeres egne billeder

                  Afleveres som PDF Lad vaeligre med at kopiere opgaveteksten ind i jeres

                  opgave Put Matlab kode i et Appendix og henvis fra teksten Eksempel rapport over oslashvelse findes paring

                  hjemmesiden under eksamen

                  DTU Compute

                  2122018Introduction to Medical Image Analysis85 DTU Compute Technical University of Denmark

                  Exercises

                  • Introduction to Medical Image Analysis
                  • Lecture 4 ndash Neighbourhood Processing
                  • What can you do after today
                  • Point processing
                  • Point processing
                  • Neighbourhood processing
                  • Use of filtering
                  • Salt and pepper noise
                  • Salt and pepper noise
                  • What is so special about noise
                  • Noise ndash go away
                  • What is the median Value
                  • The median value
                  • Noise away ndash the median filter
                  • Noise removal ndash average filter
                  • Noise removal ndash median filter
                  • Image Filtering
                  • Median filter
                  • Rank filters
                  • Median filter
                  • Correlation
                  • Why do we need similarity
                  • Correlation (1D)
                  • Correlation (1D)
                  • Normalisation
                  • Normalisation
                  • Correlation on images
                  • Correlation on images
                  • Correlation on images
                  • Draw your filter
                  • Correlation on images ndash no normalisation
                  • Correlation on images ndash no normalisation 2
                  • Mathematics of 2D Correlation
                  • Mathematics of 2D Correlation
                  • Mathematics of 2D Correlation
                  • Slide Number 40
                  • 2D Kernel Normalisation
                  • Correlation
                  • Smoothing filters
                  • Use of smoothing
                  • Use of smoothing
                  • Mean filter
                  • Border handling
                  • Border handling ndash extend the input
                  • Correlation with zero padding
                  • Border handling ndash extend the input
                  • Template Matching
                  • Template Matching
                  • Template Matching
                  • Template Matching
                  • Problematic Correlation
                  • Normalised Cross Correlation
                  • Length of template
                  • Length of image patch
                  • Normalised Cross Correlation
                  • Normalised Cross Correlation
                  • Normalised Cross Correlation
                  • Edges
                  • Edges
                  • Finite Difference
                  • Edges
                  • Edges in 2D
                  • Edge filter kernel
                  • Prewitt filter
                  • Edge detection
                  • Edge filtering
                  • 02511 - Niveau af dagens emne forelaeligsing
                  • 02512 - Niveau af dagens emne forelaeligsing
                  • 02511 - Mit eget udbytte af dagen
                  • 02512 - Mit eget udbytte af dagen
                  • 02511 - Sidste uges oslashvelser (pixelwise operations)
                  • 02512 - Sidste uges oslashvelser (pixelwise operations)
                  • Denne uges brug af clickers
                  • What can you do after today
                  • Oslashvelsesrapport over oslashvelse 4 - 02511
                  • Exercises
                    A0
                    B0
                    C5
                    D0
                    E6
                    A
                    B
                    C
                    D
                    E
                    A3
                    B0
                    C3
                    D0
                    E0
                    A
                    B
                    C
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                    E
                    A0
                    B0
                    C1
                    D4
                    E1
                    A
                    B
                    C
                    D
                    E
                    A2
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                    C3
                    D2
                    E0
                    A
                    B
                    C
                    D
                    E
                    A0
                    B0
                    C2
                    D6
                    E0
                    A
                    B
                    C
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                    E
                    A0
                    B0
                    C1
                    D0
                    E0
                    A
                    B
                    C
                    D
                    E
                    A2
                    B3
                    C6
                    D1
                    E0
                    A
                    B
                    C
                    D
                    E
                    A0
                    B8
                    C1
                    D1
                    E0
                    A
                    B
                    C
                    D
                    E
                    A1
                    B2
                    C2
                    D3
                    E2
                    A
                    B
                    C
                    D
                    E
                    A0
                    B13
                    C0
                    D0
                    E0
                    A
                    B
                    C
                    D
                    E
                    A12
                    B0
                    C0
                    D0
                    E0
                    A
                    B
                    C
                    D
                    E
                    A0
                    B0
                    C0
                    D0
                    E13
                    A
                    B
                    C
                    D
                    E
                    A13
                    B0
                    C0
                    D0
                    E0
                    A
                    B
                    C
                    D
                    E
                    A1
                    B0
                    C14
                    D0
                    E0
                    A
                    B
                    C
                    D
                    E
                    A0
                    B12
                    C1
                    D0
                    E0
                    A
                    B
                    C
                    D
                    E
                    A0
                    B13
                    C1
                    D0
                    E0
                    A
                    B
                    C
                    D
                    E
                    A13
                    B0
                    C0
                    D0
                    E2
                    A
                    B
                    C
                    D
                    E

                    DTU Compute

                    2122018Introduction to Medical Image Analysis10 DTU Compute Technical University of Denmark

                    What is so special about noise What is the value of the pixel

                    compared to the neighbours Average of the neighbours

                    ndash 170 Can we compare to the

                    averagendash Difficult ndash should we remove

                    all values bigger than average+1

                    It is difficult to detect noise

                    172 169 171 168 0 169 172 173 168

                    DTU Compute

                    2122018Introduction to Medical Image Analysis11 DTU Compute Technical University of Denmark

                    Noise ndash go away We can not tell what pixels

                    are noise One solution

                    ndash Set all pixels to the average of the neighbours (and the pixel itself)

                    Oh nondash Problemsndash The noise ldquopollutesrdquo the

                    good pixels

                    172 169 171 168 0 169 172 173 168

                    170

                    169 168 0 170 172173 170 172 170

                    149

                    DTU Compute

                    2122018Introduction to Medical Image Analysis12 DTU Compute Technical University of Denmark

                    What is the median ValueA) 170B) 173C) 169D) 171E) 172

                    13

                    0 0 02

                    A B C D E

                    169 168 0 170172 173 170 172 170

                    Chart1

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                    2122018Introduction to Medical Image Analysis13 DTU Compute Technical University of Denmark

                    The median value The values are sorted from low to high The middle number is picked

                    ndash The median value

                    169 168 0 170172 173 170 172 170

                    0168 169 170 170 170172 172173

                    Median

                    Noise has no influence on the median

                    DTU Compute

                    2122018Introduction to Medical Image Analysis14 DTU Compute Technical University of Denmark

                    Noise away ndash the median filter All pixels are set to the

                    median of its neighbourhood Noise pixels do not pollute

                    good pixels

                    172 169 171 168 0 169 172 173 168

                    170

                    169 168 0 170 172173 170 172 170

                    170

                    DTU Compute

                    2122018Introduction to Medical Image Analysis15 DTU Compute Technical University of Denmark

                    Noise removal ndash average filter

                    Scanned X-ray with salt and pepper noise

                    Average filter (3x3)

                    DTU Compute

                    2122018Introduction to Medical Image Analysis16 DTU Compute Technical University of Denmark

                    Noise removal ndash median filter

                    Scanned X-ray with salt and pepper noise

                    Median filter (3x3)

                    DTU Compute

                    2122018Introduction to Medical Image Analysis17 DTU Compute Technical University of Denmark

                    Image Filtering Creates a new filtered image Output pixel is computed based

                    on a neighbourhood in the input image

                    3 x 3 neighbourhoodndash Filter size 3 x 3ndash Kernel size 3 x 3ndash Mask size 3 x 3

                    Larger filters often usedndash Size

                    7 x 7ndash Number of elements

                    49

                    DTU Compute

                    2122018Introduction to Medical Image Analysis18 DTU Compute Technical University of Denmark

                    Median filterA) 25B) 90C) 198D) 86E) 103

                    0

                    13

                    1 0 0

                    A B C D E

                    Chart1

                    0
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                    DTU Compute

                    2122018Introduction to Medical Image Analysis20 DTU Compute Technical University of Denmark

                    Rank filters Based on sorting the pixel

                    values in the neighbouring region

                    Minimum rank filterndash Darker image Noise problems

                    Maximum rank filterndash Lighter image Noise problems

                    Difference filterndash Enhances changes (edges)

                    0168 169 170 170 170172 172173

                    -

                    DTU Compute

                    2122018Introduction to Medical Image Analysis21 DTU Compute Technical University of Denmark

                    Median filter

                    A) 3B) 84C) 112D) 73E) 202

                    0

                    12

                    10 0

                    A B C D E

                    Chart1

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                    DTU Compute

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                    Correlation What is it Two measurements

                    ndash Low correlationndash High correlation

                    High correlation means that there is a relation between the values

                    They look the same Correlation is a measure of

                    similarity

                    Low

                    High

                    Muscles

                    Mat

                    h Ski

                    lls

                    Muscles

                    Ben

                    ch P

                    ress

                    DTU Compute

                    2122018Introduction to Medical Image Analysis24 DTU Compute Technical University of Denmark

                    Why do we need similarity Image analysis is also about recognition of patterns Often an example pattern is used We need something to tell us if there is a high match

                    between our pattern and a part of the image

                    Example pattern

                    Image

                    Find matches

                    DTU Compute

                    2122018Introduction to Medical Image Analysis25 DTU Compute Technical University of Denmark

                    Correlation (1D)

                    1 1 2 2 1 1 2 2 1 1

                    1 2 1

                    45

                    41

                    1 1 + 2 1 + 1 2 = 5

                    Normalise

                    Kernel

                    Signal (1D image)

                    41

                    DTU Compute

                    2122018Introduction to Medical Image Analysis26 DTU Compute Technical University of Denmark

                    Correlation (1D)

                    1 1 2 2 1 1 2 2 1 1

                    1 2 1

                    45

                    47

                    47

                    45

                    45

                    47

                    47

                    45

                    41

                    DTU Compute

                    2122018Introduction to Medical Image Analysis27 DTU Compute Technical University of Denmark

                    Normalisation

                    1 1 2 2 1 1 2 2 1 1

                    1 2 1

                    45

                    41

                    1 1 + 2 1 + 1 2 = 5

                    Normalise41

                    bull The sum of the kernel elements is used

                    bull Keep the values in the same range as the input image

                    Sum is 4

                    DTU Compute

                    2122018Introduction to Medical Image Analysis28 DTU Compute Technical University of Denmark

                    Normalisation Normalisation factor

                    ndash Sum of kernel coefficients

                    1 2 1h(x)

                    119909119909

                    ℎ 119909119909 = 1 + 2 + 1

                    DTU Compute

                    2122018Introduction to Medical Image Analysis29 DTU Compute Technical University of Denmark

                    Correlation on images The filter is now 2D 1 1 1

                    1 1 1

                    1 1 1

                    0 2 4

                    1 2 2

                    1 6 3

                    1 2 12 5 3

                    2 1 3

                    1 3 1

                    2 2 2

                    0 1 3

                    1 2 0

                    2 1 4

                    1 0 1

                    912

                    91

                    Input OutputKernel

                    Kernel coefficients

                    DTU Compute

                    2122018Introduction to Medical Image Analysis30 DTU Compute Technical University of Denmark

                    Correlation on images

                    1 1 11 1 11 1 1

                    0 2 4

                    1 2 2

                    1 6 3

                    1 2 0

                    2 1 4

                    1 0 1

                    912

                    911

                    91

                    Input Output

                    1 3 1

                    2 2 2

                    0 1 3

                    1 2 12 5 3

                    2 1 3

                    DTU Compute

                    2122018Introduction to Medical Image Analysis31 DTU Compute Technical University of Denmark

                    Correlation on images

                    Input Output

                    The mask is moved row by row

                    No values at the border

                    0 2 4

                    1 2 2

                    1 6 3

                    1 2 0

                    2 1 4

                    1 0 1

                    1 3 1

                    2 2 2

                    0 1 3

                    1 2 12 5 3

                    2 1 3

                    DTU Compute

                    2122018Introduction to Medical Image Analysis32 DTU Compute Technical University of Denmark

                    1 2 1

                    1 3 1

                    1 2 1

                    -1 -2 -1

                    0 0 0

                    1 2 1

                    Draw your filter

                    DTU Compute

                    2122018Introduction to Medical Image Analysis33 DTU Compute Technical University of Denmark

                    Correlation on images ndash no normalisationA) 4B) 7C) 16D) 23E) 25

                    1 2 11 3 11 2 1

                    0 2 41 2 2

                    1 6 3

                    1 2 12 5 3

                    2 1 3

                    1 3 1

                    2 2 2

                    0 1 3

                    1 2 0

                    2 1 4

                    1 0 11 0

                    14

                    0 0

                    A B C D E

                    Chart1

                    1
                    0
                    14
                    0
                    0

                    Sheet1

                    DTU Compute

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                    Correlation on images ndash no normalisation 2A) 010B) 3 3C) 6 2D) 10 15E) 11 32

                    13

                    0 0 0 0

                    A B C D E

                    -1 -2 -10 0 01 2 1

                    0 2 41 2 2

                    1 6 3

                    1 2 12 5 3

                    2 1 3

                    1 3 1

                    2 2 2

                    0 1 3

                    1 2 0

                    2 1 4

                    1 0 1

                    Chart1

                    13
                    0
                    0
                    0
                    0

                    Sheet1

                    DTU Compute

                    2122018Introduction to Medical Image Analysis37 DTU Compute Technical University of Denmark

                    Mathematics of 2D Correlation

                    h

                    f

                    Correlation operator

                    1 2 11 3 11 2 1

                    0 2 4

                    1 2 2

                    1 6 3

                    1 2 1

                    2 5 3

                    2 1 3

                    1 3 1

                    2 2 2

                    0 1 3

                    1 2 0

                    2 1 4

                    1 0 1

                    119892119892 119909119909119910119910 = 119891119891 119909119909119910119910 ∘ ℎ(119909119909119910119910)

                    DTU Compute

                    2122018Introduction to Medical Image Analysis38 DTU Compute Technical University of Denmark

                    Mathematics of 2D Correlation

                    1 2 11 3 11 2 1

                    0 2 4

                    1 2 2

                    1 6 3

                    1 2 1

                    2 5 3

                    2 1 3

                    1 3 1

                    2 2 2

                    0 1 3

                    1 2 0

                    2 1 4

                    1 0 1

                    h

                    fh(00)

                    f(21)

                    Example g(21)

                    i = -1 j = -1

                    i = 1 j = 0

                    119892119892 119909119909119910119910 = 119895119895=minus119877119877

                    119877119877

                    119894119894=minus119877119877

                    119877119877

                    ℎ(119894119894 119895119895) 119891119891(119909119909 + 119894119894119910119910 + 119895119895)

                    DTU Compute

                    2122018Introduction to Medical Image Analysis39 DTU Compute Technical University of Denmark

                    Mathematics of 2D Correlation

                    1 2 11 3 11 2 1

                    0 2 4

                    1 2 2

                    1 6 3

                    1 2 1

                    2 5 3

                    2 1 3

                    1 3 1

                    2 2 2

                    0 1 3

                    1 2 0

                    2 1 4

                    1 0 1

                    h

                    f

                    119892119892 119909119909119910119910 = 119895119895=minus119877119877

                    119877119877

                    119894119894=minus119877119877

                    119877119877

                    ℎ(119894119894 119895119895) 119891119891(119909119909 + 119894119894119910119910 + 119895119895)

                    119892119892(119909119909119910119910 = 1 2 + 2 0 + 1 1 + 1 1 + 3 4 + 1 2 + 1 0 + 2 1 + 1 0

                    DTU Compute

                    2122018Introduction to Medical Image Analysis40 DTU Compute Technical University of Denmark

                    119892119892 119909119909 119910119910 = 119895119895=minus119877119877

                    119877119877

                    119894119894=minus119877119877

                    119877119877

                    ℎ(119894119894 119895119895) 119891119891(119909119909 + 119894119894119910119910 + 119895119895)

                    119892119892 22 =ℎ minus1minus1 sdot 119891119891 11 + ℎ 0minus1 sdot 119891119891 21 + ℎ 1minus1 sdot 119891119891 31 +ℎ minus10 sdot 119891119891 12 + ℎ 00 sdot 119891119891 22 + ℎ 10 sdot 119891119891 32 +ℎ minus11 sdot 119891119891 13 + ℎ 01 sdot 119891119891 23 + ℎ 11 sdot 119891119891 33

                    DTU Compute

                    2122018Introduction to Medical Image Analysis41 DTU Compute Technical University of Denmark

                    2D Kernel Normalisation

                    1 2 11 3 11 2 1

                    h

                    Normalisation factor

                    1 + 2 + 1 + 1 + 3 + 1 + 1 + 2 + 1 = 13

                    119909119909

                    119910119910

                    ℎ(119909119909119910119910)

                    DTU Compute

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                    CorrelationA) 50122B) 123001C) 11233D) 2550E) 90454

                    0 0 0 0

                    13

                    A B C D E

                    Chart1

                    0
                    0
                    0
                    0
                    13

                    Sheet1

                    DTU Compute

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                    Smoothing filters

                    Also know as ndash Smoothing kernel Mean filter Low pass filter blurring

                    The simplest filter ndash Spatial low pass filterndash Removes high frequencies

                    Another mask ndash Gaussian filter

                    1 1 1

                    1 1 1

                    1 1 191

                    1 2 1

                    2 4 2

                    1 2 1161

                    Why Gaussian

                    DTU Compute

                    2122018Introduction to Medical Image Analysis45 DTU Compute Technical University of Denmark

                    Use of smoothing

                    3x3 7x7 11x11 15x15

                    DTU Compute

                    2122018Introduction to Medical Image Analysis46 DTU Compute Technical University of Denmark

                    Use of smoothing Large kernels smooth more Removes high frequency information Good at enhancing big structures

                    3x3 15x15

                    DTU Compute

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                    Mean filterA) 166B) 113C) 12D) 51E) 245

                    0 0 0 0

                    A B C D E

                    Chart1

                    12
                    0
                    0
                    0
                    0

                    Sheet1

                    DTU Compute

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                    Border handling

                    0 2 41 2 2

                    1 6 3

                    1 2 12 5 3

                    2 1 3

                    1 3 1

                    2 2 2

                    0 1 3

                    1 2 0

                    2 1 4

                    1 0 1

                    Input Output

                    No values at the border

                    DTU Compute

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                    Border handling ndash extend the input

                    0 2 41 2 2

                    1 6 3

                    1 2 12 5 3

                    2 1 3

                    1 3 1

                    2 2 2

                    0 1 3

                    1 2 0

                    2 1 4

                    1 0 1

                    Input

                    0 0 0 0 000000

                    bull Zero padding ndash what happens

                    bull Zero is black ndash creates dark border around the image

                    DTU Compute

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                    Correlation with zero paddingA) 5 8B) 12 16C) 13 3D) 15 21E) 17 12

                    1 2 11 3 11 2 1

                    0 2 41 2 2

                    1 6 3

                    1 2 12 5 3

                    2 1 3

                    1 3 1

                    2 2 2

                    0 1 3

                    1 2 0

                    2 1 4

                    1 0 1

                    0

                    13

                    0 0 0

                    A B C D E

                    Chart1

                    0
                    13
                    0
                    0
                    0

                    Sheet1

                    DTU Compute

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                    Border handling ndash extend the input

                    0 2 41 2 2

                    1 6 3

                    1 2 12 5 3

                    2 1 3

                    1 3 1

                    2 2 2

                    0 1 3

                    1 2 0

                    2 1 4

                    1 0 1

                    Input

                    1 2 0 1 311211

                    bull Reflection

                    bull Normally better than zero padding

                    DTU Compute

                    2122018Introduction to Medical Image Analysis54 DTU Compute Technical University of Denmark

                    Template Matching Template

                    ndash Skabelon paring dansk Locates objects in images

                    Input

                    Template

                    Output Correlation image

                    DTU Compute

                    2122018Introduction to Medical Image Analysis55 DTU Compute Technical University of Denmark

                    Template Matching The correlation between the template and the input

                    image is computed for each pixel

                    Input

                    Template

                    Output Correlation image

                    DTU Compute

                    2122018Introduction to Medical Image Analysis56 DTU Compute Technical University of Denmark

                    Template Matching The pixel with the highest value is found in the

                    output imagendash Here is the highest correlation

                    Input

                    Template

                    Output Correlation image

                    DTU Compute

                    2122018Introduction to Medical Image Analysis57 DTU Compute Technical University of Denmark

                    Template Matching This corresponds to the found pattern in the input

                    image

                    Input

                    Template

                    Output Correlation image

                    DTU Compute

                    2122018Introduction to Medical Image Analysis58 DTU Compute Technical University of Denmark

                    Problematic Correlation Correlation matching has problem with light areas ndash

                    why

                    Input (f)

                    Template (h)

                    Output Correlation imageFake max

                    Real max

                    Very High119892119892 119909119909119910119910 = 119895119895=minus119877119877

                    119877119877

                    119894119894=minus119877119877

                    119877119877

                    ℎ(119894119894 119895119895) 119891119891(119909119909 + 119894119894119910119910 + 119895119895)

                    DTU Compute

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                    Normalised Cross Correlation

                    Input (f)

                    Template (h)

                    Output Correlation image

                    Real max

                    NCC x y =Correlation

                    Length of image patch sdot Length of template

                    DTU Compute

                    2122018Introduction to Medical Image Analysis60 DTU Compute Technical University of Denmark

                    Length of template Vector length

                    ndash Put all pixel values into a vectorndash Compute the length of this vector

                    Describes the intensity of the templatendash Bright template has a large lengthndash Dark template has a small length

                    Template (h)

                    Length of template = 119895119895=minus119877119877

                    119877119877

                    119894119894=minus119877119877

                    119877119877

                    ℎ(119894119894 119895119895) ℎ(119894119894 119895119895)

                    DTU Compute

                    2122018Introduction to Medical Image Analysis61 DTU Compute Technical University of Denmark

                    Length of image patch Vector length based on pixel values in image patch Describes the intensity of the image patch

                    Template (h)

                    Input (f) with patch

                    DTU Compute

                    2122018Introduction to Medical Image Analysis62 DTU Compute Technical University of Denmark

                    Normalised Cross Correlation The length of the image patch and the length of

                    template normalise the NCC If the image is very bright the NCC will be ldquopulled

                    downrdquo

                    NCC x y =Correlation

                    Length of image patch sdot Length of template

                    DTU Compute

                    2122018Introduction to Medical Image Analysis63 DTU Compute Technical University of Denmark

                    Normalised Cross Correlation NCC will be between

                    ndash 0 No similarity between template and image patchndash 1 Template and image patch are identical

                    Input (f)

                    Template (h)

                    Output Correlation image

                    Real max

                    NCC x y =Correlation

                    Length of image patch sdot Length of template

                    DTU Compute

                    2122018Introduction to Medical Image Analysis64 DTU Compute Technical University of Denmark

                    Normalised Cross Correlation

                    A) 010B) 033C) 083D) 062E) 098

                    Der udfoslashres template matching med og normalized crosscorrelation (NCC) beregnes Hvad bliver NNC i den markerede pixel

                    1

                    2 2

                    3

                    2

                    A B C D E

                    Chart1

                    1
                    2
                    2
                    3
                    2

                    Sheet1

                    DTU Compute

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                    Edges An edge is where there is a

                    high change in gray level values

                    Objects are often separated from the background by edgesGray level profile

                    DTU Compute

                    2122018Introduction to Medical Image Analysis67 DTU Compute Technical University of Denmark

                    Edges The profile as a function f(d) What value is high when there

                    is an edgendash The slope of fndash The slope of the tangent at d

                    f(d)

                    119891119891prime(119889119889)

                    DTU Compute

                    2122018Introduction to Medical Image Analysis68 DTU Compute Technical University of Denmark

                    Finite Difference Definition of slope

                    Approximation

                    Simpler approximationh = 1

                    119891119891prime 119889119889 = limℎrarr0

                    119891119891 119889119889 + ℎ minus 119891119891(119889119889)ℎ

                    119891119891prime 119889119889 asymp119891119891 119889119889 + ℎ minus 119891119891(119889119889)

                    ℎ

                    119891119891prime 119889119889 asymp 119891119891 119889119889 + 1 minus 119891119891(119889119889)

                    DTU Compute

                    2122018Introduction to Medical Image Analysis69 DTU Compute Technical University of Denmark

                    Edges Discrete approximation of frsquo(d) Can be implemented as a filter

                    -1 0 1

                    f(d-2) f(d-1) f(d) f(d+1) f(d+2) f(d+3)

                    f(d)

                    119891119891prime 119889119889 asymp 119891119891 119889119889 + 1 minus 119891119891(119889119889)

                    DTU Compute

                    2122018Introduction to Medical Image Analysis70 DTU Compute Technical University of Denmark

                    Edges in 2D Changes in gray level values

                    ndash Image gradientndash Gradient is the 2D derivative of a 2D function f(xy)ndash Equal to the slope of the imagendash A steep slope is equal to an edge

                    120571120571119891119891 119909119909119910119910 = 119866(119892119892119909119909119892119892119910119910)

                    DTU Compute

                    2122018Introduction to Medical Image Analysis71 DTU Compute Technical University of Denmark

                    Edge filter kernel The Prewitt filter is a typical

                    edge filter Output image has high

                    values where there are edges

                    -1 0 1

                    -1 0 1

                    -1 0 1Vertical Prewitt filter

                    DTU Compute

                    2122018Introduction to Medical Image Analysis72 DTU Compute Technical University of Denmark

                    Prewitt filter

                    Original Prewitt Prewitt

                    Hot colormapSmooth 15x15

                    Smooth 15x15

                    Prewitt

                    DTU Compute

                    2122018Introduction to Medical Image Analysis73 DTU Compute Technical University of Denmark

                    Edge detection Edge filter

                    ndash Prewitt for example Thresholding

                    ndash Separate edges from non-edges

                    Output is binary imagendash Edges are white

                    DTU Compute

                    2122018Introduction to Medical Image Analysis74 DTU Compute Technical University of Denmark

                    Edge filtering

                    A) MeanB) Horizontal SobelC) Vertical PrewittD) Horisontal PrewittE) Median

                    Der udfoslashres en filtrering (correlation) med et filter paring billedet Der bruges ikke coefficient normalization Den filtrerede vaeligrdi i den markerede pixel bliver -119 Hvilket et 3x3 filter blev benyttet

                    0

                    8

                    1 10

                    A B C D E

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                    0
                    8
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                    1
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                    DTU Compute

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                    02511 - Niveau af dagens emne forelaeligsingA) Meget letB) LetC) PassendeD) SvaeligrtE) Meget svaeligrt

                    23

                    6

                    10

                    A B C D E

                    Chart1

                    2
                    3
                    6
                    1
                    0

                    Sheet1

                    DTU Compute

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                    02512 - Niveau af dagens emne forelaeligsingA) Meget letB) LetC) PassendeD) SvaeligrtE) Meget svaeligrt

                    0 0

                    1

                    0 0

                    A B C D E

                    Chart1

                    0
                    0
                    1
                    0
                    0

                    Sheet1

                    DTU Compute

                    2122018Introduction to Medical Image Analysis78 DTU Compute Technical University of Denmark

                    02511 - Mit eget udbytte af dagenA) Jeg har laeligrt meget lidtB) Lidt laeligringC) PassendeD) God laeligringE) Jeg har laeligrt meget

                    0 0

                    2

                    6

                    0

                    A B C D E

                    Chart1

                    0
                    0
                    2
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                    0

                    Sheet1

                    DTU Compute

                    2122018Introduction to Medical Image Analysis79 DTU Compute Technical University of Denmark

                    02512 - Mit eget udbytte af dagenA) Jeg har laeligrt meget lidtB) Lidt laeligringC) PassendeD) God laeligringE) Jeg har laeligrt meget

                    2

                    1

                    3

                    2

                    0

                    A B C D E

                    Chart1

                    2
                    1
                    3
                    2
                    0

                    Sheet1

                    DTU Compute

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                    02511 - Sidste uges oslashvelser (pixelwiseoperations)A) Meget letteB) LetteC) PassendeD) SvaeligreE) Meget svaeligre

                    0 0

                    1

                    4

                    1

                    A B C D E

                    Chart1

                    0
                    0
                    1
                    4
                    1

                    Sheet1

                    DTU Compute

                    2122018Introduction to Medical Image Analysis81 DTU Compute Technical University of Denmark

                    02512 - Sidste uges oslashvelser (pixelwiseoperations)A) Meget letteB) LetteC) PassendeD) SvaeligreE) Meget svaeligre

                    3

                    0

                    3

                    0 0

                    A B C D E

                    Chart1

                    3
                    0
                    3
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                    Sheet1

                    DTU Compute

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                    Denne uges brug af clickersA) click click click ndash jeg bliver

                    sindssygB) For meget clickC) PassendeD) Jeg vil gerne have lidt mereE) Jeg kan ikrsquo faring nok

                    0 0

                    5

                    0

                    6

                    A B C D E

                    Chart1

                    0
                    0
                    5
                    0
                    6

                    Sheet1

                    DTU Compute

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                    What can you do after today Describe the difference between point processing and neighbourhood

                    processing Compute a rank filtered image using the min max median and

                    difference rank filters Compute a mean filtered image Decide if median or average filtering should be used for noise removal Choose the appropriate image border handling based on a given input

                    image Implement and apply template matching Compute the normalised cross correlation and explain why it should be

                    used Apply given image filter kernels to images Use edge filters on images Describe finite difference approximation of image gradients Describe the concept of edge detection

                    DTU Compute

                    2122018Introduction to Medical Image Analysis84 DTU Compute Technical University of Denmark

                    Oslashvelsesrapport over oslashvelse 4 - 02511 Oslashvelser taeligller cirka 30 af karakteren Skal afleveres senest den 7 marts kl 2359 Kan afleveres af 1 eller 2 personer

                    ndash I skal skrive jeres egen oslashvelsesrapportndash Brug mindst et af jeres egne billeder

                    Afleveres som PDF Lad vaeligre med at kopiere opgaveteksten ind i jeres

                    opgave Put Matlab kode i et Appendix og henvis fra teksten Eksempel rapport over oslashvelse findes paring

                    hjemmesiden under eksamen

                    DTU Compute

                    2122018Introduction to Medical Image Analysis85 DTU Compute Technical University of Denmark

                    Exercises

                    • Introduction to Medical Image Analysis
                    • Lecture 4 ndash Neighbourhood Processing
                    • What can you do after today
                    • Point processing
                    • Point processing
                    • Neighbourhood processing
                    • Use of filtering
                    • Salt and pepper noise
                    • Salt and pepper noise
                    • What is so special about noise
                    • Noise ndash go away
                    • What is the median Value
                    • The median value
                    • Noise away ndash the median filter
                    • Noise removal ndash average filter
                    • Noise removal ndash median filter
                    • Image Filtering
                    • Median filter
                    • Rank filters
                    • Median filter
                    • Correlation
                    • Why do we need similarity
                    • Correlation (1D)
                    • Correlation (1D)
                    • Normalisation
                    • Normalisation
                    • Correlation on images
                    • Correlation on images
                    • Correlation on images
                    • Draw your filter
                    • Correlation on images ndash no normalisation
                    • Correlation on images ndash no normalisation 2
                    • Mathematics of 2D Correlation
                    • Mathematics of 2D Correlation
                    • Mathematics of 2D Correlation
                    • Slide Number 40
                    • 2D Kernel Normalisation
                    • Correlation
                    • Smoothing filters
                    • Use of smoothing
                    • Use of smoothing
                    • Mean filter
                    • Border handling
                    • Border handling ndash extend the input
                    • Correlation with zero padding
                    • Border handling ndash extend the input
                    • Template Matching
                    • Template Matching
                    • Template Matching
                    • Template Matching
                    • Problematic Correlation
                    • Normalised Cross Correlation
                    • Length of template
                    • Length of image patch
                    • Normalised Cross Correlation
                    • Normalised Cross Correlation
                    • Normalised Cross Correlation
                    • Edges
                    • Edges
                    • Finite Difference
                    • Edges
                    • Edges in 2D
                    • Edge filter kernel
                    • Prewitt filter
                    • Edge detection
                    • Edge filtering
                    • 02511 - Niveau af dagens emne forelaeligsing
                    • 02512 - Niveau af dagens emne forelaeligsing
                    • 02511 - Mit eget udbytte af dagen
                    • 02512 - Mit eget udbytte af dagen
                    • 02511 - Sidste uges oslashvelser (pixelwise operations)
                    • 02512 - Sidste uges oslashvelser (pixelwise operations)
                    • Denne uges brug af clickers
                    • What can you do after today
                    • Oslashvelsesrapport over oslashvelse 4 - 02511
                    • Exercises
                      A0
                      B0
                      C5
                      D0
                      E6
                      A
                      B
                      C
                      D
                      E
                      A3
                      B0
                      C3
                      D0
                      E0
                      A
                      B
                      C
                      D
                      E
                      A0
                      B0
                      C1
                      D4
                      E1
                      A
                      B
                      C
                      D
                      E
                      A2
                      B1
                      C3
                      D2
                      E0
                      A
                      B
                      C
                      D
                      E
                      A0
                      B0
                      C2
                      D6
                      E0
                      A
                      B
                      C
                      D
                      E
                      A0
                      B0
                      C1
                      D0
                      E0
                      A
                      B
                      C
                      D
                      E
                      A2
                      B3
                      C6
                      D1
                      E0
                      A
                      B
                      C
                      D
                      E
                      A0
                      B8
                      C1
                      D1
                      E0
                      A
                      B
                      C
                      D
                      E
                      A1
                      B2
                      C2
                      D3
                      E2
                      A
                      B
                      C
                      D
                      E
                      A0
                      B13
                      C0
                      D0
                      E0
                      A
                      B
                      C
                      D
                      E
                      A12
                      B0
                      C0
                      D0
                      E0
                      A
                      B
                      C
                      D
                      E
                      A0
                      B0
                      C0
                      D0
                      E13
                      A
                      B
                      C
                      D
                      E
                      A13
                      B0
                      C0
                      D0
                      E0
                      A
                      B
                      C
                      D
                      E
                      A1
                      B0
                      C14
                      D0
                      E0
                      A
                      B
                      C
                      D
                      E
                      A0
                      B12
                      C1
                      D0
                      E0
                      A
                      B
                      C
                      D
                      E
                      A0
                      B13
                      C1
                      D0
                      E0
                      A
                      B
                      C
                      D
                      E
                      A13
                      B0
                      C0
                      D0
                      E2
                      A
                      B
                      C
                      D
                      E

                      DTU Compute

                      2122018Introduction to Medical Image Analysis11 DTU Compute Technical University of Denmark

                      Noise ndash go away We can not tell what pixels

                      are noise One solution

                      ndash Set all pixels to the average of the neighbours (and the pixel itself)

                      Oh nondash Problemsndash The noise ldquopollutesrdquo the

                      good pixels

                      172 169 171 168 0 169 172 173 168

                      170

                      169 168 0 170 172173 170 172 170

                      149

                      DTU Compute

                      2122018Introduction to Medical Image Analysis12 DTU Compute Technical University of Denmark

                      What is the median ValueA) 170B) 173C) 169D) 171E) 172

                      13

                      0 0 02

                      A B C D E

                      169 168 0 170172 173 170 172 170

                      Chart1

                      13
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                      DTU Compute

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                      The median value The values are sorted from low to high The middle number is picked

                      ndash The median value

                      169 168 0 170172 173 170 172 170

                      0168 169 170 170 170172 172173

                      Median

                      Noise has no influence on the median

                      DTU Compute

                      2122018Introduction to Medical Image Analysis14 DTU Compute Technical University of Denmark

                      Noise away ndash the median filter All pixels are set to the

                      median of its neighbourhood Noise pixels do not pollute

                      good pixels

                      172 169 171 168 0 169 172 173 168

                      170

                      169 168 0 170 172173 170 172 170

                      170

                      DTU Compute

                      2122018Introduction to Medical Image Analysis15 DTU Compute Technical University of Denmark

                      Noise removal ndash average filter

                      Scanned X-ray with salt and pepper noise

                      Average filter (3x3)

                      DTU Compute

                      2122018Introduction to Medical Image Analysis16 DTU Compute Technical University of Denmark

                      Noise removal ndash median filter

                      Scanned X-ray with salt and pepper noise

                      Median filter (3x3)

                      DTU Compute

                      2122018Introduction to Medical Image Analysis17 DTU Compute Technical University of Denmark

                      Image Filtering Creates a new filtered image Output pixel is computed based

                      on a neighbourhood in the input image

                      3 x 3 neighbourhoodndash Filter size 3 x 3ndash Kernel size 3 x 3ndash Mask size 3 x 3

                      Larger filters often usedndash Size

                      7 x 7ndash Number of elements

                      49

                      DTU Compute

                      2122018Introduction to Medical Image Analysis18 DTU Compute Technical University of Denmark

                      Median filterA) 25B) 90C) 198D) 86E) 103

                      0

                      13

                      1 0 0

                      A B C D E

                      Chart1

                      0
                      13
                      1
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                      Sheet1

                      DTU Compute

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                      Rank filters Based on sorting the pixel

                      values in the neighbouring region

                      Minimum rank filterndash Darker image Noise problems

                      Maximum rank filterndash Lighter image Noise problems

                      Difference filterndash Enhances changes (edges)

                      0168 169 170 170 170172 172173

                      -

                      DTU Compute

                      2122018Introduction to Medical Image Analysis21 DTU Compute Technical University of Denmark

                      Median filter

                      A) 3B) 84C) 112D) 73E) 202

                      0

                      12

                      10 0

                      A B C D E

                      Chart1

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                      DTU Compute

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                      Correlation What is it Two measurements

                      ndash Low correlationndash High correlation

                      High correlation means that there is a relation between the values

                      They look the same Correlation is a measure of

                      similarity

                      Low

                      High

                      Muscles

                      Mat

                      h Ski

                      lls

                      Muscles

                      Ben

                      ch P

                      ress

                      DTU Compute

                      2122018Introduction to Medical Image Analysis24 DTU Compute Technical University of Denmark

                      Why do we need similarity Image analysis is also about recognition of patterns Often an example pattern is used We need something to tell us if there is a high match

                      between our pattern and a part of the image

                      Example pattern

                      Image

                      Find matches

                      DTU Compute

                      2122018Introduction to Medical Image Analysis25 DTU Compute Technical University of Denmark

                      Correlation (1D)

                      1 1 2 2 1 1 2 2 1 1

                      1 2 1

                      45

                      41

                      1 1 + 2 1 + 1 2 = 5

                      Normalise

                      Kernel

                      Signal (1D image)

                      41

                      DTU Compute

                      2122018Introduction to Medical Image Analysis26 DTU Compute Technical University of Denmark

                      Correlation (1D)

                      1 1 2 2 1 1 2 2 1 1

                      1 2 1

                      45

                      47

                      47

                      45

                      45

                      47

                      47

                      45

                      41

                      DTU Compute

                      2122018Introduction to Medical Image Analysis27 DTU Compute Technical University of Denmark

                      Normalisation

                      1 1 2 2 1 1 2 2 1 1

                      1 2 1

                      45

                      41

                      1 1 + 2 1 + 1 2 = 5

                      Normalise41

                      bull The sum of the kernel elements is used

                      bull Keep the values in the same range as the input image

                      Sum is 4

                      DTU Compute

                      2122018Introduction to Medical Image Analysis28 DTU Compute Technical University of Denmark

                      Normalisation Normalisation factor

                      ndash Sum of kernel coefficients

                      1 2 1h(x)

                      119909119909

                      ℎ 119909119909 = 1 + 2 + 1

                      DTU Compute

                      2122018Introduction to Medical Image Analysis29 DTU Compute Technical University of Denmark

                      Correlation on images The filter is now 2D 1 1 1

                      1 1 1

                      1 1 1

                      0 2 4

                      1 2 2

                      1 6 3

                      1 2 12 5 3

                      2 1 3

                      1 3 1

                      2 2 2

                      0 1 3

                      1 2 0

                      2 1 4

                      1 0 1

                      912

                      91

                      Input OutputKernel

                      Kernel coefficients

                      DTU Compute

                      2122018Introduction to Medical Image Analysis30 DTU Compute Technical University of Denmark

                      Correlation on images

                      1 1 11 1 11 1 1

                      0 2 4

                      1 2 2

                      1 6 3

                      1 2 0

                      2 1 4

                      1 0 1

                      912

                      911

                      91

                      Input Output

                      1 3 1

                      2 2 2

                      0 1 3

                      1 2 12 5 3

                      2 1 3

                      DTU Compute

                      2122018Introduction to Medical Image Analysis31 DTU Compute Technical University of Denmark

                      Correlation on images

                      Input Output

                      The mask is moved row by row

                      No values at the border

                      0 2 4

                      1 2 2

                      1 6 3

                      1 2 0

                      2 1 4

                      1 0 1

                      1 3 1

                      2 2 2

                      0 1 3

                      1 2 12 5 3

                      2 1 3

                      DTU Compute

                      2122018Introduction to Medical Image Analysis32 DTU Compute Technical University of Denmark

                      1 2 1

                      1 3 1

                      1 2 1

                      -1 -2 -1

                      0 0 0

                      1 2 1

                      Draw your filter

                      DTU Compute

                      2122018Introduction to Medical Image Analysis33 DTU Compute Technical University of Denmark

                      Correlation on images ndash no normalisationA) 4B) 7C) 16D) 23E) 25

                      1 2 11 3 11 2 1

                      0 2 41 2 2

                      1 6 3

                      1 2 12 5 3

                      2 1 3

                      1 3 1

                      2 2 2

                      0 1 3

                      1 2 0

                      2 1 4

                      1 0 11 0

                      14

                      0 0

                      A B C D E

                      Chart1

                      1
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                      14
                      0
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                      Sheet1

                      DTU Compute

                      2122018Introduction to Medical Image Analysis34 DTU Compute Technical University of Denmark

                      Correlation on images ndash no normalisation 2A) 010B) 3 3C) 6 2D) 10 15E) 11 32

                      13

                      0 0 0 0

                      A B C D E

                      -1 -2 -10 0 01 2 1

                      0 2 41 2 2

                      1 6 3

                      1 2 12 5 3

                      2 1 3

                      1 3 1

                      2 2 2

                      0 1 3

                      1 2 0

                      2 1 4

                      1 0 1

                      Chart1

                      13
                      0
                      0
                      0
                      0

                      Sheet1

                      DTU Compute

                      2122018Introduction to Medical Image Analysis37 DTU Compute Technical University of Denmark

                      Mathematics of 2D Correlation

                      h

                      f

                      Correlation operator

                      1 2 11 3 11 2 1

                      0 2 4

                      1 2 2

                      1 6 3

                      1 2 1

                      2 5 3

                      2 1 3

                      1 3 1

                      2 2 2

                      0 1 3

                      1 2 0

                      2 1 4

                      1 0 1

                      119892119892 119909119909119910119910 = 119891119891 119909119909119910119910 ∘ ℎ(119909119909119910119910)

                      DTU Compute

                      2122018Introduction to Medical Image Analysis38 DTU Compute Technical University of Denmark

                      Mathematics of 2D Correlation

                      1 2 11 3 11 2 1

                      0 2 4

                      1 2 2

                      1 6 3

                      1 2 1

                      2 5 3

                      2 1 3

                      1 3 1

                      2 2 2

                      0 1 3

                      1 2 0

                      2 1 4

                      1 0 1

                      h

                      fh(00)

                      f(21)

                      Example g(21)

                      i = -1 j = -1

                      i = 1 j = 0

                      119892119892 119909119909119910119910 = 119895119895=minus119877119877

                      119877119877

                      119894119894=minus119877119877

                      119877119877

                      ℎ(119894119894 119895119895) 119891119891(119909119909 + 119894119894119910119910 + 119895119895)

                      DTU Compute

                      2122018Introduction to Medical Image Analysis39 DTU Compute Technical University of Denmark

                      Mathematics of 2D Correlation

                      1 2 11 3 11 2 1

                      0 2 4

                      1 2 2

                      1 6 3

                      1 2 1

                      2 5 3

                      2 1 3

                      1 3 1

                      2 2 2

                      0 1 3

                      1 2 0

                      2 1 4

                      1 0 1

                      h

                      f

                      119892119892 119909119909119910119910 = 119895119895=minus119877119877

                      119877119877

                      119894119894=minus119877119877

                      119877119877

                      ℎ(119894119894 119895119895) 119891119891(119909119909 + 119894119894119910119910 + 119895119895)

                      119892119892(119909119909119910119910 = 1 2 + 2 0 + 1 1 + 1 1 + 3 4 + 1 2 + 1 0 + 2 1 + 1 0

                      DTU Compute

                      2122018Introduction to Medical Image Analysis40 DTU Compute Technical University of Denmark

                      119892119892 119909119909 119910119910 = 119895119895=minus119877119877

                      119877119877

                      119894119894=minus119877119877

                      119877119877

                      ℎ(119894119894 119895119895) 119891119891(119909119909 + 119894119894119910119910 + 119895119895)

                      119892119892 22 =ℎ minus1minus1 sdot 119891119891 11 + ℎ 0minus1 sdot 119891119891 21 + ℎ 1minus1 sdot 119891119891 31 +ℎ minus10 sdot 119891119891 12 + ℎ 00 sdot 119891119891 22 + ℎ 10 sdot 119891119891 32 +ℎ minus11 sdot 119891119891 13 + ℎ 01 sdot 119891119891 23 + ℎ 11 sdot 119891119891 33

                      DTU Compute

                      2122018Introduction to Medical Image Analysis41 DTU Compute Technical University of Denmark

                      2D Kernel Normalisation

                      1 2 11 3 11 2 1

                      h

                      Normalisation factor

                      1 + 2 + 1 + 1 + 3 + 1 + 1 + 2 + 1 = 13

                      119909119909

                      119910119910

                      ℎ(119909119909119910119910)

                      DTU Compute

                      2122018Introduction to Medical Image Analysis42 DTU Compute Technical University of Denmark

                      CorrelationA) 50122B) 123001C) 11233D) 2550E) 90454

                      0 0 0 0

                      13

                      A B C D E

                      Chart1

                      0
                      0
                      0
                      0
                      13

                      Sheet1

                      DTU Compute

                      2122018Introduction to Medical Image Analysis44 DTU Compute Technical University of Denmark

                      Smoothing filters

                      Also know as ndash Smoothing kernel Mean filter Low pass filter blurring

                      The simplest filter ndash Spatial low pass filterndash Removes high frequencies

                      Another mask ndash Gaussian filter

                      1 1 1

                      1 1 1

                      1 1 191

                      1 2 1

                      2 4 2

                      1 2 1161

                      Why Gaussian

                      DTU Compute

                      2122018Introduction to Medical Image Analysis45 DTU Compute Technical University of Denmark

                      Use of smoothing

                      3x3 7x7 11x11 15x15

                      DTU Compute

                      2122018Introduction to Medical Image Analysis46 DTU Compute Technical University of Denmark

                      Use of smoothing Large kernels smooth more Removes high frequency information Good at enhancing big structures

                      3x3 15x15

                      DTU Compute

                      2122018Introduction to Medical Image Analysis47 DTU Compute Technical University of Denmark

                      Mean filterA) 166B) 113C) 12D) 51E) 245

                      0 0 0 0

                      A B C D E

                      Chart1

                      12
                      0
                      0
                      0
                      0

                      Sheet1

                      DTU Compute

                      2122018Introduction to Medical Image Analysis49 DTU Compute Technical University of Denmark

                      Border handling

                      0 2 41 2 2

                      1 6 3

                      1 2 12 5 3

                      2 1 3

                      1 3 1

                      2 2 2

                      0 1 3

                      1 2 0

                      2 1 4

                      1 0 1

                      Input Output

                      No values at the border

                      DTU Compute

                      2122018Introduction to Medical Image Analysis50 DTU Compute Technical University of Denmark

                      Border handling ndash extend the input

                      0 2 41 2 2

                      1 6 3

                      1 2 12 5 3

                      2 1 3

                      1 3 1

                      2 2 2

                      0 1 3

                      1 2 0

                      2 1 4

                      1 0 1

                      Input

                      0 0 0 0 000000

                      bull Zero padding ndash what happens

                      bull Zero is black ndash creates dark border around the image

                      DTU Compute

                      2122018Introduction to Medical Image Analysis51 DTU Compute Technical University of Denmark

                      Correlation with zero paddingA) 5 8B) 12 16C) 13 3D) 15 21E) 17 12

                      1 2 11 3 11 2 1

                      0 2 41 2 2

                      1 6 3

                      1 2 12 5 3

                      2 1 3

                      1 3 1

                      2 2 2

                      0 1 3

                      1 2 0

                      2 1 4

                      1 0 1

                      0

                      13

                      0 0 0

                      A B C D E

                      Chart1

                      0
                      13
                      0
                      0
                      0

                      Sheet1

                      DTU Compute

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                      Border handling ndash extend the input

                      0 2 41 2 2

                      1 6 3

                      1 2 12 5 3

                      2 1 3

                      1 3 1

                      2 2 2

                      0 1 3

                      1 2 0

                      2 1 4

                      1 0 1

                      Input

                      1 2 0 1 311211

                      bull Reflection

                      bull Normally better than zero padding

                      DTU Compute

                      2122018Introduction to Medical Image Analysis54 DTU Compute Technical University of Denmark

                      Template Matching Template

                      ndash Skabelon paring dansk Locates objects in images

                      Input

                      Template

                      Output Correlation image

                      DTU Compute

                      2122018Introduction to Medical Image Analysis55 DTU Compute Technical University of Denmark

                      Template Matching The correlation between the template and the input

                      image is computed for each pixel

                      Input

                      Template

                      Output Correlation image

                      DTU Compute

                      2122018Introduction to Medical Image Analysis56 DTU Compute Technical University of Denmark

                      Template Matching The pixel with the highest value is found in the

                      output imagendash Here is the highest correlation

                      Input

                      Template

                      Output Correlation image

                      DTU Compute

                      2122018Introduction to Medical Image Analysis57 DTU Compute Technical University of Denmark

                      Template Matching This corresponds to the found pattern in the input

                      image

                      Input

                      Template

                      Output Correlation image

                      DTU Compute

                      2122018Introduction to Medical Image Analysis58 DTU Compute Technical University of Denmark

                      Problematic Correlation Correlation matching has problem with light areas ndash

                      why

                      Input (f)

                      Template (h)

                      Output Correlation imageFake max

                      Real max

                      Very High119892119892 119909119909119910119910 = 119895119895=minus119877119877

                      119877119877

                      119894119894=minus119877119877

                      119877119877

                      ℎ(119894119894 119895119895) 119891119891(119909119909 + 119894119894119910119910 + 119895119895)

                      DTU Compute

                      2122018Introduction to Medical Image Analysis59 DTU Compute Technical University of Denmark

                      Normalised Cross Correlation

                      Input (f)

                      Template (h)

                      Output Correlation image

                      Real max

                      NCC x y =Correlation

                      Length of image patch sdot Length of template

                      DTU Compute

                      2122018Introduction to Medical Image Analysis60 DTU Compute Technical University of Denmark

                      Length of template Vector length

                      ndash Put all pixel values into a vectorndash Compute the length of this vector

                      Describes the intensity of the templatendash Bright template has a large lengthndash Dark template has a small length

                      Template (h)

                      Length of template = 119895119895=minus119877119877

                      119877119877

                      119894119894=minus119877119877

                      119877119877

                      ℎ(119894119894 119895119895) ℎ(119894119894 119895119895)

                      DTU Compute

                      2122018Introduction to Medical Image Analysis61 DTU Compute Technical University of Denmark

                      Length of image patch Vector length based on pixel values in image patch Describes the intensity of the image patch

                      Template (h)

                      Input (f) with patch

                      DTU Compute

                      2122018Introduction to Medical Image Analysis62 DTU Compute Technical University of Denmark

                      Normalised Cross Correlation The length of the image patch and the length of

                      template normalise the NCC If the image is very bright the NCC will be ldquopulled

                      downrdquo

                      NCC x y =Correlation

                      Length of image patch sdot Length of template

                      DTU Compute

                      2122018Introduction to Medical Image Analysis63 DTU Compute Technical University of Denmark

                      Normalised Cross Correlation NCC will be between

                      ndash 0 No similarity between template and image patchndash 1 Template and image patch are identical

                      Input (f)

                      Template (h)

                      Output Correlation image

                      Real max

                      NCC x y =Correlation

                      Length of image patch sdot Length of template

                      DTU Compute

                      2122018Introduction to Medical Image Analysis64 DTU Compute Technical University of Denmark

                      Normalised Cross Correlation

                      A) 010B) 033C) 083D) 062E) 098

                      Der udfoslashres template matching med og normalized crosscorrelation (NCC) beregnes Hvad bliver NNC i den markerede pixel

                      1

                      2 2

                      3

                      2

                      A B C D E

                      Chart1

                      1
                      2
                      2
                      3
                      2

                      Sheet1

                      DTU Compute

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                      Edges An edge is where there is a

                      high change in gray level values

                      Objects are often separated from the background by edgesGray level profile

                      DTU Compute

                      2122018Introduction to Medical Image Analysis67 DTU Compute Technical University of Denmark

                      Edges The profile as a function f(d) What value is high when there

                      is an edgendash The slope of fndash The slope of the tangent at d

                      f(d)

                      119891119891prime(119889119889)

                      DTU Compute

                      2122018Introduction to Medical Image Analysis68 DTU Compute Technical University of Denmark

                      Finite Difference Definition of slope

                      Approximation

                      Simpler approximationh = 1

                      119891119891prime 119889119889 = limℎrarr0

                      119891119891 119889119889 + ℎ minus 119891119891(119889119889)ℎ

                      119891119891prime 119889119889 asymp119891119891 119889119889 + ℎ minus 119891119891(119889119889)

                      ℎ

                      119891119891prime 119889119889 asymp 119891119891 119889119889 + 1 minus 119891119891(119889119889)

                      DTU Compute

                      2122018Introduction to Medical Image Analysis69 DTU Compute Technical University of Denmark

                      Edges Discrete approximation of frsquo(d) Can be implemented as a filter

                      -1 0 1

                      f(d-2) f(d-1) f(d) f(d+1) f(d+2) f(d+3)

                      f(d)

                      119891119891prime 119889119889 asymp 119891119891 119889119889 + 1 minus 119891119891(119889119889)

                      DTU Compute

                      2122018Introduction to Medical Image Analysis70 DTU Compute Technical University of Denmark

                      Edges in 2D Changes in gray level values

                      ndash Image gradientndash Gradient is the 2D derivative of a 2D function f(xy)ndash Equal to the slope of the imagendash A steep slope is equal to an edge

                      120571120571119891119891 119909119909119910119910 = 119866(119892119892119909119909119892119892119910119910)

                      DTU Compute

                      2122018Introduction to Medical Image Analysis71 DTU Compute Technical University of Denmark

                      Edge filter kernel The Prewitt filter is a typical

                      edge filter Output image has high

                      values where there are edges

                      -1 0 1

                      -1 0 1

                      -1 0 1Vertical Prewitt filter

                      DTU Compute

                      2122018Introduction to Medical Image Analysis72 DTU Compute Technical University of Denmark

                      Prewitt filter

                      Original Prewitt Prewitt

                      Hot colormapSmooth 15x15

                      Smooth 15x15

                      Prewitt

                      DTU Compute

                      2122018Introduction to Medical Image Analysis73 DTU Compute Technical University of Denmark

                      Edge detection Edge filter

                      ndash Prewitt for example Thresholding

                      ndash Separate edges from non-edges

                      Output is binary imagendash Edges are white

                      DTU Compute

                      2122018Introduction to Medical Image Analysis74 DTU Compute Technical University of Denmark

                      Edge filtering

                      A) MeanB) Horizontal SobelC) Vertical PrewittD) Horisontal PrewittE) Median

                      Der udfoslashres en filtrering (correlation) med et filter paring billedet Der bruges ikke coefficient normalization Den filtrerede vaeligrdi i den markerede pixel bliver -119 Hvilket et 3x3 filter blev benyttet

                      0

                      8

                      1 10

                      A B C D E

                      Chart1

                      0
                      8
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                      1
                      0

                      Sheet1

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                      02511 - Niveau af dagens emne forelaeligsingA) Meget letB) LetC) PassendeD) SvaeligrtE) Meget svaeligrt

                      23

                      6

                      10

                      A B C D E

                      Chart1

                      2
                      3
                      6
                      1
                      0

                      Sheet1

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                      02512 - Niveau af dagens emne forelaeligsingA) Meget letB) LetC) PassendeD) SvaeligrtE) Meget svaeligrt

                      0 0

                      1

                      0 0

                      A B C D E

                      Chart1

                      0
                      0
                      1
                      0
                      0

                      Sheet1

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                      02511 - Mit eget udbytte af dagenA) Jeg har laeligrt meget lidtB) Lidt laeligringC) PassendeD) God laeligringE) Jeg har laeligrt meget

                      0 0

                      2

                      6

                      0

                      A B C D E

                      Chart1

                      0
                      0
                      2
                      6
                      0

                      Sheet1

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                      02512 - Mit eget udbytte af dagenA) Jeg har laeligrt meget lidtB) Lidt laeligringC) PassendeD) God laeligringE) Jeg har laeligrt meget

                      2

                      1

                      3

                      2

                      0

                      A B C D E

                      Chart1

                      2
                      1
                      3
                      2
                      0

                      Sheet1

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                      02511 - Sidste uges oslashvelser (pixelwiseoperations)A) Meget letteB) LetteC) PassendeD) SvaeligreE) Meget svaeligre

                      0 0

                      1

                      4

                      1

                      A B C D E

                      Chart1

                      0
                      0
                      1
                      4
                      1

                      Sheet1

                      DTU Compute

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                      02512 - Sidste uges oslashvelser (pixelwiseoperations)A) Meget letteB) LetteC) PassendeD) SvaeligreE) Meget svaeligre

                      3

                      0

                      3

                      0 0

                      A B C D E

                      Chart1

                      3
                      0
                      3
                      0
                      0

                      Sheet1

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                      2122018Introduction to Medical Image Analysis82 DTU Compute Technical University of Denmark

                      Denne uges brug af clickersA) click click click ndash jeg bliver

                      sindssygB) For meget clickC) PassendeD) Jeg vil gerne have lidt mereE) Jeg kan ikrsquo faring nok

                      0 0

                      5

                      0

                      6

                      A B C D E

                      Chart1

                      0
                      0
                      5
                      0
                      6

                      Sheet1

                      DTU Compute

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                      What can you do after today Describe the difference between point processing and neighbourhood

                      processing Compute a rank filtered image using the min max median and

                      difference rank filters Compute a mean filtered image Decide if median or average filtering should be used for noise removal Choose the appropriate image border handling based on a given input

                      image Implement and apply template matching Compute the normalised cross correlation and explain why it should be

                      used Apply given image filter kernels to images Use edge filters on images Describe finite difference approximation of image gradients Describe the concept of edge detection

                      DTU Compute

                      2122018Introduction to Medical Image Analysis84 DTU Compute Technical University of Denmark

                      Oslashvelsesrapport over oslashvelse 4 - 02511 Oslashvelser taeligller cirka 30 af karakteren Skal afleveres senest den 7 marts kl 2359 Kan afleveres af 1 eller 2 personer

                      ndash I skal skrive jeres egen oslashvelsesrapportndash Brug mindst et af jeres egne billeder

                      Afleveres som PDF Lad vaeligre med at kopiere opgaveteksten ind i jeres

                      opgave Put Matlab kode i et Appendix og henvis fra teksten Eksempel rapport over oslashvelse findes paring

                      hjemmesiden under eksamen

                      DTU Compute

                      2122018Introduction to Medical Image Analysis85 DTU Compute Technical University of Denmark

                      Exercises

                      • Introduction to Medical Image Analysis
                      • Lecture 4 ndash Neighbourhood Processing
                      • What can you do after today
                      • Point processing
                      • Point processing
                      • Neighbourhood processing
                      • Use of filtering
                      • Salt and pepper noise
                      • Salt and pepper noise
                      • What is so special about noise
                      • Noise ndash go away
                      • What is the median Value
                      • The median value
                      • Noise away ndash the median filter
                      • Noise removal ndash average filter
                      • Noise removal ndash median filter
                      • Image Filtering
                      • Median filter
                      • Rank filters
                      • Median filter
                      • Correlation
                      • Why do we need similarity
                      • Correlation (1D)
                      • Correlation (1D)
                      • Normalisation
                      • Normalisation
                      • Correlation on images
                      • Correlation on images
                      • Correlation on images
                      • Draw your filter
                      • Correlation on images ndash no normalisation
                      • Correlation on images ndash no normalisation 2
                      • Mathematics of 2D Correlation
                      • Mathematics of 2D Correlation
                      • Mathematics of 2D Correlation
                      • Slide Number 40
                      • 2D Kernel Normalisation
                      • Correlation
                      • Smoothing filters
                      • Use of smoothing
                      • Use of smoothing
                      • Mean filter
                      • Border handling
                      • Border handling ndash extend the input
                      • Correlation with zero padding
                      • Border handling ndash extend the input
                      • Template Matching
                      • Template Matching
                      • Template Matching
                      • Template Matching
                      • Problematic Correlation
                      • Normalised Cross Correlation
                      • Length of template
                      • Length of image patch
                      • Normalised Cross Correlation
                      • Normalised Cross Correlation
                      • Normalised Cross Correlation
                      • Edges
                      • Edges
                      • Finite Difference
                      • Edges
                      • Edges in 2D
                      • Edge filter kernel
                      • Prewitt filter
                      • Edge detection
                      • Edge filtering
                      • 02511 - Niveau af dagens emne forelaeligsing
                      • 02512 - Niveau af dagens emne forelaeligsing
                      • 02511 - Mit eget udbytte af dagen
                      • 02512 - Mit eget udbytte af dagen
                      • 02511 - Sidste uges oslashvelser (pixelwise operations)
                      • 02512 - Sidste uges oslashvelser (pixelwise operations)
                      • Denne uges brug af clickers
                      • What can you do after today
                      • Oslashvelsesrapport over oslashvelse 4 - 02511
                      • Exercises
                        A0
                        B0
                        C5
                        D0
                        E6
                        A
                        B
                        C
                        D
                        E
                        A3
                        B0
                        C3
                        D0
                        E0
                        A
                        B
                        C
                        D
                        E
                        A0
                        B0
                        C1
                        D4
                        E1
                        A
                        B
                        C
                        D
                        E
                        A2
                        B1
                        C3
                        D2
                        E0
                        A
                        B
                        C
                        D
                        E
                        A0
                        B0
                        C2
                        D6
                        E0
                        A
                        B
                        C
                        D
                        E
                        A0
                        B0
                        C1
                        D0
                        E0
                        A
                        B
                        C
                        D
                        E
                        A2
                        B3
                        C6
                        D1
                        E0
                        A
                        B
                        C
                        D
                        E
                        A0
                        B8
                        C1
                        D1
                        E0
                        A
                        B
                        C
                        D
                        E
                        A1
                        B2
                        C2
                        D3
                        E2
                        A
                        B
                        C
                        D
                        E
                        A0
                        B13
                        C0
                        D0
                        E0
                        A
                        B
                        C
                        D
                        E
                        A12
                        B0
                        C0
                        D0
                        E0
                        A
                        B
                        C
                        D
                        E
                        A0
                        B0
                        C0
                        D0
                        E13
                        A
                        B
                        C
                        D
                        E
                        A13
                        B0
                        C0
                        D0
                        E0
                        A
                        B
                        C
                        D
                        E
                        A1
                        B0
                        C14
                        D0
                        E0
                        A
                        B
                        C
                        D
                        E
                        A0
                        B12
                        C1
                        D0
                        E0
                        A
                        B
                        C
                        D
                        E
                        A0
                        B13
                        C1
                        D0
                        E0
                        A
                        B
                        C
                        D
                        E
                        A13
                        B0
                        C0
                        D0
                        E2
                        A
                        B
                        C
                        D
                        E

                        DTU Compute

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                        What is the median ValueA) 170B) 173C) 169D) 171E) 172

                        13

                        0 0 02

                        A B C D E

                        169 168 0 170172 173 170 172 170

                        Chart1

                        13
                        0
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                        The median value The values are sorted from low to high The middle number is picked

                        ndash The median value

                        169 168 0 170172 173 170 172 170

                        0168 169 170 170 170172 172173

                        Median

                        Noise has no influence on the median

                        DTU Compute

                        2122018Introduction to Medical Image Analysis14 DTU Compute Technical University of Denmark

                        Noise away ndash the median filter All pixels are set to the

                        median of its neighbourhood Noise pixels do not pollute

                        good pixels

                        172 169 171 168 0 169 172 173 168

                        170

                        169 168 0 170 172173 170 172 170

                        170

                        DTU Compute

                        2122018Introduction to Medical Image Analysis15 DTU Compute Technical University of Denmark

                        Noise removal ndash average filter

                        Scanned X-ray with salt and pepper noise

                        Average filter (3x3)

                        DTU Compute

                        2122018Introduction to Medical Image Analysis16 DTU Compute Technical University of Denmark

                        Noise removal ndash median filter

                        Scanned X-ray with salt and pepper noise

                        Median filter (3x3)

                        DTU Compute

                        2122018Introduction to Medical Image Analysis17 DTU Compute Technical University of Denmark

                        Image Filtering Creates a new filtered image Output pixel is computed based

                        on a neighbourhood in the input image

                        3 x 3 neighbourhoodndash Filter size 3 x 3ndash Kernel size 3 x 3ndash Mask size 3 x 3

                        Larger filters often usedndash Size

                        7 x 7ndash Number of elements

                        49

                        DTU Compute

                        2122018Introduction to Medical Image Analysis18 DTU Compute Technical University of Denmark

                        Median filterA) 25B) 90C) 198D) 86E) 103

                        0

                        13

                        1 0 0

                        A B C D E

                        Chart1

                        0
                        13
                        1
                        0
                        0

                        Sheet1

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                        Rank filters Based on sorting the pixel

                        values in the neighbouring region

                        Minimum rank filterndash Darker image Noise problems

                        Maximum rank filterndash Lighter image Noise problems

                        Difference filterndash Enhances changes (edges)

                        0168 169 170 170 170172 172173

                        -

                        DTU Compute

                        2122018Introduction to Medical Image Analysis21 DTU Compute Technical University of Denmark

                        Median filter

                        A) 3B) 84C) 112D) 73E) 202

                        0

                        12

                        10 0

                        A B C D E

                        Chart1

                        0
                        12
                        1
                        0
                        0

                        Sheet1

                        DTU Compute

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                        Correlation What is it Two measurements

                        ndash Low correlationndash High correlation

                        High correlation means that there is a relation between the values

                        They look the same Correlation is a measure of

                        similarity

                        Low

                        High

                        Muscles

                        Mat

                        h Ski

                        lls

                        Muscles

                        Ben

                        ch P

                        ress

                        DTU Compute

                        2122018Introduction to Medical Image Analysis24 DTU Compute Technical University of Denmark

                        Why do we need similarity Image analysis is also about recognition of patterns Often an example pattern is used We need something to tell us if there is a high match

                        between our pattern and a part of the image

                        Example pattern

                        Image

                        Find matches

                        DTU Compute

                        2122018Introduction to Medical Image Analysis25 DTU Compute Technical University of Denmark

                        Correlation (1D)

                        1 1 2 2 1 1 2 2 1 1

                        1 2 1

                        45

                        41

                        1 1 + 2 1 + 1 2 = 5

                        Normalise

                        Kernel

                        Signal (1D image)

                        41

                        DTU Compute

                        2122018Introduction to Medical Image Analysis26 DTU Compute Technical University of Denmark

                        Correlation (1D)

                        1 1 2 2 1 1 2 2 1 1

                        1 2 1

                        45

                        47

                        47

                        45

                        45

                        47

                        47

                        45

                        41

                        DTU Compute

                        2122018Introduction to Medical Image Analysis27 DTU Compute Technical University of Denmark

                        Normalisation

                        1 1 2 2 1 1 2 2 1 1

                        1 2 1

                        45

                        41

                        1 1 + 2 1 + 1 2 = 5

                        Normalise41

                        bull The sum of the kernel elements is used

                        bull Keep the values in the same range as the input image

                        Sum is 4

                        DTU Compute

                        2122018Introduction to Medical Image Analysis28 DTU Compute Technical University of Denmark

                        Normalisation Normalisation factor

                        ndash Sum of kernel coefficients

                        1 2 1h(x)

                        119909119909

                        ℎ 119909119909 = 1 + 2 + 1

                        DTU Compute

                        2122018Introduction to Medical Image Analysis29 DTU Compute Technical University of Denmark

                        Correlation on images The filter is now 2D 1 1 1

                        1 1 1

                        1 1 1

                        0 2 4

                        1 2 2

                        1 6 3

                        1 2 12 5 3

                        2 1 3

                        1 3 1

                        2 2 2

                        0 1 3

                        1 2 0

                        2 1 4

                        1 0 1

                        912

                        91

                        Input OutputKernel

                        Kernel coefficients

                        DTU Compute

                        2122018Introduction to Medical Image Analysis30 DTU Compute Technical University of Denmark

                        Correlation on images

                        1 1 11 1 11 1 1

                        0 2 4

                        1 2 2

                        1 6 3

                        1 2 0

                        2 1 4

                        1 0 1

                        912

                        911

                        91

                        Input Output

                        1 3 1

                        2 2 2

                        0 1 3

                        1 2 12 5 3

                        2 1 3

                        DTU Compute

                        2122018Introduction to Medical Image Analysis31 DTU Compute Technical University of Denmark

                        Correlation on images

                        Input Output

                        The mask is moved row by row

                        No values at the border

                        0 2 4

                        1 2 2

                        1 6 3

                        1 2 0

                        2 1 4

                        1 0 1

                        1 3 1

                        2 2 2

                        0 1 3

                        1 2 12 5 3

                        2 1 3

                        DTU Compute

                        2122018Introduction to Medical Image Analysis32 DTU Compute Technical University of Denmark

                        1 2 1

                        1 3 1

                        1 2 1

                        -1 -2 -1

                        0 0 0

                        1 2 1

                        Draw your filter

                        DTU Compute

                        2122018Introduction to Medical Image Analysis33 DTU Compute Technical University of Denmark

                        Correlation on images ndash no normalisationA) 4B) 7C) 16D) 23E) 25

                        1 2 11 3 11 2 1

                        0 2 41 2 2

                        1 6 3

                        1 2 12 5 3

                        2 1 3

                        1 3 1

                        2 2 2

                        0 1 3

                        1 2 0

                        2 1 4

                        1 0 11 0

                        14

                        0 0

                        A B C D E

                        Chart1

                        1
                        0
                        14
                        0
                        0

                        Sheet1

                        DTU Compute

                        2122018Introduction to Medical Image Analysis34 DTU Compute Technical University of Denmark

                        Correlation on images ndash no normalisation 2A) 010B) 3 3C) 6 2D) 10 15E) 11 32

                        13

                        0 0 0 0

                        A B C D E

                        -1 -2 -10 0 01 2 1

                        0 2 41 2 2

                        1 6 3

                        1 2 12 5 3

                        2 1 3

                        1 3 1

                        2 2 2

                        0 1 3

                        1 2 0

                        2 1 4

                        1 0 1

                        Chart1

                        13
                        0
                        0
                        0
                        0

                        Sheet1

                        DTU Compute

                        2122018Introduction to Medical Image Analysis37 DTU Compute Technical University of Denmark

                        Mathematics of 2D Correlation

                        h

                        f

                        Correlation operator

                        1 2 11 3 11 2 1

                        0 2 4

                        1 2 2

                        1 6 3

                        1 2 1

                        2 5 3

                        2 1 3

                        1 3 1

                        2 2 2

                        0 1 3

                        1 2 0

                        2 1 4

                        1 0 1

                        119892119892 119909119909119910119910 = 119891119891 119909119909119910119910 ∘ ℎ(119909119909119910119910)

                        DTU Compute

                        2122018Introduction to Medical Image Analysis38 DTU Compute Technical University of Denmark

                        Mathematics of 2D Correlation

                        1 2 11 3 11 2 1

                        0 2 4

                        1 2 2

                        1 6 3

                        1 2 1

                        2 5 3

                        2 1 3

                        1 3 1

                        2 2 2

                        0 1 3

                        1 2 0

                        2 1 4

                        1 0 1

                        h

                        fh(00)

                        f(21)

                        Example g(21)

                        i = -1 j = -1

                        i = 1 j = 0

                        119892119892 119909119909119910119910 = 119895119895=minus119877119877

                        119877119877

                        119894119894=minus119877119877

                        119877119877

                        ℎ(119894119894 119895119895) 119891119891(119909119909 + 119894119894119910119910 + 119895119895)

                        DTU Compute

                        2122018Introduction to Medical Image Analysis39 DTU Compute Technical University of Denmark

                        Mathematics of 2D Correlation

                        1 2 11 3 11 2 1

                        0 2 4

                        1 2 2

                        1 6 3

                        1 2 1

                        2 5 3

                        2 1 3

                        1 3 1

                        2 2 2

                        0 1 3

                        1 2 0

                        2 1 4

                        1 0 1

                        h

                        f

                        119892119892 119909119909119910119910 = 119895119895=minus119877119877

                        119877119877

                        119894119894=minus119877119877

                        119877119877

                        ℎ(119894119894 119895119895) 119891119891(119909119909 + 119894119894119910119910 + 119895119895)

                        119892119892(119909119909119910119910 = 1 2 + 2 0 + 1 1 + 1 1 + 3 4 + 1 2 + 1 0 + 2 1 + 1 0

                        DTU Compute

                        2122018Introduction to Medical Image Analysis40 DTU Compute Technical University of Denmark

                        119892119892 119909119909 119910119910 = 119895119895=minus119877119877

                        119877119877

                        119894119894=minus119877119877

                        119877119877

                        ℎ(119894119894 119895119895) 119891119891(119909119909 + 119894119894119910119910 + 119895119895)

                        119892119892 22 =ℎ minus1minus1 sdot 119891119891 11 + ℎ 0minus1 sdot 119891119891 21 + ℎ 1minus1 sdot 119891119891 31 +ℎ minus10 sdot 119891119891 12 + ℎ 00 sdot 119891119891 22 + ℎ 10 sdot 119891119891 32 +ℎ minus11 sdot 119891119891 13 + ℎ 01 sdot 119891119891 23 + ℎ 11 sdot 119891119891 33

                        DTU Compute

                        2122018Introduction to Medical Image Analysis41 DTU Compute Technical University of Denmark

                        2D Kernel Normalisation

                        1 2 11 3 11 2 1

                        h

                        Normalisation factor

                        1 + 2 + 1 + 1 + 3 + 1 + 1 + 2 + 1 = 13

                        119909119909

                        119910119910

                        ℎ(119909119909119910119910)

                        DTU Compute

                        2122018Introduction to Medical Image Analysis42 DTU Compute Technical University of Denmark

                        CorrelationA) 50122B) 123001C) 11233D) 2550E) 90454

                        0 0 0 0

                        13

                        A B C D E

                        Chart1

                        0
                        0
                        0
                        0
                        13

                        Sheet1

                        DTU Compute

                        2122018Introduction to Medical Image Analysis44 DTU Compute Technical University of Denmark

                        Smoothing filters

                        Also know as ndash Smoothing kernel Mean filter Low pass filter blurring

                        The simplest filter ndash Spatial low pass filterndash Removes high frequencies

                        Another mask ndash Gaussian filter

                        1 1 1

                        1 1 1

                        1 1 191

                        1 2 1

                        2 4 2

                        1 2 1161

                        Why Gaussian

                        DTU Compute

                        2122018Introduction to Medical Image Analysis45 DTU Compute Technical University of Denmark

                        Use of smoothing

                        3x3 7x7 11x11 15x15

                        DTU Compute

                        2122018Introduction to Medical Image Analysis46 DTU Compute Technical University of Denmark

                        Use of smoothing Large kernels smooth more Removes high frequency information Good at enhancing big structures

                        3x3 15x15

                        DTU Compute

                        2122018Introduction to Medical Image Analysis47 DTU Compute Technical University of Denmark

                        Mean filterA) 166B) 113C) 12D) 51E) 245

                        0 0 0 0

                        A B C D E

                        Chart1

                        12
                        0
                        0
                        0
                        0

                        Sheet1

                        DTU Compute

                        2122018Introduction to Medical Image Analysis49 DTU Compute Technical University of Denmark

                        Border handling

                        0 2 41 2 2

                        1 6 3

                        1 2 12 5 3

                        2 1 3

                        1 3 1

                        2 2 2

                        0 1 3

                        1 2 0

                        2 1 4

                        1 0 1

                        Input Output

                        No values at the border

                        DTU Compute

                        2122018Introduction to Medical Image Analysis50 DTU Compute Technical University of Denmark

                        Border handling ndash extend the input

                        0 2 41 2 2

                        1 6 3

                        1 2 12 5 3

                        2 1 3

                        1 3 1

                        2 2 2

                        0 1 3

                        1 2 0

                        2 1 4

                        1 0 1

                        Input

                        0 0 0 0 000000

                        bull Zero padding ndash what happens

                        bull Zero is black ndash creates dark border around the image

                        DTU Compute

                        2122018Introduction to Medical Image Analysis51 DTU Compute Technical University of Denmark

                        Correlation with zero paddingA) 5 8B) 12 16C) 13 3D) 15 21E) 17 12

                        1 2 11 3 11 2 1

                        0 2 41 2 2

                        1 6 3

                        1 2 12 5 3

                        2 1 3

                        1 3 1

                        2 2 2

                        0 1 3

                        1 2 0

                        2 1 4

                        1 0 1

                        0

                        13

                        0 0 0

                        A B C D E

                        Chart1

                        0
                        13
                        0
                        0
                        0

                        Sheet1

                        DTU Compute

                        2122018Introduction to Medical Image Analysis53 DTU Compute Technical University of Denmark

                        Border handling ndash extend the input

                        0 2 41 2 2

                        1 6 3

                        1 2 12 5 3

                        2 1 3

                        1 3 1

                        2 2 2

                        0 1 3

                        1 2 0

                        2 1 4

                        1 0 1

                        Input

                        1 2 0 1 311211

                        bull Reflection

                        bull Normally better than zero padding

                        DTU Compute

                        2122018Introduction to Medical Image Analysis54 DTU Compute Technical University of Denmark

                        Template Matching Template

                        ndash Skabelon paring dansk Locates objects in images

                        Input

                        Template

                        Output Correlation image

                        DTU Compute

                        2122018Introduction to Medical Image Analysis55 DTU Compute Technical University of Denmark

                        Template Matching The correlation between the template and the input

                        image is computed for each pixel

                        Input

                        Template

                        Output Correlation image

                        DTU Compute

                        2122018Introduction to Medical Image Analysis56 DTU Compute Technical University of Denmark

                        Template Matching The pixel with the highest value is found in the

                        output imagendash Here is the highest correlation

                        Input

                        Template

                        Output Correlation image

                        DTU Compute

                        2122018Introduction to Medical Image Analysis57 DTU Compute Technical University of Denmark

                        Template Matching This corresponds to the found pattern in the input

                        image

                        Input

                        Template

                        Output Correlation image

                        DTU Compute

                        2122018Introduction to Medical Image Analysis58 DTU Compute Technical University of Denmark

                        Problematic Correlation Correlation matching has problem with light areas ndash

                        why

                        Input (f)

                        Template (h)

                        Output Correlation imageFake max

                        Real max

                        Very High119892119892 119909119909119910119910 = 119895119895=minus119877119877

                        119877119877

                        119894119894=minus119877119877

                        119877119877

                        ℎ(119894119894 119895119895) 119891119891(119909119909 + 119894119894119910119910 + 119895119895)

                        DTU Compute

                        2122018Introduction to Medical Image Analysis59 DTU Compute Technical University of Denmark

                        Normalised Cross Correlation

                        Input (f)

                        Template (h)

                        Output Correlation image

                        Real max

                        NCC x y =Correlation

                        Length of image patch sdot Length of template

                        DTU Compute

                        2122018Introduction to Medical Image Analysis60 DTU Compute Technical University of Denmark

                        Length of template Vector length

                        ndash Put all pixel values into a vectorndash Compute the length of this vector

                        Describes the intensity of the templatendash Bright template has a large lengthndash Dark template has a small length

                        Template (h)

                        Length of template = 119895119895=minus119877119877

                        119877119877

                        119894119894=minus119877119877

                        119877119877

                        ℎ(119894119894 119895119895) ℎ(119894119894 119895119895)

                        DTU Compute

                        2122018Introduction to Medical Image Analysis61 DTU Compute Technical University of Denmark

                        Length of image patch Vector length based on pixel values in image patch Describes the intensity of the image patch

                        Template (h)

                        Input (f) with patch

                        DTU Compute

                        2122018Introduction to Medical Image Analysis62 DTU Compute Technical University of Denmark

                        Normalised Cross Correlation The length of the image patch and the length of

                        template normalise the NCC If the image is very bright the NCC will be ldquopulled

                        downrdquo

                        NCC x y =Correlation

                        Length of image patch sdot Length of template

                        DTU Compute

                        2122018Introduction to Medical Image Analysis63 DTU Compute Technical University of Denmark

                        Normalised Cross Correlation NCC will be between

                        ndash 0 No similarity between template and image patchndash 1 Template and image patch are identical

                        Input (f)

                        Template (h)

                        Output Correlation image

                        Real max

                        NCC x y =Correlation

                        Length of image patch sdot Length of template

                        DTU Compute

                        2122018Introduction to Medical Image Analysis64 DTU Compute Technical University of Denmark

                        Normalised Cross Correlation

                        A) 010B) 033C) 083D) 062E) 098

                        Der udfoslashres template matching med og normalized crosscorrelation (NCC) beregnes Hvad bliver NNC i den markerede pixel

                        1

                        2 2

                        3

                        2

                        A B C D E

                        Chart1

                        1
                        2
                        2
                        3
                        2

                        Sheet1

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                        Edges An edge is where there is a

                        high change in gray level values

                        Objects are often separated from the background by edgesGray level profile

                        DTU Compute

                        2122018Introduction to Medical Image Analysis67 DTU Compute Technical University of Denmark

                        Edges The profile as a function f(d) What value is high when there

                        is an edgendash The slope of fndash The slope of the tangent at d

                        f(d)

                        119891119891prime(119889119889)

                        DTU Compute

                        2122018Introduction to Medical Image Analysis68 DTU Compute Technical University of Denmark

                        Finite Difference Definition of slope

                        Approximation

                        Simpler approximationh = 1

                        119891119891prime 119889119889 = limℎrarr0

                        119891119891 119889119889 + ℎ minus 119891119891(119889119889)ℎ

                        119891119891prime 119889119889 asymp119891119891 119889119889 + ℎ minus 119891119891(119889119889)

                        ℎ

                        119891119891prime 119889119889 asymp 119891119891 119889119889 + 1 minus 119891119891(119889119889)

                        DTU Compute

                        2122018Introduction to Medical Image Analysis69 DTU Compute Technical University of Denmark

                        Edges Discrete approximation of frsquo(d) Can be implemented as a filter

                        -1 0 1

                        f(d-2) f(d-1) f(d) f(d+1) f(d+2) f(d+3)

                        f(d)

                        119891119891prime 119889119889 asymp 119891119891 119889119889 + 1 minus 119891119891(119889119889)

                        DTU Compute

                        2122018Introduction to Medical Image Analysis70 DTU Compute Technical University of Denmark

                        Edges in 2D Changes in gray level values

                        ndash Image gradientndash Gradient is the 2D derivative of a 2D function f(xy)ndash Equal to the slope of the imagendash A steep slope is equal to an edge

                        120571120571119891119891 119909119909119910119910 = 119866(119892119892119909119909119892119892119910119910)

                        DTU Compute

                        2122018Introduction to Medical Image Analysis71 DTU Compute Technical University of Denmark

                        Edge filter kernel The Prewitt filter is a typical

                        edge filter Output image has high

                        values where there are edges

                        -1 0 1

                        -1 0 1

                        -1 0 1Vertical Prewitt filter

                        DTU Compute

                        2122018Introduction to Medical Image Analysis72 DTU Compute Technical University of Denmark

                        Prewitt filter

                        Original Prewitt Prewitt

                        Hot colormapSmooth 15x15

                        Smooth 15x15

                        Prewitt

                        DTU Compute

                        2122018Introduction to Medical Image Analysis73 DTU Compute Technical University of Denmark

                        Edge detection Edge filter

                        ndash Prewitt for example Thresholding

                        ndash Separate edges from non-edges

                        Output is binary imagendash Edges are white

                        DTU Compute

                        2122018Introduction to Medical Image Analysis74 DTU Compute Technical University of Denmark

                        Edge filtering

                        A) MeanB) Horizontal SobelC) Vertical PrewittD) Horisontal PrewittE) Median

                        Der udfoslashres en filtrering (correlation) med et filter paring billedet Der bruges ikke coefficient normalization Den filtrerede vaeligrdi i den markerede pixel bliver -119 Hvilket et 3x3 filter blev benyttet

                        0

                        8

                        1 10

                        A B C D E

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                        0
                        8
                        1
                        1
                        0

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                        02511 - Niveau af dagens emne forelaeligsingA) Meget letB) LetC) PassendeD) SvaeligrtE) Meget svaeligrt

                        23

                        6

                        10

                        A B C D E

                        Chart1

                        2
                        3
                        6
                        1
                        0

                        Sheet1

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                        02512 - Niveau af dagens emne forelaeligsingA) Meget letB) LetC) PassendeD) SvaeligrtE) Meget svaeligrt

                        0 0

                        1

                        0 0

                        A B C D E

                        Chart1

                        0
                        0
                        1
                        0
                        0

                        Sheet1

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                        02511 - Mit eget udbytte af dagenA) Jeg har laeligrt meget lidtB) Lidt laeligringC) PassendeD) God laeligringE) Jeg har laeligrt meget

                        0 0

                        2

                        6

                        0

                        A B C D E

                        Chart1

                        0
                        0
                        2
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                        0

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                        02512 - Mit eget udbytte af dagenA) Jeg har laeligrt meget lidtB) Lidt laeligringC) PassendeD) God laeligringE) Jeg har laeligrt meget

                        2

                        1

                        3

                        2

                        0

                        A B C D E

                        Chart1

                        2
                        1
                        3
                        2
                        0

                        Sheet1

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                        02511 - Sidste uges oslashvelser (pixelwiseoperations)A) Meget letteB) LetteC) PassendeD) SvaeligreE) Meget svaeligre

                        0 0

                        1

                        4

                        1

                        A B C D E

                        Chart1

                        0
                        0
                        1
                        4
                        1

                        Sheet1

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                        02512 - Sidste uges oslashvelser (pixelwiseoperations)A) Meget letteB) LetteC) PassendeD) SvaeligreE) Meget svaeligre

                        3

                        0

                        3

                        0 0

                        A B C D E

                        Chart1

                        3
                        0
                        3
                        0
                        0

                        Sheet1

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                        2122018Introduction to Medical Image Analysis82 DTU Compute Technical University of Denmark

                        Denne uges brug af clickersA) click click click ndash jeg bliver

                        sindssygB) For meget clickC) PassendeD) Jeg vil gerne have lidt mereE) Jeg kan ikrsquo faring nok

                        0 0

                        5

                        0

                        6

                        A B C D E

                        Chart1

                        0
                        0
                        5
                        0
                        6

                        Sheet1

                        DTU Compute

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                        What can you do after today Describe the difference between point processing and neighbourhood

                        processing Compute a rank filtered image using the min max median and

                        difference rank filters Compute a mean filtered image Decide if median or average filtering should be used for noise removal Choose the appropriate image border handling based on a given input

                        image Implement and apply template matching Compute the normalised cross correlation and explain why it should be

                        used Apply given image filter kernels to images Use edge filters on images Describe finite difference approximation of image gradients Describe the concept of edge detection

                        DTU Compute

                        2122018Introduction to Medical Image Analysis84 DTU Compute Technical University of Denmark

                        Oslashvelsesrapport over oslashvelse 4 - 02511 Oslashvelser taeligller cirka 30 af karakteren Skal afleveres senest den 7 marts kl 2359 Kan afleveres af 1 eller 2 personer

                        ndash I skal skrive jeres egen oslashvelsesrapportndash Brug mindst et af jeres egne billeder

                        Afleveres som PDF Lad vaeligre med at kopiere opgaveteksten ind i jeres

                        opgave Put Matlab kode i et Appendix og henvis fra teksten Eksempel rapport over oslashvelse findes paring

                        hjemmesiden under eksamen

                        DTU Compute

                        2122018Introduction to Medical Image Analysis85 DTU Compute Technical University of Denmark

                        Exercises

                        • Introduction to Medical Image Analysis
                        • Lecture 4 ndash Neighbourhood Processing
                        • What can you do after today
                        • Point processing
                        • Point processing
                        • Neighbourhood processing
                        • Use of filtering
                        • Salt and pepper noise
                        • Salt and pepper noise
                        • What is so special about noise
                        • Noise ndash go away
                        • What is the median Value
                        • The median value
                        • Noise away ndash the median filter
                        • Noise removal ndash average filter
                        • Noise removal ndash median filter
                        • Image Filtering
                        • Median filter
                        • Rank filters
                        • Median filter
                        • Correlation
                        • Why do we need similarity
                        • Correlation (1D)
                        • Correlation (1D)
                        • Normalisation
                        • Normalisation
                        • Correlation on images
                        • Correlation on images
                        • Correlation on images
                        • Draw your filter
                        • Correlation on images ndash no normalisation
                        • Correlation on images ndash no normalisation 2
                        • Mathematics of 2D Correlation
                        • Mathematics of 2D Correlation
                        • Mathematics of 2D Correlation
                        • Slide Number 40
                        • 2D Kernel Normalisation
                        • Correlation
                        • Smoothing filters
                        • Use of smoothing
                        • Use of smoothing
                        • Mean filter
                        • Border handling
                        • Border handling ndash extend the input
                        • Correlation with zero padding
                        • Border handling ndash extend the input
                        • Template Matching
                        • Template Matching
                        • Template Matching
                        • Template Matching
                        • Problematic Correlation
                        • Normalised Cross Correlation
                        • Length of template
                        • Length of image patch
                        • Normalised Cross Correlation
                        • Normalised Cross Correlation
                        • Normalised Cross Correlation
                        • Edges
                        • Edges
                        • Finite Difference
                        • Edges
                        • Edges in 2D
                        • Edge filter kernel
                        • Prewitt filter
                        • Edge detection
                        • Edge filtering
                        • 02511 - Niveau af dagens emne forelaeligsing
                        • 02512 - Niveau af dagens emne forelaeligsing
                        • 02511 - Mit eget udbytte af dagen
                        • 02512 - Mit eget udbytte af dagen
                        • 02511 - Sidste uges oslashvelser (pixelwise operations)
                        • 02512 - Sidste uges oslashvelser (pixelwise operations)
                        • Denne uges brug af clickers
                        • What can you do after today
                        • Oslashvelsesrapport over oslashvelse 4 - 02511
                        • Exercises
                          A0
                          B0
                          C5
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                          A
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                          A
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                          E2
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                          A
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                          A0
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                          A
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                          E
                          A13
                          B0
                          C0
                          D0
                          E2
                          A
                          B
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                          E

                          Chart1

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                          DTU Compute

                          2122018Introduction to Medical Image Analysis13 DTU Compute Technical University of Denmark

                          The median value The values are sorted from low to high The middle number is picked

                          ndash The median value

                          169 168 0 170172 173 170 172 170

                          0168 169 170 170 170172 172173

                          Median

                          Noise has no influence on the median

                          DTU Compute

                          2122018Introduction to Medical Image Analysis14 DTU Compute Technical University of Denmark

                          Noise away ndash the median filter All pixels are set to the

                          median of its neighbourhood Noise pixels do not pollute

                          good pixels

                          172 169 171 168 0 169 172 173 168

                          170

                          169 168 0 170 172173 170 172 170

                          170

                          DTU Compute

                          2122018Introduction to Medical Image Analysis15 DTU Compute Technical University of Denmark

                          Noise removal ndash average filter

                          Scanned X-ray with salt and pepper noise

                          Average filter (3x3)

                          DTU Compute

                          2122018Introduction to Medical Image Analysis16 DTU Compute Technical University of Denmark

                          Noise removal ndash median filter

                          Scanned X-ray with salt and pepper noise

                          Median filter (3x3)

                          DTU Compute

                          2122018Introduction to Medical Image Analysis17 DTU Compute Technical University of Denmark

                          Image Filtering Creates a new filtered image Output pixel is computed based

                          on a neighbourhood in the input image

                          3 x 3 neighbourhoodndash Filter size 3 x 3ndash Kernel size 3 x 3ndash Mask size 3 x 3

                          Larger filters often usedndash Size

                          7 x 7ndash Number of elements

                          49

                          DTU Compute

                          2122018Introduction to Medical Image Analysis18 DTU Compute Technical University of Denmark

                          Median filterA) 25B) 90C) 198D) 86E) 103

                          0

                          13

                          1 0 0

                          A B C D E

                          Chart1

                          0
                          13
                          1
                          0
                          0

                          Sheet1

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                          2122018Introduction to Medical Image Analysis20 DTU Compute Technical University of Denmark

                          Rank filters Based on sorting the pixel

                          values in the neighbouring region

                          Minimum rank filterndash Darker image Noise problems

                          Maximum rank filterndash Lighter image Noise problems

                          Difference filterndash Enhances changes (edges)

                          0168 169 170 170 170172 172173

                          -

                          DTU Compute

                          2122018Introduction to Medical Image Analysis21 DTU Compute Technical University of Denmark

                          Median filter

                          A) 3B) 84C) 112D) 73E) 202

                          0

                          12

                          10 0

                          A B C D E

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                          0
                          12
                          1
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                          Sheet1

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                          2122018Introduction to Medical Image Analysis23 DTU Compute Technical University of Denmark

                          Correlation What is it Two measurements

                          ndash Low correlationndash High correlation

                          High correlation means that there is a relation between the values

                          They look the same Correlation is a measure of

                          similarity

                          Low

                          High

                          Muscles

                          Mat

                          h Ski

                          lls

                          Muscles

                          Ben

                          ch P

                          ress

                          DTU Compute

                          2122018Introduction to Medical Image Analysis24 DTU Compute Technical University of Denmark

                          Why do we need similarity Image analysis is also about recognition of patterns Often an example pattern is used We need something to tell us if there is a high match

                          between our pattern and a part of the image

                          Example pattern

                          Image

                          Find matches

                          DTU Compute

                          2122018Introduction to Medical Image Analysis25 DTU Compute Technical University of Denmark

                          Correlation (1D)

                          1 1 2 2 1 1 2 2 1 1

                          1 2 1

                          45

                          41

                          1 1 + 2 1 + 1 2 = 5

                          Normalise

                          Kernel

                          Signal (1D image)

                          41

                          DTU Compute

                          2122018Introduction to Medical Image Analysis26 DTU Compute Technical University of Denmark

                          Correlation (1D)

                          1 1 2 2 1 1 2 2 1 1

                          1 2 1

                          45

                          47

                          47

                          45

                          45

                          47

                          47

                          45

                          41

                          DTU Compute

                          2122018Introduction to Medical Image Analysis27 DTU Compute Technical University of Denmark

                          Normalisation

                          1 1 2 2 1 1 2 2 1 1

                          1 2 1

                          45

                          41

                          1 1 + 2 1 + 1 2 = 5

                          Normalise41

                          bull The sum of the kernel elements is used

                          bull Keep the values in the same range as the input image

                          Sum is 4

                          DTU Compute

                          2122018Introduction to Medical Image Analysis28 DTU Compute Technical University of Denmark

                          Normalisation Normalisation factor

                          ndash Sum of kernel coefficients

                          1 2 1h(x)

                          119909119909

                          ℎ 119909119909 = 1 + 2 + 1

                          DTU Compute

                          2122018Introduction to Medical Image Analysis29 DTU Compute Technical University of Denmark

                          Correlation on images The filter is now 2D 1 1 1

                          1 1 1

                          1 1 1

                          0 2 4

                          1 2 2

                          1 6 3

                          1 2 12 5 3

                          2 1 3

                          1 3 1

                          2 2 2

                          0 1 3

                          1 2 0

                          2 1 4

                          1 0 1

                          912

                          91

                          Input OutputKernel

                          Kernel coefficients

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                          2122018Introduction to Medical Image Analysis30 DTU Compute Technical University of Denmark

                          Correlation on images

                          1 1 11 1 11 1 1

                          0 2 4

                          1 2 2

                          1 6 3

                          1 2 0

                          2 1 4

                          1 0 1

                          912

                          911

                          91

                          Input Output

                          1 3 1

                          2 2 2

                          0 1 3

                          1 2 12 5 3

                          2 1 3

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                          2122018Introduction to Medical Image Analysis31 DTU Compute Technical University of Denmark

                          Correlation on images

                          Input Output

                          The mask is moved row by row

                          No values at the border

                          0 2 4

                          1 2 2

                          1 6 3

                          1 2 0

                          2 1 4

                          1 0 1

                          1 3 1

                          2 2 2

                          0 1 3

                          1 2 12 5 3

                          2 1 3

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                          2122018Introduction to Medical Image Analysis32 DTU Compute Technical University of Denmark

                          1 2 1

                          1 3 1

                          1 2 1

                          -1 -2 -1

                          0 0 0

                          1 2 1

                          Draw your filter

                          DTU Compute

                          2122018Introduction to Medical Image Analysis33 DTU Compute Technical University of Denmark

                          Correlation on images ndash no normalisationA) 4B) 7C) 16D) 23E) 25

                          1 2 11 3 11 2 1

                          0 2 41 2 2

                          1 6 3

                          1 2 12 5 3

                          2 1 3

                          1 3 1

                          2 2 2

                          0 1 3

                          1 2 0

                          2 1 4

                          1 0 11 0

                          14

                          0 0

                          A B C D E

                          Chart1

                          1
                          0
                          14
                          0
                          0

                          Sheet1

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                          Correlation on images ndash no normalisation 2A) 010B) 3 3C) 6 2D) 10 15E) 11 32

                          13

                          0 0 0 0

                          A B C D E

                          -1 -2 -10 0 01 2 1

                          0 2 41 2 2

                          1 6 3

                          1 2 12 5 3

                          2 1 3

                          1 3 1

                          2 2 2

                          0 1 3

                          1 2 0

                          2 1 4

                          1 0 1

                          Chart1

                          13
                          0
                          0
                          0
                          0

                          Sheet1

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                          Mathematics of 2D Correlation

                          h

                          f

                          Correlation operator

                          1 2 11 3 11 2 1

                          0 2 4

                          1 2 2

                          1 6 3

                          1 2 1

                          2 5 3

                          2 1 3

                          1 3 1

                          2 2 2

                          0 1 3

                          1 2 0

                          2 1 4

                          1 0 1

                          119892119892 119909119909119910119910 = 119891119891 119909119909119910119910 ∘ ℎ(119909119909119910119910)

                          DTU Compute

                          2122018Introduction to Medical Image Analysis38 DTU Compute Technical University of Denmark

                          Mathematics of 2D Correlation

                          1 2 11 3 11 2 1

                          0 2 4

                          1 2 2

                          1 6 3

                          1 2 1

                          2 5 3

                          2 1 3

                          1 3 1

                          2 2 2

                          0 1 3

                          1 2 0

                          2 1 4

                          1 0 1

                          h

                          fh(00)

                          f(21)

                          Example g(21)

                          i = -1 j = -1

                          i = 1 j = 0

                          119892119892 119909119909119910119910 = 119895119895=minus119877119877

                          119877119877

                          119894119894=minus119877119877

                          119877119877

                          ℎ(119894119894 119895119895) 119891119891(119909119909 + 119894119894119910119910 + 119895119895)

                          DTU Compute

                          2122018Introduction to Medical Image Analysis39 DTU Compute Technical University of Denmark

                          Mathematics of 2D Correlation

                          1 2 11 3 11 2 1

                          0 2 4

                          1 2 2

                          1 6 3

                          1 2 1

                          2 5 3

                          2 1 3

                          1 3 1

                          2 2 2

                          0 1 3

                          1 2 0

                          2 1 4

                          1 0 1

                          h

                          f

                          119892119892 119909119909119910119910 = 119895119895=minus119877119877

                          119877119877

                          119894119894=minus119877119877

                          119877119877

                          ℎ(119894119894 119895119895) 119891119891(119909119909 + 119894119894119910119910 + 119895119895)

                          119892119892(119909119909119910119910 = 1 2 + 2 0 + 1 1 + 1 1 + 3 4 + 1 2 + 1 0 + 2 1 + 1 0

                          DTU Compute

                          2122018Introduction to Medical Image Analysis40 DTU Compute Technical University of Denmark

                          119892119892 119909119909 119910119910 = 119895119895=minus119877119877

                          119877119877

                          119894119894=minus119877119877

                          119877119877

                          ℎ(119894119894 119895119895) 119891119891(119909119909 + 119894119894119910119910 + 119895119895)

                          119892119892 22 =ℎ minus1minus1 sdot 119891119891 11 + ℎ 0minus1 sdot 119891119891 21 + ℎ 1minus1 sdot 119891119891 31 +ℎ minus10 sdot 119891119891 12 + ℎ 00 sdot 119891119891 22 + ℎ 10 sdot 119891119891 32 +ℎ minus11 sdot 119891119891 13 + ℎ 01 sdot 119891119891 23 + ℎ 11 sdot 119891119891 33

                          DTU Compute

                          2122018Introduction to Medical Image Analysis41 DTU Compute Technical University of Denmark

                          2D Kernel Normalisation

                          1 2 11 3 11 2 1

                          h

                          Normalisation factor

                          1 + 2 + 1 + 1 + 3 + 1 + 1 + 2 + 1 = 13

                          119909119909

                          119910119910

                          ℎ(119909119909119910119910)

                          DTU Compute

                          2122018Introduction to Medical Image Analysis42 DTU Compute Technical University of Denmark

                          CorrelationA) 50122B) 123001C) 11233D) 2550E) 90454

                          0 0 0 0

                          13

                          A B C D E

                          Chart1

                          0
                          0
                          0
                          0
                          13

                          Sheet1

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                          Smoothing filters

                          Also know as ndash Smoothing kernel Mean filter Low pass filter blurring

                          The simplest filter ndash Spatial low pass filterndash Removes high frequencies

                          Another mask ndash Gaussian filter

                          1 1 1

                          1 1 1

                          1 1 191

                          1 2 1

                          2 4 2

                          1 2 1161

                          Why Gaussian

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                          Use of smoothing

                          3x3 7x7 11x11 15x15

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                          2122018Introduction to Medical Image Analysis46 DTU Compute Technical University of Denmark

                          Use of smoothing Large kernels smooth more Removes high frequency information Good at enhancing big structures

                          3x3 15x15

                          DTU Compute

                          2122018Introduction to Medical Image Analysis47 DTU Compute Technical University of Denmark

                          Mean filterA) 166B) 113C) 12D) 51E) 245

                          0 0 0 0

                          A B C D E

                          Chart1

                          12
                          0
                          0
                          0
                          0

                          Sheet1

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                          Border handling

                          0 2 41 2 2

                          1 6 3

                          1 2 12 5 3

                          2 1 3

                          1 3 1

                          2 2 2

                          0 1 3

                          1 2 0

                          2 1 4

                          1 0 1

                          Input Output

                          No values at the border

                          DTU Compute

                          2122018Introduction to Medical Image Analysis50 DTU Compute Technical University of Denmark

                          Border handling ndash extend the input

                          0 2 41 2 2

                          1 6 3

                          1 2 12 5 3

                          2 1 3

                          1 3 1

                          2 2 2

                          0 1 3

                          1 2 0

                          2 1 4

                          1 0 1

                          Input

                          0 0 0 0 000000

                          bull Zero padding ndash what happens

                          bull Zero is black ndash creates dark border around the image

                          DTU Compute

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                          Correlation with zero paddingA) 5 8B) 12 16C) 13 3D) 15 21E) 17 12

                          1 2 11 3 11 2 1

                          0 2 41 2 2

                          1 6 3

                          1 2 12 5 3

                          2 1 3

                          1 3 1

                          2 2 2

                          0 1 3

                          1 2 0

                          2 1 4

                          1 0 1

                          0

                          13

                          0 0 0

                          A B C D E

                          Chart1

                          0
                          13
                          0
                          0
                          0

                          Sheet1

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                          Border handling ndash extend the input

                          0 2 41 2 2

                          1 6 3

                          1 2 12 5 3

                          2 1 3

                          1 3 1

                          2 2 2

                          0 1 3

                          1 2 0

                          2 1 4

                          1 0 1

                          Input

                          1 2 0 1 311211

                          bull Reflection

                          bull Normally better than zero padding

                          DTU Compute

                          2122018Introduction to Medical Image Analysis54 DTU Compute Technical University of Denmark

                          Template Matching Template

                          ndash Skabelon paring dansk Locates objects in images

                          Input

                          Template

                          Output Correlation image

                          DTU Compute

                          2122018Introduction to Medical Image Analysis55 DTU Compute Technical University of Denmark

                          Template Matching The correlation between the template and the input

                          image is computed for each pixel

                          Input

                          Template

                          Output Correlation image

                          DTU Compute

                          2122018Introduction to Medical Image Analysis56 DTU Compute Technical University of Denmark

                          Template Matching The pixel with the highest value is found in the

                          output imagendash Here is the highest correlation

                          Input

                          Template

                          Output Correlation image

                          DTU Compute

                          2122018Introduction to Medical Image Analysis57 DTU Compute Technical University of Denmark

                          Template Matching This corresponds to the found pattern in the input

                          image

                          Input

                          Template

                          Output Correlation image

                          DTU Compute

                          2122018Introduction to Medical Image Analysis58 DTU Compute Technical University of Denmark

                          Problematic Correlation Correlation matching has problem with light areas ndash

                          why

                          Input (f)

                          Template (h)

                          Output Correlation imageFake max

                          Real max

                          Very High119892119892 119909119909119910119910 = 119895119895=minus119877119877

                          119877119877

                          119894119894=minus119877119877

                          119877119877

                          ℎ(119894119894 119895119895) 119891119891(119909119909 + 119894119894119910119910 + 119895119895)

                          DTU Compute

                          2122018Introduction to Medical Image Analysis59 DTU Compute Technical University of Denmark

                          Normalised Cross Correlation

                          Input (f)

                          Template (h)

                          Output Correlation image

                          Real max

                          NCC x y =Correlation

                          Length of image patch sdot Length of template

                          DTU Compute

                          2122018Introduction to Medical Image Analysis60 DTU Compute Technical University of Denmark

                          Length of template Vector length

                          ndash Put all pixel values into a vectorndash Compute the length of this vector

                          Describes the intensity of the templatendash Bright template has a large lengthndash Dark template has a small length

                          Template (h)

                          Length of template = 119895119895=minus119877119877

                          119877119877

                          119894119894=minus119877119877

                          119877119877

                          ℎ(119894119894 119895119895) ℎ(119894119894 119895119895)

                          DTU Compute

                          2122018Introduction to Medical Image Analysis61 DTU Compute Technical University of Denmark

                          Length of image patch Vector length based on pixel values in image patch Describes the intensity of the image patch

                          Template (h)

                          Input (f) with patch

                          DTU Compute

                          2122018Introduction to Medical Image Analysis62 DTU Compute Technical University of Denmark

                          Normalised Cross Correlation The length of the image patch and the length of

                          template normalise the NCC If the image is very bright the NCC will be ldquopulled

                          downrdquo

                          NCC x y =Correlation

                          Length of image patch sdot Length of template

                          DTU Compute

                          2122018Introduction to Medical Image Analysis63 DTU Compute Technical University of Denmark

                          Normalised Cross Correlation NCC will be between

                          ndash 0 No similarity between template and image patchndash 1 Template and image patch are identical

                          Input (f)

                          Template (h)

                          Output Correlation image

                          Real max

                          NCC x y =Correlation

                          Length of image patch sdot Length of template

                          DTU Compute

                          2122018Introduction to Medical Image Analysis64 DTU Compute Technical University of Denmark

                          Normalised Cross Correlation

                          A) 010B) 033C) 083D) 062E) 098

                          Der udfoslashres template matching med og normalized crosscorrelation (NCC) beregnes Hvad bliver NNC i den markerede pixel

                          1

                          2 2

                          3

                          2

                          A B C D E

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                          1
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                          Edges An edge is where there is a

                          high change in gray level values

                          Objects are often separated from the background by edgesGray level profile

                          DTU Compute

                          2122018Introduction to Medical Image Analysis67 DTU Compute Technical University of Denmark

                          Edges The profile as a function f(d) What value is high when there

                          is an edgendash The slope of fndash The slope of the tangent at d

                          f(d)

                          119891119891prime(119889119889)

                          DTU Compute

                          2122018Introduction to Medical Image Analysis68 DTU Compute Technical University of Denmark

                          Finite Difference Definition of slope

                          Approximation

                          Simpler approximationh = 1

                          119891119891prime 119889119889 = limℎrarr0

                          119891119891 119889119889 + ℎ minus 119891119891(119889119889)ℎ

                          119891119891prime 119889119889 asymp119891119891 119889119889 + ℎ minus 119891119891(119889119889)

                          ℎ

                          119891119891prime 119889119889 asymp 119891119891 119889119889 + 1 minus 119891119891(119889119889)

                          DTU Compute

                          2122018Introduction to Medical Image Analysis69 DTU Compute Technical University of Denmark

                          Edges Discrete approximation of frsquo(d) Can be implemented as a filter

                          -1 0 1

                          f(d-2) f(d-1) f(d) f(d+1) f(d+2) f(d+3)

                          f(d)

                          119891119891prime 119889119889 asymp 119891119891 119889119889 + 1 minus 119891119891(119889119889)

                          DTU Compute

                          2122018Introduction to Medical Image Analysis70 DTU Compute Technical University of Denmark

                          Edges in 2D Changes in gray level values

                          ndash Image gradientndash Gradient is the 2D derivative of a 2D function f(xy)ndash Equal to the slope of the imagendash A steep slope is equal to an edge

                          120571120571119891119891 119909119909119910119910 = 119866(119892119892119909119909119892119892119910119910)

                          DTU Compute

                          2122018Introduction to Medical Image Analysis71 DTU Compute Technical University of Denmark

                          Edge filter kernel The Prewitt filter is a typical

                          edge filter Output image has high

                          values where there are edges

                          -1 0 1

                          -1 0 1

                          -1 0 1Vertical Prewitt filter

                          DTU Compute

                          2122018Introduction to Medical Image Analysis72 DTU Compute Technical University of Denmark

                          Prewitt filter

                          Original Prewitt Prewitt

                          Hot colormapSmooth 15x15

                          Smooth 15x15

                          Prewitt

                          DTU Compute

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                          Edge detection Edge filter

                          ndash Prewitt for example Thresholding

                          ndash Separate edges from non-edges

                          Output is binary imagendash Edges are white

                          DTU Compute

                          2122018Introduction to Medical Image Analysis74 DTU Compute Technical University of Denmark

                          Edge filtering

                          A) MeanB) Horizontal SobelC) Vertical PrewittD) Horisontal PrewittE) Median

                          Der udfoslashres en filtrering (correlation) med et filter paring billedet Der bruges ikke coefficient normalization Den filtrerede vaeligrdi i den markerede pixel bliver -119 Hvilket et 3x3 filter blev benyttet

                          0

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                          02511 - Niveau af dagens emne forelaeligsingA) Meget letB) LetC) PassendeD) SvaeligrtE) Meget svaeligrt

                          23

                          6

                          10

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                          02512 - Niveau af dagens emne forelaeligsingA) Meget letB) LetC) PassendeD) SvaeligrtE) Meget svaeligrt

                          0 0

                          1

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                          02511 - Mit eget udbytte af dagenA) Jeg har laeligrt meget lidtB) Lidt laeligringC) PassendeD) God laeligringE) Jeg har laeligrt meget

                          0 0

                          2

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                          02512 - Mit eget udbytte af dagenA) Jeg har laeligrt meget lidtB) Lidt laeligringC) PassendeD) God laeligringE) Jeg har laeligrt meget

                          2

                          1

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                          2122018Introduction to Medical Image Analysis80 DTU Compute Technical University of Denmark

                          02511 - Sidste uges oslashvelser (pixelwiseoperations)A) Meget letteB) LetteC) PassendeD) SvaeligreE) Meget svaeligre

                          0 0

                          1

                          4

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                          2122018Introduction to Medical Image Analysis81 DTU Compute Technical University of Denmark

                          02512 - Sidste uges oslashvelser (pixelwiseoperations)A) Meget letteB) LetteC) PassendeD) SvaeligreE) Meget svaeligre

                          3

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                          2122018Introduction to Medical Image Analysis82 DTU Compute Technical University of Denmark

                          Denne uges brug af clickersA) click click click ndash jeg bliver

                          sindssygB) For meget clickC) PassendeD) Jeg vil gerne have lidt mereE) Jeg kan ikrsquo faring nok

                          0 0

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                          What can you do after today Describe the difference between point processing and neighbourhood

                          processing Compute a rank filtered image using the min max median and

                          difference rank filters Compute a mean filtered image Decide if median or average filtering should be used for noise removal Choose the appropriate image border handling based on a given input

                          image Implement and apply template matching Compute the normalised cross correlation and explain why it should be

                          used Apply given image filter kernels to images Use edge filters on images Describe finite difference approximation of image gradients Describe the concept of edge detection

                          DTU Compute

                          2122018Introduction to Medical Image Analysis84 DTU Compute Technical University of Denmark

                          Oslashvelsesrapport over oslashvelse 4 - 02511 Oslashvelser taeligller cirka 30 af karakteren Skal afleveres senest den 7 marts kl 2359 Kan afleveres af 1 eller 2 personer

                          ndash I skal skrive jeres egen oslashvelsesrapportndash Brug mindst et af jeres egne billeder

                          Afleveres som PDF Lad vaeligre med at kopiere opgaveteksten ind i jeres

                          opgave Put Matlab kode i et Appendix og henvis fra teksten Eksempel rapport over oslashvelse findes paring

                          hjemmesiden under eksamen

                          DTU Compute

                          2122018Introduction to Medical Image Analysis85 DTU Compute Technical University of Denmark

                          Exercises

                          • Introduction to Medical Image Analysis
                          • Lecture 4 ndash Neighbourhood Processing
                          • What can you do after today
                          • Point processing
                          • Point processing
                          • Neighbourhood processing
                          • Use of filtering
                          • Salt and pepper noise
                          • Salt and pepper noise
                          • What is so special about noise
                          • Noise ndash go away
                          • What is the median Value
                          • The median value
                          • Noise away ndash the median filter
                          • Noise removal ndash average filter
                          • Noise removal ndash median filter
                          • Image Filtering
                          • Median filter
                          • Rank filters
                          • Median filter
                          • Correlation
                          • Why do we need similarity
                          • Correlation (1D)
                          • Correlation (1D)
                          • Normalisation
                          • Normalisation
                          • Correlation on images
                          • Correlation on images
                          • Correlation on images
                          • Draw your filter
                          • Correlation on images ndash no normalisation
                          • Correlation on images ndash no normalisation 2
                          • Mathematics of 2D Correlation
                          • Mathematics of 2D Correlation
                          • Mathematics of 2D Correlation
                          • Slide Number 40
                          • 2D Kernel Normalisation
                          • Correlation
                          • Smoothing filters
                          • Use of smoothing
                          • Use of smoothing
                          • Mean filter
                          • Border handling
                          • Border handling ndash extend the input
                          • Correlation with zero padding
                          • Border handling ndash extend the input
                          • Template Matching
                          • Template Matching
                          • Template Matching
                          • Template Matching
                          • Problematic Correlation
                          • Normalised Cross Correlation
                          • Length of template
                          • Length of image patch
                          • Normalised Cross Correlation
                          • Normalised Cross Correlation
                          • Normalised Cross Correlation
                          • Edges
                          • Edges
                          • Finite Difference
                          • Edges
                          • Edges in 2D
                          • Edge filter kernel
                          • Prewitt filter
                          • Edge detection
                          • Edge filtering
                          • 02511 - Niveau af dagens emne forelaeligsing
                          • 02512 - Niveau af dagens emne forelaeligsing
                          • 02511 - Mit eget udbytte af dagen
                          • 02512 - Mit eget udbytte af dagen
                          • 02511 - Sidste uges oslashvelser (pixelwise operations)
                          • 02512 - Sidste uges oslashvelser (pixelwise operations)
                          • Denne uges brug af clickers
                          • What can you do after today
                          • Oslashvelsesrapport over oslashvelse 4 - 02511
                          • Exercises
                            A0
                            B0
                            C5
                            D0
                            E6
                            A
                            B
                            C
                            D
                            E
                            A3
                            B0
                            C3
                            D0
                            E0
                            A
                            B
                            C
                            D
                            E
                            A0
                            B0
                            C1
                            D4
                            E1
                            A
                            B
                            C
                            D
                            E
                            A2
                            B1
                            C3
                            D2
                            E0
                            A
                            B
                            C
                            D
                            E
                            A0
                            B0
                            C2
                            D6
                            E0
                            A
                            B
                            C
                            D
                            E
                            A0
                            B0
                            C1
                            D0
                            E0
                            A
                            B
                            C
                            D
                            E
                            A2
                            B3
                            C6
                            D1
                            E0
                            A
                            B
                            C
                            D
                            E
                            A0
                            B8
                            C1
                            D1
                            E0
                            A
                            B
                            C
                            D
                            E
                            A1
                            B2
                            C2
                            D3
                            E2
                            A
                            B
                            C
                            D
                            E
                            A0
                            B13
                            C0
                            D0
                            E0
                            A
                            B
                            C
                            D
                            E
                            A12
                            B0
                            C0
                            D0
                            E0
                            A
                            B
                            C
                            D
                            E
                            A0
                            B0
                            C0
                            D0
                            E13
                            A
                            B
                            C
                            D
                            E
                            A13
                            B0
                            C0
                            D0
                            E0
                            A
                            B
                            C
                            D
                            E
                            A1
                            B0
                            C14
                            D0
                            E0
                            A
                            B
                            C
                            D
                            E
                            A0
                            B12
                            C1
                            D0
                            E0
                            A
                            B
                            C
                            D
                            E
                            A0
                            B13
                            C1
                            D0
                            E0
                            A
                            B
                            C
                            D
                            E
                            A13
                            B0
                            C0
                            D0
                            E2
                            A
                            B
                            C
                            D
                            E

                            Sheet1

                            DTU Compute

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                            The median value The values are sorted from low to high The middle number is picked

                            ndash The median value

                            169 168 0 170172 173 170 172 170

                            0168 169 170 170 170172 172173

                            Median

                            Noise has no influence on the median

                            DTU Compute

                            2122018Introduction to Medical Image Analysis14 DTU Compute Technical University of Denmark

                            Noise away ndash the median filter All pixels are set to the

                            median of its neighbourhood Noise pixels do not pollute

                            good pixels

                            172 169 171 168 0 169 172 173 168

                            170

                            169 168 0 170 172173 170 172 170

                            170

                            DTU Compute

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                            Noise removal ndash average filter

                            Scanned X-ray with salt and pepper noise

                            Average filter (3x3)

                            DTU Compute

                            2122018Introduction to Medical Image Analysis16 DTU Compute Technical University of Denmark

                            Noise removal ndash median filter

                            Scanned X-ray with salt and pepper noise

                            Median filter (3x3)

                            DTU Compute

                            2122018Introduction to Medical Image Analysis17 DTU Compute Technical University of Denmark

                            Image Filtering Creates a new filtered image Output pixel is computed based

                            on a neighbourhood in the input image

                            3 x 3 neighbourhoodndash Filter size 3 x 3ndash Kernel size 3 x 3ndash Mask size 3 x 3

                            Larger filters often usedndash Size

                            7 x 7ndash Number of elements

                            49

                            DTU Compute

                            2122018Introduction to Medical Image Analysis18 DTU Compute Technical University of Denmark

                            Median filterA) 25B) 90C) 198D) 86E) 103

                            0

                            13

                            1 0 0

                            A B C D E

                            Chart1

                            0
                            13
                            1
                            0
                            0

                            Sheet1

                            DTU Compute

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                            Rank filters Based on sorting the pixel

                            values in the neighbouring region

                            Minimum rank filterndash Darker image Noise problems

                            Maximum rank filterndash Lighter image Noise problems

                            Difference filterndash Enhances changes (edges)

                            0168 169 170 170 170172 172173

                            -

                            DTU Compute

                            2122018Introduction to Medical Image Analysis21 DTU Compute Technical University of Denmark

                            Median filter

                            A) 3B) 84C) 112D) 73E) 202

                            0

                            12

                            10 0

                            A B C D E

                            Chart1

                            0
                            12
                            1
                            0
                            0

                            Sheet1

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                            Correlation What is it Two measurements

                            ndash Low correlationndash High correlation

                            High correlation means that there is a relation between the values

                            They look the same Correlation is a measure of

                            similarity

                            Low

                            High

                            Muscles

                            Mat

                            h Ski

                            lls

                            Muscles

                            Ben

                            ch P

                            ress

                            DTU Compute

                            2122018Introduction to Medical Image Analysis24 DTU Compute Technical University of Denmark

                            Why do we need similarity Image analysis is also about recognition of patterns Often an example pattern is used We need something to tell us if there is a high match

                            between our pattern and a part of the image

                            Example pattern

                            Image

                            Find matches

                            DTU Compute

                            2122018Introduction to Medical Image Analysis25 DTU Compute Technical University of Denmark

                            Correlation (1D)

                            1 1 2 2 1 1 2 2 1 1

                            1 2 1

                            45

                            41

                            1 1 + 2 1 + 1 2 = 5

                            Normalise

                            Kernel

                            Signal (1D image)

                            41

                            DTU Compute

                            2122018Introduction to Medical Image Analysis26 DTU Compute Technical University of Denmark

                            Correlation (1D)

                            1 1 2 2 1 1 2 2 1 1

                            1 2 1

                            45

                            47

                            47

                            45

                            45

                            47

                            47

                            45

                            41

                            DTU Compute

                            2122018Introduction to Medical Image Analysis27 DTU Compute Technical University of Denmark

                            Normalisation

                            1 1 2 2 1 1 2 2 1 1

                            1 2 1

                            45

                            41

                            1 1 + 2 1 + 1 2 = 5

                            Normalise41

                            bull The sum of the kernel elements is used

                            bull Keep the values in the same range as the input image

                            Sum is 4

                            DTU Compute

                            2122018Introduction to Medical Image Analysis28 DTU Compute Technical University of Denmark

                            Normalisation Normalisation factor

                            ndash Sum of kernel coefficients

                            1 2 1h(x)

                            119909119909

                            ℎ 119909119909 = 1 + 2 + 1

                            DTU Compute

                            2122018Introduction to Medical Image Analysis29 DTU Compute Technical University of Denmark

                            Correlation on images The filter is now 2D 1 1 1

                            1 1 1

                            1 1 1

                            0 2 4

                            1 2 2

                            1 6 3

                            1 2 12 5 3

                            2 1 3

                            1 3 1

                            2 2 2

                            0 1 3

                            1 2 0

                            2 1 4

                            1 0 1

                            912

                            91

                            Input OutputKernel

                            Kernel coefficients

                            DTU Compute

                            2122018Introduction to Medical Image Analysis30 DTU Compute Technical University of Denmark

                            Correlation on images

                            1 1 11 1 11 1 1

                            0 2 4

                            1 2 2

                            1 6 3

                            1 2 0

                            2 1 4

                            1 0 1

                            912

                            911

                            91

                            Input Output

                            1 3 1

                            2 2 2

                            0 1 3

                            1 2 12 5 3

                            2 1 3

                            DTU Compute

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                            Correlation on images

                            Input Output

                            The mask is moved row by row

                            No values at the border

                            0 2 4

                            1 2 2

                            1 6 3

                            1 2 0

                            2 1 4

                            1 0 1

                            1 3 1

                            2 2 2

                            0 1 3

                            1 2 12 5 3

                            2 1 3

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                            1 2 1

                            1 3 1

                            1 2 1

                            -1 -2 -1

                            0 0 0

                            1 2 1

                            Draw your filter

                            DTU Compute

                            2122018Introduction to Medical Image Analysis33 DTU Compute Technical University of Denmark

                            Correlation on images ndash no normalisationA) 4B) 7C) 16D) 23E) 25

                            1 2 11 3 11 2 1

                            0 2 41 2 2

                            1 6 3

                            1 2 12 5 3

                            2 1 3

                            1 3 1

                            2 2 2

                            0 1 3

                            1 2 0

                            2 1 4

                            1 0 11 0

                            14

                            0 0

                            A B C D E

                            Chart1

                            1
                            0
                            14
                            0
                            0

                            Sheet1

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                            Correlation on images ndash no normalisation 2A) 010B) 3 3C) 6 2D) 10 15E) 11 32

                            13

                            0 0 0 0

                            A B C D E

                            -1 -2 -10 0 01 2 1

                            0 2 41 2 2

                            1 6 3

                            1 2 12 5 3

                            2 1 3

                            1 3 1

                            2 2 2

                            0 1 3

                            1 2 0

                            2 1 4

                            1 0 1

                            Chart1

                            13
                            0
                            0
                            0
                            0

                            Sheet1

                            DTU Compute

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                            Mathematics of 2D Correlation

                            h

                            f

                            Correlation operator

                            1 2 11 3 11 2 1

                            0 2 4

                            1 2 2

                            1 6 3

                            1 2 1

                            2 5 3

                            2 1 3

                            1 3 1

                            2 2 2

                            0 1 3

                            1 2 0

                            2 1 4

                            1 0 1

                            119892119892 119909119909119910119910 = 119891119891 119909119909119910119910 ∘ ℎ(119909119909119910119910)

                            DTU Compute

                            2122018Introduction to Medical Image Analysis38 DTU Compute Technical University of Denmark

                            Mathematics of 2D Correlation

                            1 2 11 3 11 2 1

                            0 2 4

                            1 2 2

                            1 6 3

                            1 2 1

                            2 5 3

                            2 1 3

                            1 3 1

                            2 2 2

                            0 1 3

                            1 2 0

                            2 1 4

                            1 0 1

                            h

                            fh(00)

                            f(21)

                            Example g(21)

                            i = -1 j = -1

                            i = 1 j = 0

                            119892119892 119909119909119910119910 = 119895119895=minus119877119877

                            119877119877

                            119894119894=minus119877119877

                            119877119877

                            ℎ(119894119894 119895119895) 119891119891(119909119909 + 119894119894119910119910 + 119895119895)

                            DTU Compute

                            2122018Introduction to Medical Image Analysis39 DTU Compute Technical University of Denmark

                            Mathematics of 2D Correlation

                            1 2 11 3 11 2 1

                            0 2 4

                            1 2 2

                            1 6 3

                            1 2 1

                            2 5 3

                            2 1 3

                            1 3 1

                            2 2 2

                            0 1 3

                            1 2 0

                            2 1 4

                            1 0 1

                            h

                            f

                            119892119892 119909119909119910119910 = 119895119895=minus119877119877

                            119877119877

                            119894119894=minus119877119877

                            119877119877

                            ℎ(119894119894 119895119895) 119891119891(119909119909 + 119894119894119910119910 + 119895119895)

                            119892119892(119909119909119910119910 = 1 2 + 2 0 + 1 1 + 1 1 + 3 4 + 1 2 + 1 0 + 2 1 + 1 0

                            DTU Compute

                            2122018Introduction to Medical Image Analysis40 DTU Compute Technical University of Denmark

                            119892119892 119909119909 119910119910 = 119895119895=minus119877119877

                            119877119877

                            119894119894=minus119877119877

                            119877119877

                            ℎ(119894119894 119895119895) 119891119891(119909119909 + 119894119894119910119910 + 119895119895)

                            119892119892 22 =ℎ minus1minus1 sdot 119891119891 11 + ℎ 0minus1 sdot 119891119891 21 + ℎ 1minus1 sdot 119891119891 31 +ℎ minus10 sdot 119891119891 12 + ℎ 00 sdot 119891119891 22 + ℎ 10 sdot 119891119891 32 +ℎ minus11 sdot 119891119891 13 + ℎ 01 sdot 119891119891 23 + ℎ 11 sdot 119891119891 33

                            DTU Compute

                            2122018Introduction to Medical Image Analysis41 DTU Compute Technical University of Denmark

                            2D Kernel Normalisation

                            1 2 11 3 11 2 1

                            h

                            Normalisation factor

                            1 + 2 + 1 + 1 + 3 + 1 + 1 + 2 + 1 = 13

                            119909119909

                            119910119910

                            ℎ(119909119909119910119910)

                            DTU Compute

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                            CorrelationA) 50122B) 123001C) 11233D) 2550E) 90454

                            0 0 0 0

                            13

                            A B C D E

                            Chart1

                            0
                            0
                            0
                            0
                            13

                            Sheet1

                            DTU Compute

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                            Smoothing filters

                            Also know as ndash Smoothing kernel Mean filter Low pass filter blurring

                            The simplest filter ndash Spatial low pass filterndash Removes high frequencies

                            Another mask ndash Gaussian filter

                            1 1 1

                            1 1 1

                            1 1 191

                            1 2 1

                            2 4 2

                            1 2 1161

                            Why Gaussian

                            DTU Compute

                            2122018Introduction to Medical Image Analysis45 DTU Compute Technical University of Denmark

                            Use of smoothing

                            3x3 7x7 11x11 15x15

                            DTU Compute

                            2122018Introduction to Medical Image Analysis46 DTU Compute Technical University of Denmark

                            Use of smoothing Large kernels smooth more Removes high frequency information Good at enhancing big structures

                            3x3 15x15

                            DTU Compute

                            2122018Introduction to Medical Image Analysis47 DTU Compute Technical University of Denmark

                            Mean filterA) 166B) 113C) 12D) 51E) 245

                            0 0 0 0

                            A B C D E

                            Chart1

                            12
                            0
                            0
                            0
                            0

                            Sheet1

                            DTU Compute

                            2122018Introduction to Medical Image Analysis49 DTU Compute Technical University of Denmark

                            Border handling

                            0 2 41 2 2

                            1 6 3

                            1 2 12 5 3

                            2 1 3

                            1 3 1

                            2 2 2

                            0 1 3

                            1 2 0

                            2 1 4

                            1 0 1

                            Input Output

                            No values at the border

                            DTU Compute

                            2122018Introduction to Medical Image Analysis50 DTU Compute Technical University of Denmark

                            Border handling ndash extend the input

                            0 2 41 2 2

                            1 6 3

                            1 2 12 5 3

                            2 1 3

                            1 3 1

                            2 2 2

                            0 1 3

                            1 2 0

                            2 1 4

                            1 0 1

                            Input

                            0 0 0 0 000000

                            bull Zero padding ndash what happens

                            bull Zero is black ndash creates dark border around the image

                            DTU Compute

                            2122018Introduction to Medical Image Analysis51 DTU Compute Technical University of Denmark

                            Correlation with zero paddingA) 5 8B) 12 16C) 13 3D) 15 21E) 17 12

                            1 2 11 3 11 2 1

                            0 2 41 2 2

                            1 6 3

                            1 2 12 5 3

                            2 1 3

                            1 3 1

                            2 2 2

                            0 1 3

                            1 2 0

                            2 1 4

                            1 0 1

                            0

                            13

                            0 0 0

                            A B C D E

                            Chart1

                            0
                            13
                            0
                            0
                            0

                            Sheet1

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                            Border handling ndash extend the input

                            0 2 41 2 2

                            1 6 3

                            1 2 12 5 3

                            2 1 3

                            1 3 1

                            2 2 2

                            0 1 3

                            1 2 0

                            2 1 4

                            1 0 1

                            Input

                            1 2 0 1 311211

                            bull Reflection

                            bull Normally better than zero padding

                            DTU Compute

                            2122018Introduction to Medical Image Analysis54 DTU Compute Technical University of Denmark

                            Template Matching Template

                            ndash Skabelon paring dansk Locates objects in images

                            Input

                            Template

                            Output Correlation image

                            DTU Compute

                            2122018Introduction to Medical Image Analysis55 DTU Compute Technical University of Denmark

                            Template Matching The correlation between the template and the input

                            image is computed for each pixel

                            Input

                            Template

                            Output Correlation image

                            DTU Compute

                            2122018Introduction to Medical Image Analysis56 DTU Compute Technical University of Denmark

                            Template Matching The pixel with the highest value is found in the

                            output imagendash Here is the highest correlation

                            Input

                            Template

                            Output Correlation image

                            DTU Compute

                            2122018Introduction to Medical Image Analysis57 DTU Compute Technical University of Denmark

                            Template Matching This corresponds to the found pattern in the input

                            image

                            Input

                            Template

                            Output Correlation image

                            DTU Compute

                            2122018Introduction to Medical Image Analysis58 DTU Compute Technical University of Denmark

                            Problematic Correlation Correlation matching has problem with light areas ndash

                            why

                            Input (f)

                            Template (h)

                            Output Correlation imageFake max

                            Real max

                            Very High119892119892 119909119909119910119910 = 119895119895=minus119877119877

                            119877119877

                            119894119894=minus119877119877

                            119877119877

                            ℎ(119894119894 119895119895) 119891119891(119909119909 + 119894119894119910119910 + 119895119895)

                            DTU Compute

                            2122018Introduction to Medical Image Analysis59 DTU Compute Technical University of Denmark

                            Normalised Cross Correlation

                            Input (f)

                            Template (h)

                            Output Correlation image

                            Real max

                            NCC x y =Correlation

                            Length of image patch sdot Length of template

                            DTU Compute

                            2122018Introduction to Medical Image Analysis60 DTU Compute Technical University of Denmark

                            Length of template Vector length

                            ndash Put all pixel values into a vectorndash Compute the length of this vector

                            Describes the intensity of the templatendash Bright template has a large lengthndash Dark template has a small length

                            Template (h)

                            Length of template = 119895119895=minus119877119877

                            119877119877

                            119894119894=minus119877119877

                            119877119877

                            ℎ(119894119894 119895119895) ℎ(119894119894 119895119895)

                            DTU Compute

                            2122018Introduction to Medical Image Analysis61 DTU Compute Technical University of Denmark

                            Length of image patch Vector length based on pixel values in image patch Describes the intensity of the image patch

                            Template (h)

                            Input (f) with patch

                            DTU Compute

                            2122018Introduction to Medical Image Analysis62 DTU Compute Technical University of Denmark

                            Normalised Cross Correlation The length of the image patch and the length of

                            template normalise the NCC If the image is very bright the NCC will be ldquopulled

                            downrdquo

                            NCC x y =Correlation

                            Length of image patch sdot Length of template

                            DTU Compute

                            2122018Introduction to Medical Image Analysis63 DTU Compute Technical University of Denmark

                            Normalised Cross Correlation NCC will be between

                            ndash 0 No similarity between template and image patchndash 1 Template and image patch are identical

                            Input (f)

                            Template (h)

                            Output Correlation image

                            Real max

                            NCC x y =Correlation

                            Length of image patch sdot Length of template

                            DTU Compute

                            2122018Introduction to Medical Image Analysis64 DTU Compute Technical University of Denmark

                            Normalised Cross Correlation

                            A) 010B) 033C) 083D) 062E) 098

                            Der udfoslashres template matching med og normalized crosscorrelation (NCC) beregnes Hvad bliver NNC i den markerede pixel

                            1

                            2 2

                            3

                            2

                            A B C D E

                            Chart1

                            1
                            2
                            2
                            3
                            2

                            Sheet1

                            DTU Compute

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                            Edges An edge is where there is a

                            high change in gray level values

                            Objects are often separated from the background by edgesGray level profile

                            DTU Compute

                            2122018Introduction to Medical Image Analysis67 DTU Compute Technical University of Denmark

                            Edges The profile as a function f(d) What value is high when there

                            is an edgendash The slope of fndash The slope of the tangent at d

                            f(d)

                            119891119891prime(119889119889)

                            DTU Compute

                            2122018Introduction to Medical Image Analysis68 DTU Compute Technical University of Denmark

                            Finite Difference Definition of slope

                            Approximation

                            Simpler approximationh = 1

                            119891119891prime 119889119889 = limℎrarr0

                            119891119891 119889119889 + ℎ minus 119891119891(119889119889)ℎ

                            119891119891prime 119889119889 asymp119891119891 119889119889 + ℎ minus 119891119891(119889119889)

                            ℎ

                            119891119891prime 119889119889 asymp 119891119891 119889119889 + 1 minus 119891119891(119889119889)

                            DTU Compute

                            2122018Introduction to Medical Image Analysis69 DTU Compute Technical University of Denmark

                            Edges Discrete approximation of frsquo(d) Can be implemented as a filter

                            -1 0 1

                            f(d-2) f(d-1) f(d) f(d+1) f(d+2) f(d+3)

                            f(d)

                            119891119891prime 119889119889 asymp 119891119891 119889119889 + 1 minus 119891119891(119889119889)

                            DTU Compute

                            2122018Introduction to Medical Image Analysis70 DTU Compute Technical University of Denmark

                            Edges in 2D Changes in gray level values

                            ndash Image gradientndash Gradient is the 2D derivative of a 2D function f(xy)ndash Equal to the slope of the imagendash A steep slope is equal to an edge

                            120571120571119891119891 119909119909119910119910 = 119866(119892119892119909119909119892119892119910119910)

                            DTU Compute

                            2122018Introduction to Medical Image Analysis71 DTU Compute Technical University of Denmark

                            Edge filter kernel The Prewitt filter is a typical

                            edge filter Output image has high

                            values where there are edges

                            -1 0 1

                            -1 0 1

                            -1 0 1Vertical Prewitt filter

                            DTU Compute

                            2122018Introduction to Medical Image Analysis72 DTU Compute Technical University of Denmark

                            Prewitt filter

                            Original Prewitt Prewitt

                            Hot colormapSmooth 15x15

                            Smooth 15x15

                            Prewitt

                            DTU Compute

                            2122018Introduction to Medical Image Analysis73 DTU Compute Technical University of Denmark

                            Edge detection Edge filter

                            ndash Prewitt for example Thresholding

                            ndash Separate edges from non-edges

                            Output is binary imagendash Edges are white

                            DTU Compute

                            2122018Introduction to Medical Image Analysis74 DTU Compute Technical University of Denmark

                            Edge filtering

                            A) MeanB) Horizontal SobelC) Vertical PrewittD) Horisontal PrewittE) Median

                            Der udfoslashres en filtrering (correlation) med et filter paring billedet Der bruges ikke coefficient normalization Den filtrerede vaeligrdi i den markerede pixel bliver -119 Hvilket et 3x3 filter blev benyttet

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                            02511 - Niveau af dagens emne forelaeligsingA) Meget letB) LetC) PassendeD) SvaeligrtE) Meget svaeligrt

                            23

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                            02512 - Niveau af dagens emne forelaeligsingA) Meget letB) LetC) PassendeD) SvaeligrtE) Meget svaeligrt

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                            02511 - Mit eget udbytte af dagenA) Jeg har laeligrt meget lidtB) Lidt laeligringC) PassendeD) God laeligringE) Jeg har laeligrt meget

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                            02512 - Mit eget udbytte af dagenA) Jeg har laeligrt meget lidtB) Lidt laeligringC) PassendeD) God laeligringE) Jeg har laeligrt meget

                            2

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                            02511 - Sidste uges oslashvelser (pixelwiseoperations)A) Meget letteB) LetteC) PassendeD) SvaeligreE) Meget svaeligre

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                            02512 - Sidste uges oslashvelser (pixelwiseoperations)A) Meget letteB) LetteC) PassendeD) SvaeligreE) Meget svaeligre

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                            Denne uges brug af clickersA) click click click ndash jeg bliver

                            sindssygB) For meget clickC) PassendeD) Jeg vil gerne have lidt mereE) Jeg kan ikrsquo faring nok

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                            What can you do after today Describe the difference between point processing and neighbourhood

                            processing Compute a rank filtered image using the min max median and

                            difference rank filters Compute a mean filtered image Decide if median or average filtering should be used for noise removal Choose the appropriate image border handling based on a given input

                            image Implement and apply template matching Compute the normalised cross correlation and explain why it should be

                            used Apply given image filter kernels to images Use edge filters on images Describe finite difference approximation of image gradients Describe the concept of edge detection

                            DTU Compute

                            2122018Introduction to Medical Image Analysis84 DTU Compute Technical University of Denmark

                            Oslashvelsesrapport over oslashvelse 4 - 02511 Oslashvelser taeligller cirka 30 af karakteren Skal afleveres senest den 7 marts kl 2359 Kan afleveres af 1 eller 2 personer

                            ndash I skal skrive jeres egen oslashvelsesrapportndash Brug mindst et af jeres egne billeder

                            Afleveres som PDF Lad vaeligre med at kopiere opgaveteksten ind i jeres

                            opgave Put Matlab kode i et Appendix og henvis fra teksten Eksempel rapport over oslashvelse findes paring

                            hjemmesiden under eksamen

                            DTU Compute

                            2122018Introduction to Medical Image Analysis85 DTU Compute Technical University of Denmark

                            Exercises

                            • Introduction to Medical Image Analysis
                            • Lecture 4 ndash Neighbourhood Processing
                            • What can you do after today
                            • Point processing
                            • Point processing
                            • Neighbourhood processing
                            • Use of filtering
                            • Salt and pepper noise
                            • Salt and pepper noise
                            • What is so special about noise
                            • Noise ndash go away
                            • What is the median Value
                            • The median value
                            • Noise away ndash the median filter
                            • Noise removal ndash average filter
                            • Noise removal ndash median filter
                            • Image Filtering
                            • Median filter
                            • Rank filters
                            • Median filter
                            • Correlation
                            • Why do we need similarity
                            • Correlation (1D)
                            • Correlation (1D)
                            • Normalisation
                            • Normalisation
                            • Correlation on images
                            • Correlation on images
                            • Correlation on images
                            • Draw your filter
                            • Correlation on images ndash no normalisation
                            • Correlation on images ndash no normalisation 2
                            • Mathematics of 2D Correlation
                            • Mathematics of 2D Correlation
                            • Mathematics of 2D Correlation
                            • Slide Number 40
                            • 2D Kernel Normalisation
                            • Correlation
                            • Smoothing filters
                            • Use of smoothing
                            • Use of smoothing
                            • Mean filter
                            • Border handling
                            • Border handling ndash extend the input
                            • Correlation with zero padding
                            • Border handling ndash extend the input
                            • Template Matching
                            • Template Matching
                            • Template Matching
                            • Template Matching
                            • Problematic Correlation
                            • Normalised Cross Correlation
                            • Length of template
                            • Length of image patch
                            • Normalised Cross Correlation
                            • Normalised Cross Correlation
                            • Normalised Cross Correlation
                            • Edges
                            • Edges
                            • Finite Difference
                            • Edges
                            • Edges in 2D
                            • Edge filter kernel
                            • Prewitt filter
                            • Edge detection
                            • Edge filtering
                            • 02511 - Niveau af dagens emne forelaeligsing
                            • 02512 - Niveau af dagens emne forelaeligsing
                            • 02511 - Mit eget udbytte af dagen
                            • 02512 - Mit eget udbytte af dagen
                            • 02511 - Sidste uges oslashvelser (pixelwise operations)
                            • 02512 - Sidste uges oslashvelser (pixelwise operations)
                            • Denne uges brug af clickers
                            • What can you do after today
                            • Oslashvelsesrapport over oslashvelse 4 - 02511
                            • Exercises
                              A0
                              B0
                              C5
                              D0
                              E6
                              A
                              B
                              C
                              D
                              E
                              A3
                              B0
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                              D
                              E
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                              E1
                              A
                              B
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                              D
                              E
                              A2
                              B1
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                              D2
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                              A
                              B
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                              E
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                              B0
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                              D6
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                              A2
                              B3
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                              D1
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                              B
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                              B8
                              C1
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                              C1
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                              A
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                              A13
                              B0
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                              E2

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                              2122018Introduction to Medical Image Analysis13 DTU Compute Technical University of Denmark

                              The median value The values are sorted from low to high The middle number is picked

                              ndash The median value

                              169 168 0 170172 173 170 172 170

                              0168 169 170 170 170172 172173

                              Median

                              Noise has no influence on the median

                              DTU Compute

                              2122018Introduction to Medical Image Analysis14 DTU Compute Technical University of Denmark

                              Noise away ndash the median filter All pixels are set to the

                              median of its neighbourhood Noise pixels do not pollute

                              good pixels

                              172 169 171 168 0 169 172 173 168

                              170

                              169 168 0 170 172173 170 172 170

                              170

                              DTU Compute

                              2122018Introduction to Medical Image Analysis15 DTU Compute Technical University of Denmark

                              Noise removal ndash average filter

                              Scanned X-ray with salt and pepper noise

                              Average filter (3x3)

                              DTU Compute

                              2122018Introduction to Medical Image Analysis16 DTU Compute Technical University of Denmark

                              Noise removal ndash median filter

                              Scanned X-ray with salt and pepper noise

                              Median filter (3x3)

                              DTU Compute

                              2122018Introduction to Medical Image Analysis17 DTU Compute Technical University of Denmark

                              Image Filtering Creates a new filtered image Output pixel is computed based

                              on a neighbourhood in the input image

                              3 x 3 neighbourhoodndash Filter size 3 x 3ndash Kernel size 3 x 3ndash Mask size 3 x 3

                              Larger filters often usedndash Size

                              7 x 7ndash Number of elements

                              49

                              DTU Compute

                              2122018Introduction to Medical Image Analysis18 DTU Compute Technical University of Denmark

                              Median filterA) 25B) 90C) 198D) 86E) 103

                              0

                              13

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                              Rank filters Based on sorting the pixel

                              values in the neighbouring region

                              Minimum rank filterndash Darker image Noise problems

                              Maximum rank filterndash Lighter image Noise problems

                              Difference filterndash Enhances changes (edges)

                              0168 169 170 170 170172 172173

                              -

                              DTU Compute

                              2122018Introduction to Medical Image Analysis21 DTU Compute Technical University of Denmark

                              Median filter

                              A) 3B) 84C) 112D) 73E) 202

                              0

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                              Correlation What is it Two measurements

                              ndash Low correlationndash High correlation

                              High correlation means that there is a relation between the values

                              They look the same Correlation is a measure of

                              similarity

                              Low

                              High

                              Muscles

                              Mat

                              h Ski

                              lls

                              Muscles

                              Ben

                              ch P

                              ress

                              DTU Compute

                              2122018Introduction to Medical Image Analysis24 DTU Compute Technical University of Denmark

                              Why do we need similarity Image analysis is also about recognition of patterns Often an example pattern is used We need something to tell us if there is a high match

                              between our pattern and a part of the image

                              Example pattern

                              Image

                              Find matches

                              DTU Compute

                              2122018Introduction to Medical Image Analysis25 DTU Compute Technical University of Denmark

                              Correlation (1D)

                              1 1 2 2 1 1 2 2 1 1

                              1 2 1

                              45

                              41

                              1 1 + 2 1 + 1 2 = 5

                              Normalise

                              Kernel

                              Signal (1D image)

                              41

                              DTU Compute

                              2122018Introduction to Medical Image Analysis26 DTU Compute Technical University of Denmark

                              Correlation (1D)

                              1 1 2 2 1 1 2 2 1 1

                              1 2 1

                              45

                              47

                              47

                              45

                              45

                              47

                              47

                              45

                              41

                              DTU Compute

                              2122018Introduction to Medical Image Analysis27 DTU Compute Technical University of Denmark

                              Normalisation

                              1 1 2 2 1 1 2 2 1 1

                              1 2 1

                              45

                              41

                              1 1 + 2 1 + 1 2 = 5

                              Normalise41

                              bull The sum of the kernel elements is used

                              bull Keep the values in the same range as the input image

                              Sum is 4

                              DTU Compute

                              2122018Introduction to Medical Image Analysis28 DTU Compute Technical University of Denmark

                              Normalisation Normalisation factor

                              ndash Sum of kernel coefficients

                              1 2 1h(x)

                              119909119909

                              ℎ 119909119909 = 1 + 2 + 1

                              DTU Compute

                              2122018Introduction to Medical Image Analysis29 DTU Compute Technical University of Denmark

                              Correlation on images The filter is now 2D 1 1 1

                              1 1 1

                              1 1 1

                              0 2 4

                              1 2 2

                              1 6 3

                              1 2 12 5 3

                              2 1 3

                              1 3 1

                              2 2 2

                              0 1 3

                              1 2 0

                              2 1 4

                              1 0 1

                              912

                              91

                              Input OutputKernel

                              Kernel coefficients

                              DTU Compute

                              2122018Introduction to Medical Image Analysis30 DTU Compute Technical University of Denmark

                              Correlation on images

                              1 1 11 1 11 1 1

                              0 2 4

                              1 2 2

                              1 6 3

                              1 2 0

                              2 1 4

                              1 0 1

                              912

                              911

                              91

                              Input Output

                              1 3 1

                              2 2 2

                              0 1 3

                              1 2 12 5 3

                              2 1 3

                              DTU Compute

                              2122018Introduction to Medical Image Analysis31 DTU Compute Technical University of Denmark

                              Correlation on images

                              Input Output

                              The mask is moved row by row

                              No values at the border

                              0 2 4

                              1 2 2

                              1 6 3

                              1 2 0

                              2 1 4

                              1 0 1

                              1 3 1

                              2 2 2

                              0 1 3

                              1 2 12 5 3

                              2 1 3

                              DTU Compute

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                              1 2 1

                              1 3 1

                              1 2 1

                              -1 -2 -1

                              0 0 0

                              1 2 1

                              Draw your filter

                              DTU Compute

                              2122018Introduction to Medical Image Analysis33 DTU Compute Technical University of Denmark

                              Correlation on images ndash no normalisationA) 4B) 7C) 16D) 23E) 25

                              1 2 11 3 11 2 1

                              0 2 41 2 2

                              1 6 3

                              1 2 12 5 3

                              2 1 3

                              1 3 1

                              2 2 2

                              0 1 3

                              1 2 0

                              2 1 4

                              1 0 11 0

                              14

                              0 0

                              A B C D E

                              Chart1

                              1
                              0
                              14
                              0
                              0

                              Sheet1

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                              Correlation on images ndash no normalisation 2A) 010B) 3 3C) 6 2D) 10 15E) 11 32

                              13

                              0 0 0 0

                              A B C D E

                              -1 -2 -10 0 01 2 1

                              0 2 41 2 2

                              1 6 3

                              1 2 12 5 3

                              2 1 3

                              1 3 1

                              2 2 2

                              0 1 3

                              1 2 0

                              2 1 4

                              1 0 1

                              Chart1

                              13
                              0
                              0
                              0
                              0

                              Sheet1

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                              Mathematics of 2D Correlation

                              h

                              f

                              Correlation operator

                              1 2 11 3 11 2 1

                              0 2 4

                              1 2 2

                              1 6 3

                              1 2 1

                              2 5 3

                              2 1 3

                              1 3 1

                              2 2 2

                              0 1 3

                              1 2 0

                              2 1 4

                              1 0 1

                              119892119892 119909119909119910119910 = 119891119891 119909119909119910119910 ∘ ℎ(119909119909119910119910)

                              DTU Compute

                              2122018Introduction to Medical Image Analysis38 DTU Compute Technical University of Denmark

                              Mathematics of 2D Correlation

                              1 2 11 3 11 2 1

                              0 2 4

                              1 2 2

                              1 6 3

                              1 2 1

                              2 5 3

                              2 1 3

                              1 3 1

                              2 2 2

                              0 1 3

                              1 2 0

                              2 1 4

                              1 0 1

                              h

                              fh(00)

                              f(21)

                              Example g(21)

                              i = -1 j = -1

                              i = 1 j = 0

                              119892119892 119909119909119910119910 = 119895119895=minus119877119877

                              119877119877

                              119894119894=minus119877119877

                              119877119877

                              ℎ(119894119894 119895119895) 119891119891(119909119909 + 119894119894119910119910 + 119895119895)

                              DTU Compute

                              2122018Introduction to Medical Image Analysis39 DTU Compute Technical University of Denmark

                              Mathematics of 2D Correlation

                              1 2 11 3 11 2 1

                              0 2 4

                              1 2 2

                              1 6 3

                              1 2 1

                              2 5 3

                              2 1 3

                              1 3 1

                              2 2 2

                              0 1 3

                              1 2 0

                              2 1 4

                              1 0 1

                              h

                              f

                              119892119892 119909119909119910119910 = 119895119895=minus119877119877

                              119877119877

                              119894119894=minus119877119877

                              119877119877

                              ℎ(119894119894 119895119895) 119891119891(119909119909 + 119894119894119910119910 + 119895119895)

                              119892119892(119909119909119910119910 = 1 2 + 2 0 + 1 1 + 1 1 + 3 4 + 1 2 + 1 0 + 2 1 + 1 0

                              DTU Compute

                              2122018Introduction to Medical Image Analysis40 DTU Compute Technical University of Denmark

                              119892119892 119909119909 119910119910 = 119895119895=minus119877119877

                              119877119877

                              119894119894=minus119877119877

                              119877119877

                              ℎ(119894119894 119895119895) 119891119891(119909119909 + 119894119894119910119910 + 119895119895)

                              119892119892 22 =ℎ minus1minus1 sdot 119891119891 11 + ℎ 0minus1 sdot 119891119891 21 + ℎ 1minus1 sdot 119891119891 31 +ℎ minus10 sdot 119891119891 12 + ℎ 00 sdot 119891119891 22 + ℎ 10 sdot 119891119891 32 +ℎ minus11 sdot 119891119891 13 + ℎ 01 sdot 119891119891 23 + ℎ 11 sdot 119891119891 33

                              DTU Compute

                              2122018Introduction to Medical Image Analysis41 DTU Compute Technical University of Denmark

                              2D Kernel Normalisation

                              1 2 11 3 11 2 1

                              h

                              Normalisation factor

                              1 + 2 + 1 + 1 + 3 + 1 + 1 + 2 + 1 = 13

                              119909119909

                              119910119910

                              ℎ(119909119909119910119910)

                              DTU Compute

                              2122018Introduction to Medical Image Analysis42 DTU Compute Technical University of Denmark

                              CorrelationA) 50122B) 123001C) 11233D) 2550E) 90454

                              0 0 0 0

                              13

                              A B C D E

                              Chart1

                              0
                              0
                              0
                              0
                              13

                              Sheet1

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                              Smoothing filters

                              Also know as ndash Smoothing kernel Mean filter Low pass filter blurring

                              The simplest filter ndash Spatial low pass filterndash Removes high frequencies

                              Another mask ndash Gaussian filter

                              1 1 1

                              1 1 1

                              1 1 191

                              1 2 1

                              2 4 2

                              1 2 1161

                              Why Gaussian

                              DTU Compute

                              2122018Introduction to Medical Image Analysis45 DTU Compute Technical University of Denmark

                              Use of smoothing

                              3x3 7x7 11x11 15x15

                              DTU Compute

                              2122018Introduction to Medical Image Analysis46 DTU Compute Technical University of Denmark

                              Use of smoothing Large kernels smooth more Removes high frequency information Good at enhancing big structures

                              3x3 15x15

                              DTU Compute

                              2122018Introduction to Medical Image Analysis47 DTU Compute Technical University of Denmark

                              Mean filterA) 166B) 113C) 12D) 51E) 245

                              0 0 0 0

                              A B C D E

                              Chart1

                              12
                              0
                              0
                              0
                              0

                              Sheet1

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                              Border handling

                              0 2 41 2 2

                              1 6 3

                              1 2 12 5 3

                              2 1 3

                              1 3 1

                              2 2 2

                              0 1 3

                              1 2 0

                              2 1 4

                              1 0 1

                              Input Output

                              No values at the border

                              DTU Compute

                              2122018Introduction to Medical Image Analysis50 DTU Compute Technical University of Denmark

                              Border handling ndash extend the input

                              0 2 41 2 2

                              1 6 3

                              1 2 12 5 3

                              2 1 3

                              1 3 1

                              2 2 2

                              0 1 3

                              1 2 0

                              2 1 4

                              1 0 1

                              Input

                              0 0 0 0 000000

                              bull Zero padding ndash what happens

                              bull Zero is black ndash creates dark border around the image

                              DTU Compute

                              2122018Introduction to Medical Image Analysis51 DTU Compute Technical University of Denmark

                              Correlation with zero paddingA) 5 8B) 12 16C) 13 3D) 15 21E) 17 12

                              1 2 11 3 11 2 1

                              0 2 41 2 2

                              1 6 3

                              1 2 12 5 3

                              2 1 3

                              1 3 1

                              2 2 2

                              0 1 3

                              1 2 0

                              2 1 4

                              1 0 1

                              0

                              13

                              0 0 0

                              A B C D E

                              Chart1

                              0
                              13
                              0
                              0
                              0

                              Sheet1

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                              2122018Introduction to Medical Image Analysis53 DTU Compute Technical University of Denmark

                              Border handling ndash extend the input

                              0 2 41 2 2

                              1 6 3

                              1 2 12 5 3

                              2 1 3

                              1 3 1

                              2 2 2

                              0 1 3

                              1 2 0

                              2 1 4

                              1 0 1

                              Input

                              1 2 0 1 311211

                              bull Reflection

                              bull Normally better than zero padding

                              DTU Compute

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                              Template Matching Template

                              ndash Skabelon paring dansk Locates objects in images

                              Input

                              Template

                              Output Correlation image

                              DTU Compute

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                              Template Matching The correlation between the template and the input

                              image is computed for each pixel

                              Input

                              Template

                              Output Correlation image

                              DTU Compute

                              2122018Introduction to Medical Image Analysis56 DTU Compute Technical University of Denmark

                              Template Matching The pixel with the highest value is found in the

                              output imagendash Here is the highest correlation

                              Input

                              Template

                              Output Correlation image

                              DTU Compute

                              2122018Introduction to Medical Image Analysis57 DTU Compute Technical University of Denmark

                              Template Matching This corresponds to the found pattern in the input

                              image

                              Input

                              Template

                              Output Correlation image

                              DTU Compute

                              2122018Introduction to Medical Image Analysis58 DTU Compute Technical University of Denmark

                              Problematic Correlation Correlation matching has problem with light areas ndash

                              why

                              Input (f)

                              Template (h)

                              Output Correlation imageFake max

                              Real max

                              Very High119892119892 119909119909119910119910 = 119895119895=minus119877119877

                              119877119877

                              119894119894=minus119877119877

                              119877119877

                              ℎ(119894119894 119895119895) 119891119891(119909119909 + 119894119894119910119910 + 119895119895)

                              DTU Compute

                              2122018Introduction to Medical Image Analysis59 DTU Compute Technical University of Denmark

                              Normalised Cross Correlation

                              Input (f)

                              Template (h)

                              Output Correlation image

                              Real max

                              NCC x y =Correlation

                              Length of image patch sdot Length of template

                              DTU Compute

                              2122018Introduction to Medical Image Analysis60 DTU Compute Technical University of Denmark

                              Length of template Vector length

                              ndash Put all pixel values into a vectorndash Compute the length of this vector

                              Describes the intensity of the templatendash Bright template has a large lengthndash Dark template has a small length

                              Template (h)

                              Length of template = 119895119895=minus119877119877

                              119877119877

                              119894119894=minus119877119877

                              119877119877

                              ℎ(119894119894 119895119895) ℎ(119894119894 119895119895)

                              DTU Compute

                              2122018Introduction to Medical Image Analysis61 DTU Compute Technical University of Denmark

                              Length of image patch Vector length based on pixel values in image patch Describes the intensity of the image patch

                              Template (h)

                              Input (f) with patch

                              DTU Compute

                              2122018Introduction to Medical Image Analysis62 DTU Compute Technical University of Denmark

                              Normalised Cross Correlation The length of the image patch and the length of

                              template normalise the NCC If the image is very bright the NCC will be ldquopulled

                              downrdquo

                              NCC x y =Correlation

                              Length of image patch sdot Length of template

                              DTU Compute

                              2122018Introduction to Medical Image Analysis63 DTU Compute Technical University of Denmark

                              Normalised Cross Correlation NCC will be between

                              ndash 0 No similarity between template and image patchndash 1 Template and image patch are identical

                              Input (f)

                              Template (h)

                              Output Correlation image

                              Real max

                              NCC x y =Correlation

                              Length of image patch sdot Length of template

                              DTU Compute

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                              Normalised Cross Correlation

                              A) 010B) 033C) 083D) 062E) 098

                              Der udfoslashres template matching med og normalized crosscorrelation (NCC) beregnes Hvad bliver NNC i den markerede pixel

                              1

                              2 2

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                              Edges An edge is where there is a

                              high change in gray level values

                              Objects are often separated from the background by edgesGray level profile

                              DTU Compute

                              2122018Introduction to Medical Image Analysis67 DTU Compute Technical University of Denmark

                              Edges The profile as a function f(d) What value is high when there

                              is an edgendash The slope of fndash The slope of the tangent at d

                              f(d)

                              119891119891prime(119889119889)

                              DTU Compute

                              2122018Introduction to Medical Image Analysis68 DTU Compute Technical University of Denmark

                              Finite Difference Definition of slope

                              Approximation

                              Simpler approximationh = 1

                              119891119891prime 119889119889 = limℎrarr0

                              119891119891 119889119889 + ℎ minus 119891119891(119889119889)ℎ

                              119891119891prime 119889119889 asymp119891119891 119889119889 + ℎ minus 119891119891(119889119889)

                              ℎ

                              119891119891prime 119889119889 asymp 119891119891 119889119889 + 1 minus 119891119891(119889119889)

                              DTU Compute

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                              Edges Discrete approximation of frsquo(d) Can be implemented as a filter

                              -1 0 1

                              f(d-2) f(d-1) f(d) f(d+1) f(d+2) f(d+3)

                              f(d)

                              119891119891prime 119889119889 asymp 119891119891 119889119889 + 1 minus 119891119891(119889119889)

                              DTU Compute

                              2122018Introduction to Medical Image Analysis70 DTU Compute Technical University of Denmark

                              Edges in 2D Changes in gray level values

                              ndash Image gradientndash Gradient is the 2D derivative of a 2D function f(xy)ndash Equal to the slope of the imagendash A steep slope is equal to an edge

                              120571120571119891119891 119909119909119910119910 = 119866(119892119892119909119909119892119892119910119910)

                              DTU Compute

                              2122018Introduction to Medical Image Analysis71 DTU Compute Technical University of Denmark

                              Edge filter kernel The Prewitt filter is a typical

                              edge filter Output image has high

                              values where there are edges

                              -1 0 1

                              -1 0 1

                              -1 0 1Vertical Prewitt filter

                              DTU Compute

                              2122018Introduction to Medical Image Analysis72 DTU Compute Technical University of Denmark

                              Prewitt filter

                              Original Prewitt Prewitt

                              Hot colormapSmooth 15x15

                              Smooth 15x15

                              Prewitt

                              DTU Compute

                              2122018Introduction to Medical Image Analysis73 DTU Compute Technical University of Denmark

                              Edge detection Edge filter

                              ndash Prewitt for example Thresholding

                              ndash Separate edges from non-edges

                              Output is binary imagendash Edges are white

                              DTU Compute

                              2122018Introduction to Medical Image Analysis74 DTU Compute Technical University of Denmark

                              Edge filtering

                              A) MeanB) Horizontal SobelC) Vertical PrewittD) Horisontal PrewittE) Median

                              Der udfoslashres en filtrering (correlation) med et filter paring billedet Der bruges ikke coefficient normalization Den filtrerede vaeligrdi i den markerede pixel bliver -119 Hvilket et 3x3 filter blev benyttet

                              0

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                              02511 - Niveau af dagens emne forelaeligsingA) Meget letB) LetC) PassendeD) SvaeligrtE) Meget svaeligrt

                              23

                              6

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                              02512 - Niveau af dagens emne forelaeligsingA) Meget letB) LetC) PassendeD) SvaeligrtE) Meget svaeligrt

                              0 0

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                              02511 - Mit eget udbytte af dagenA) Jeg har laeligrt meget lidtB) Lidt laeligringC) PassendeD) God laeligringE) Jeg har laeligrt meget

                              0 0

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                              02512 - Mit eget udbytte af dagenA) Jeg har laeligrt meget lidtB) Lidt laeligringC) PassendeD) God laeligringE) Jeg har laeligrt meget

                              2

                              1

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                              02511 - Sidste uges oslashvelser (pixelwiseoperations)A) Meget letteB) LetteC) PassendeD) SvaeligreE) Meget svaeligre

                              0 0

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                              02512 - Sidste uges oslashvelser (pixelwiseoperations)A) Meget letteB) LetteC) PassendeD) SvaeligreE) Meget svaeligre

                              3

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                              Denne uges brug af clickersA) click click click ndash jeg bliver

                              sindssygB) For meget clickC) PassendeD) Jeg vil gerne have lidt mereE) Jeg kan ikrsquo faring nok

                              0 0

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                              What can you do after today Describe the difference between point processing and neighbourhood

                              processing Compute a rank filtered image using the min max median and

                              difference rank filters Compute a mean filtered image Decide if median or average filtering should be used for noise removal Choose the appropriate image border handling based on a given input

                              image Implement and apply template matching Compute the normalised cross correlation and explain why it should be

                              used Apply given image filter kernels to images Use edge filters on images Describe finite difference approximation of image gradients Describe the concept of edge detection

                              DTU Compute

                              2122018Introduction to Medical Image Analysis84 DTU Compute Technical University of Denmark

                              Oslashvelsesrapport over oslashvelse 4 - 02511 Oslashvelser taeligller cirka 30 af karakteren Skal afleveres senest den 7 marts kl 2359 Kan afleveres af 1 eller 2 personer

                              ndash I skal skrive jeres egen oslashvelsesrapportndash Brug mindst et af jeres egne billeder

                              Afleveres som PDF Lad vaeligre med at kopiere opgaveteksten ind i jeres

                              opgave Put Matlab kode i et Appendix og henvis fra teksten Eksempel rapport over oslashvelse findes paring

                              hjemmesiden under eksamen

                              DTU Compute

                              2122018Introduction to Medical Image Analysis85 DTU Compute Technical University of Denmark

                              Exercises

                              • Introduction to Medical Image Analysis
                              • Lecture 4 ndash Neighbourhood Processing
                              • What can you do after today
                              • Point processing
                              • Point processing
                              • Neighbourhood processing
                              • Use of filtering
                              • Salt and pepper noise
                              • Salt and pepper noise
                              • What is so special about noise
                              • Noise ndash go away
                              • What is the median Value
                              • The median value
                              • Noise away ndash the median filter
                              • Noise removal ndash average filter
                              • Noise removal ndash median filter
                              • Image Filtering
                              • Median filter
                              • Rank filters
                              • Median filter
                              • Correlation
                              • Why do we need similarity
                              • Correlation (1D)
                              • Correlation (1D)
                              • Normalisation
                              • Normalisation
                              • Correlation on images
                              • Correlation on images
                              • Correlation on images
                              • Draw your filter
                              • Correlation on images ndash no normalisation
                              • Correlation on images ndash no normalisation 2
                              • Mathematics of 2D Correlation
                              • Mathematics of 2D Correlation
                              • Mathematics of 2D Correlation
                              • Slide Number 40
                              • 2D Kernel Normalisation
                              • Correlation
                              • Smoothing filters
                              • Use of smoothing
                              • Use of smoothing
                              • Mean filter
                              • Border handling
                              • Border handling ndash extend the input
                              • Correlation with zero padding
                              • Border handling ndash extend the input
                              • Template Matching
                              • Template Matching
                              • Template Matching
                              • Template Matching
                              • Problematic Correlation
                              • Normalised Cross Correlation
                              • Length of template
                              • Length of image patch
                              • Normalised Cross Correlation
                              • Normalised Cross Correlation
                              • Normalised Cross Correlation
                              • Edges
                              • Edges
                              • Finite Difference
                              • Edges
                              • Edges in 2D
                              • Edge filter kernel
                              • Prewitt filter
                              • Edge detection
                              • Edge filtering
                              • 02511 - Niveau af dagens emne forelaeligsing
                              • 02512 - Niveau af dagens emne forelaeligsing
                              • 02511 - Mit eget udbytte af dagen
                              • 02512 - Mit eget udbytte af dagen
                              • 02511 - Sidste uges oslashvelser (pixelwise operations)
                              • 02512 - Sidste uges oslashvelser (pixelwise operations)
                              • Denne uges brug af clickers
                              • What can you do after today
                              • Oslashvelsesrapport over oslashvelse 4 - 02511
                              • Exercises
                                A0
                                B0
                                C5
                                D0
                                E6
                                A
                                B
                                C
                                D
                                E
                                A3
                                B0
                                C3
                                D0
                                E0
                                A
                                B
                                C
                                D
                                E
                                A0
                                B0
                                C1
                                D4
                                E1
                                A
                                B
                                C
                                D
                                E
                                A2
                                B1
                                C3
                                D2
                                E0
                                A
                                B
                                C
                                D
                                E
                                A0
                                B0
                                C2
                                D6
                                E0
                                A
                                B
                                C
                                D
                                E
                                A0
                                B0
                                C1
                                D0
                                E0
                                A
                                B
                                C
                                D
                                E
                                A2
                                B3
                                C6
                                D1
                                E0
                                A
                                B
                                C
                                D
                                E
                                A0
                                B8
                                C1
                                D1
                                E0
                                A
                                B
                                C
                                D
                                E
                                A1
                                B2
                                C2
                                D3
                                E2
                                A
                                B
                                C
                                D
                                E
                                A0
                                B13
                                C0
                                D0
                                E0
                                A
                                B
                                C
                                D
                                E
                                A12
                                B0
                                C0
                                D0
                                E0
                                A
                                B
                                C
                                D
                                E
                                A0
                                B0
                                C0
                                D0
                                E13
                                A
                                B
                                C
                                D
                                E
                                A13
                                B0
                                C0
                                D0
                                E0
                                A
                                B
                                C
                                D
                                E
                                A1
                                B0
                                C14
                                D0
                                E0
                                A
                                B
                                C
                                D
                                E
                                A0
                                B12
                                C1
                                D0
                                E0
                                A
                                B
                                C
                                D
                                E
                                A0
                                B13
                                C1
                                D0
                                E0
                                A
                                B
                                C
                                D
                                E

                                DTU Compute

                                2122018Introduction to Medical Image Analysis14 DTU Compute Technical University of Denmark

                                Noise away ndash the median filter All pixels are set to the

                                median of its neighbourhood Noise pixels do not pollute

                                good pixels

                                172 169 171 168 0 169 172 173 168

                                170

                                169 168 0 170 172173 170 172 170

                                170

                                DTU Compute

                                2122018Introduction to Medical Image Analysis15 DTU Compute Technical University of Denmark

                                Noise removal ndash average filter

                                Scanned X-ray with salt and pepper noise

                                Average filter (3x3)

                                DTU Compute

                                2122018Introduction to Medical Image Analysis16 DTU Compute Technical University of Denmark

                                Noise removal ndash median filter

                                Scanned X-ray with salt and pepper noise

                                Median filter (3x3)

                                DTU Compute

                                2122018Introduction to Medical Image Analysis17 DTU Compute Technical University of Denmark

                                Image Filtering Creates a new filtered image Output pixel is computed based

                                on a neighbourhood in the input image

                                3 x 3 neighbourhoodndash Filter size 3 x 3ndash Kernel size 3 x 3ndash Mask size 3 x 3

                                Larger filters often usedndash Size

                                7 x 7ndash Number of elements

                                49

                                DTU Compute

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                                Median filterA) 25B) 90C) 198D) 86E) 103

                                0

                                13

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                                Rank filters Based on sorting the pixel

                                values in the neighbouring region

                                Minimum rank filterndash Darker image Noise problems

                                Maximum rank filterndash Lighter image Noise problems

                                Difference filterndash Enhances changes (edges)

                                0168 169 170 170 170172 172173

                                -

                                DTU Compute

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                                Median filter

                                A) 3B) 84C) 112D) 73E) 202

                                0

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                                Correlation What is it Two measurements

                                ndash Low correlationndash High correlation

                                High correlation means that there is a relation between the values

                                They look the same Correlation is a measure of

                                similarity

                                Low

                                High

                                Muscles

                                Mat

                                h Ski

                                lls

                                Muscles

                                Ben

                                ch P

                                ress

                                DTU Compute

                                2122018Introduction to Medical Image Analysis24 DTU Compute Technical University of Denmark

                                Why do we need similarity Image analysis is also about recognition of patterns Often an example pattern is used We need something to tell us if there is a high match

                                between our pattern and a part of the image

                                Example pattern

                                Image

                                Find matches

                                DTU Compute

                                2122018Introduction to Medical Image Analysis25 DTU Compute Technical University of Denmark

                                Correlation (1D)

                                1 1 2 2 1 1 2 2 1 1

                                1 2 1

                                45

                                41

                                1 1 + 2 1 + 1 2 = 5

                                Normalise

                                Kernel

                                Signal (1D image)

                                41

                                DTU Compute

                                2122018Introduction to Medical Image Analysis26 DTU Compute Technical University of Denmark

                                Correlation (1D)

                                1 1 2 2 1 1 2 2 1 1

                                1 2 1

                                45

                                47

                                47

                                45

                                45

                                47

                                47

                                45

                                41

                                DTU Compute

                                2122018Introduction to Medical Image Analysis27 DTU Compute Technical University of Denmark

                                Normalisation

                                1 1 2 2 1 1 2 2 1 1

                                1 2 1

                                45

                                41

                                1 1 + 2 1 + 1 2 = 5

                                Normalise41

                                bull The sum of the kernel elements is used

                                bull Keep the values in the same range as the input image

                                Sum is 4

                                DTU Compute

                                2122018Introduction to Medical Image Analysis28 DTU Compute Technical University of Denmark

                                Normalisation Normalisation factor

                                ndash Sum of kernel coefficients

                                1 2 1h(x)

                                119909119909

                                ℎ 119909119909 = 1 + 2 + 1

                                DTU Compute

                                2122018Introduction to Medical Image Analysis29 DTU Compute Technical University of Denmark

                                Correlation on images The filter is now 2D 1 1 1

                                1 1 1

                                1 1 1

                                0 2 4

                                1 2 2

                                1 6 3

                                1 2 12 5 3

                                2 1 3

                                1 3 1

                                2 2 2

                                0 1 3

                                1 2 0

                                2 1 4

                                1 0 1

                                912

                                91

                                Input OutputKernel

                                Kernel coefficients

                                DTU Compute

                                2122018Introduction to Medical Image Analysis30 DTU Compute Technical University of Denmark

                                Correlation on images

                                1 1 11 1 11 1 1

                                0 2 4

                                1 2 2

                                1 6 3

                                1 2 0

                                2 1 4

                                1 0 1

                                912

                                911

                                91

                                Input Output

                                1 3 1

                                2 2 2

                                0 1 3

                                1 2 12 5 3

                                2 1 3

                                DTU Compute

                                2122018Introduction to Medical Image Analysis31 DTU Compute Technical University of Denmark

                                Correlation on images

                                Input Output

                                The mask is moved row by row

                                No values at the border

                                0 2 4

                                1 2 2

                                1 6 3

                                1 2 0

                                2 1 4

                                1 0 1

                                1 3 1

                                2 2 2

                                0 1 3

                                1 2 12 5 3

                                2 1 3

                                DTU Compute

                                2122018Introduction to Medical Image Analysis32 DTU Compute Technical University of Denmark

                                1 2 1

                                1 3 1

                                1 2 1

                                -1 -2 -1

                                0 0 0

                                1 2 1

                                Draw your filter

                                DTU Compute

                                2122018Introduction to Medical Image Analysis33 DTU Compute Technical University of Denmark

                                Correlation on images ndash no normalisationA) 4B) 7C) 16D) 23E) 25

                                1 2 11 3 11 2 1

                                0 2 41 2 2

                                1 6 3

                                1 2 12 5 3

                                2 1 3

                                1 3 1

                                2 2 2

                                0 1 3

                                1 2 0

                                2 1 4

                                1 0 11 0

                                14

                                0 0

                                A B C D E

                                Chart1

                                1
                                0
                                14
                                0
                                0

                                Sheet1

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                                Correlation on images ndash no normalisation 2A) 010B) 3 3C) 6 2D) 10 15E) 11 32

                                13

                                0 0 0 0

                                A B C D E

                                -1 -2 -10 0 01 2 1

                                0 2 41 2 2

                                1 6 3

                                1 2 12 5 3

                                2 1 3

                                1 3 1

                                2 2 2

                                0 1 3

                                1 2 0

                                2 1 4

                                1 0 1

                                Chart1

                                13
                                0
                                0
                                0
                                0

                                Sheet1

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                                Mathematics of 2D Correlation

                                h

                                f

                                Correlation operator

                                1 2 11 3 11 2 1

                                0 2 4

                                1 2 2

                                1 6 3

                                1 2 1

                                2 5 3

                                2 1 3

                                1 3 1

                                2 2 2

                                0 1 3

                                1 2 0

                                2 1 4

                                1 0 1

                                119892119892 119909119909119910119910 = 119891119891 119909119909119910119910 ∘ ℎ(119909119909119910119910)

                                DTU Compute

                                2122018Introduction to Medical Image Analysis38 DTU Compute Technical University of Denmark

                                Mathematics of 2D Correlation

                                1 2 11 3 11 2 1

                                0 2 4

                                1 2 2

                                1 6 3

                                1 2 1

                                2 5 3

                                2 1 3

                                1 3 1

                                2 2 2

                                0 1 3

                                1 2 0

                                2 1 4

                                1 0 1

                                h

                                fh(00)

                                f(21)

                                Example g(21)

                                i = -1 j = -1

                                i = 1 j = 0

                                119892119892 119909119909119910119910 = 119895119895=minus119877119877

                                119877119877

                                119894119894=minus119877119877

                                119877119877

                                ℎ(119894119894 119895119895) 119891119891(119909119909 + 119894119894119910119910 + 119895119895)

                                DTU Compute

                                2122018Introduction to Medical Image Analysis39 DTU Compute Technical University of Denmark

                                Mathematics of 2D Correlation

                                1 2 11 3 11 2 1

                                0 2 4

                                1 2 2

                                1 6 3

                                1 2 1

                                2 5 3

                                2 1 3

                                1 3 1

                                2 2 2

                                0 1 3

                                1 2 0

                                2 1 4

                                1 0 1

                                h

                                f

                                119892119892 119909119909119910119910 = 119895119895=minus119877119877

                                119877119877

                                119894119894=minus119877119877

                                119877119877

                                ℎ(119894119894 119895119895) 119891119891(119909119909 + 119894119894119910119910 + 119895119895)

                                119892119892(119909119909119910119910 = 1 2 + 2 0 + 1 1 + 1 1 + 3 4 + 1 2 + 1 0 + 2 1 + 1 0

                                DTU Compute

                                2122018Introduction to Medical Image Analysis40 DTU Compute Technical University of Denmark

                                119892119892 119909119909 119910119910 = 119895119895=minus119877119877

                                119877119877

                                119894119894=minus119877119877

                                119877119877

                                ℎ(119894119894 119895119895) 119891119891(119909119909 + 119894119894119910119910 + 119895119895)

                                119892119892 22 =ℎ minus1minus1 sdot 119891119891 11 + ℎ 0minus1 sdot 119891119891 21 + ℎ 1minus1 sdot 119891119891 31 +ℎ minus10 sdot 119891119891 12 + ℎ 00 sdot 119891119891 22 + ℎ 10 sdot 119891119891 32 +ℎ minus11 sdot 119891119891 13 + ℎ 01 sdot 119891119891 23 + ℎ 11 sdot 119891119891 33

                                DTU Compute

                                2122018Introduction to Medical Image Analysis41 DTU Compute Technical University of Denmark

                                2D Kernel Normalisation

                                1 2 11 3 11 2 1

                                h

                                Normalisation factor

                                1 + 2 + 1 + 1 + 3 + 1 + 1 + 2 + 1 = 13

                                119909119909

                                119910119910

                                ℎ(119909119909119910119910)

                                DTU Compute

                                2122018Introduction to Medical Image Analysis42 DTU Compute Technical University of Denmark

                                CorrelationA) 50122B) 123001C) 11233D) 2550E) 90454

                                0 0 0 0

                                13

                                A B C D E

                                Chart1

                                0
                                0
                                0
                                0
                                13

                                Sheet1

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                                Smoothing filters

                                Also know as ndash Smoothing kernel Mean filter Low pass filter blurring

                                The simplest filter ndash Spatial low pass filterndash Removes high frequencies

                                Another mask ndash Gaussian filter

                                1 1 1

                                1 1 1

                                1 1 191

                                1 2 1

                                2 4 2

                                1 2 1161

                                Why Gaussian

                                DTU Compute

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                                Use of smoothing

                                3x3 7x7 11x11 15x15

                                DTU Compute

                                2122018Introduction to Medical Image Analysis46 DTU Compute Technical University of Denmark

                                Use of smoothing Large kernels smooth more Removes high frequency information Good at enhancing big structures

                                3x3 15x15

                                DTU Compute

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                                Mean filterA) 166B) 113C) 12D) 51E) 245

                                0 0 0 0

                                A B C D E

                                Chart1

                                12
                                0
                                0
                                0
                                0

                                Sheet1

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                                Border handling

                                0 2 41 2 2

                                1 6 3

                                1 2 12 5 3

                                2 1 3

                                1 3 1

                                2 2 2

                                0 1 3

                                1 2 0

                                2 1 4

                                1 0 1

                                Input Output

                                No values at the border

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                                2122018Introduction to Medical Image Analysis50 DTU Compute Technical University of Denmark

                                Border handling ndash extend the input

                                0 2 41 2 2

                                1 6 3

                                1 2 12 5 3

                                2 1 3

                                1 3 1

                                2 2 2

                                0 1 3

                                1 2 0

                                2 1 4

                                1 0 1

                                Input

                                0 0 0 0 000000

                                bull Zero padding ndash what happens

                                bull Zero is black ndash creates dark border around the image

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                                Correlation with zero paddingA) 5 8B) 12 16C) 13 3D) 15 21E) 17 12

                                1 2 11 3 11 2 1

                                0 2 41 2 2

                                1 6 3

                                1 2 12 5 3

                                2 1 3

                                1 3 1

                                2 2 2

                                0 1 3

                                1 2 0

                                2 1 4

                                1 0 1

                                0

                                13

                                0 0 0

                                A B C D E

                                Chart1

                                0
                                13
                                0
                                0
                                0

                                Sheet1

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                                Border handling ndash extend the input

                                0 2 41 2 2

                                1 6 3

                                1 2 12 5 3

                                2 1 3

                                1 3 1

                                2 2 2

                                0 1 3

                                1 2 0

                                2 1 4

                                1 0 1

                                Input

                                1 2 0 1 311211

                                bull Reflection

                                bull Normally better than zero padding

                                DTU Compute

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                                Template Matching Template

                                ndash Skabelon paring dansk Locates objects in images

                                Input

                                Template

                                Output Correlation image

                                DTU Compute

                                2122018Introduction to Medical Image Analysis55 DTU Compute Technical University of Denmark

                                Template Matching The correlation between the template and the input

                                image is computed for each pixel

                                Input

                                Template

                                Output Correlation image

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                                2122018Introduction to Medical Image Analysis56 DTU Compute Technical University of Denmark

                                Template Matching The pixel with the highest value is found in the

                                output imagendash Here is the highest correlation

                                Input

                                Template

                                Output Correlation image

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                                Template Matching This corresponds to the found pattern in the input

                                image

                                Input

                                Template

                                Output Correlation image

                                DTU Compute

                                2122018Introduction to Medical Image Analysis58 DTU Compute Technical University of Denmark

                                Problematic Correlation Correlation matching has problem with light areas ndash

                                why

                                Input (f)

                                Template (h)

                                Output Correlation imageFake max

                                Real max

                                Very High119892119892 119909119909119910119910 = 119895119895=minus119877119877

                                119877119877

                                119894119894=minus119877119877

                                119877119877

                                ℎ(119894119894 119895119895) 119891119891(119909119909 + 119894119894119910119910 + 119895119895)

                                DTU Compute

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                                Normalised Cross Correlation

                                Input (f)

                                Template (h)

                                Output Correlation image

                                Real max

                                NCC x y =Correlation

                                Length of image patch sdot Length of template

                                DTU Compute

                                2122018Introduction to Medical Image Analysis60 DTU Compute Technical University of Denmark

                                Length of template Vector length

                                ndash Put all pixel values into a vectorndash Compute the length of this vector

                                Describes the intensity of the templatendash Bright template has a large lengthndash Dark template has a small length

                                Template (h)

                                Length of template = 119895119895=minus119877119877

                                119877119877

                                119894119894=minus119877119877

                                119877119877

                                ℎ(119894119894 119895119895) ℎ(119894119894 119895119895)

                                DTU Compute

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                                Length of image patch Vector length based on pixel values in image patch Describes the intensity of the image patch

                                Template (h)

                                Input (f) with patch

                                DTU Compute

                                2122018Introduction to Medical Image Analysis62 DTU Compute Technical University of Denmark

                                Normalised Cross Correlation The length of the image patch and the length of

                                template normalise the NCC If the image is very bright the NCC will be ldquopulled

                                downrdquo

                                NCC x y =Correlation

                                Length of image patch sdot Length of template

                                DTU Compute

                                2122018Introduction to Medical Image Analysis63 DTU Compute Technical University of Denmark

                                Normalised Cross Correlation NCC will be between

                                ndash 0 No similarity between template and image patchndash 1 Template and image patch are identical

                                Input (f)

                                Template (h)

                                Output Correlation image

                                Real max

                                NCC x y =Correlation

                                Length of image patch sdot Length of template

                                DTU Compute

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                                Normalised Cross Correlation

                                A) 010B) 033C) 083D) 062E) 098

                                Der udfoslashres template matching med og normalized crosscorrelation (NCC) beregnes Hvad bliver NNC i den markerede pixel

                                1

                                2 2

                                3

                                2

                                A B C D E

                                Chart1

                                1
                                2
                                2
                                3
                                2

                                Sheet1

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                                Edges An edge is where there is a

                                high change in gray level values

                                Objects are often separated from the background by edgesGray level profile

                                DTU Compute

                                2122018Introduction to Medical Image Analysis67 DTU Compute Technical University of Denmark

                                Edges The profile as a function f(d) What value is high when there

                                is an edgendash The slope of fndash The slope of the tangent at d

                                f(d)

                                119891119891prime(119889119889)

                                DTU Compute

                                2122018Introduction to Medical Image Analysis68 DTU Compute Technical University of Denmark

                                Finite Difference Definition of slope

                                Approximation

                                Simpler approximationh = 1

                                119891119891prime 119889119889 = limℎrarr0

                                119891119891 119889119889 + ℎ minus 119891119891(119889119889)ℎ

                                119891119891prime 119889119889 asymp119891119891 119889119889 + ℎ minus 119891119891(119889119889)

                                ℎ

                                119891119891prime 119889119889 asymp 119891119891 119889119889 + 1 minus 119891119891(119889119889)

                                DTU Compute

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                                Edges Discrete approximation of frsquo(d) Can be implemented as a filter

                                -1 0 1

                                f(d-2) f(d-1) f(d) f(d+1) f(d+2) f(d+3)

                                f(d)

                                119891119891prime 119889119889 asymp 119891119891 119889119889 + 1 minus 119891119891(119889119889)

                                DTU Compute

                                2122018Introduction to Medical Image Analysis70 DTU Compute Technical University of Denmark

                                Edges in 2D Changes in gray level values

                                ndash Image gradientndash Gradient is the 2D derivative of a 2D function f(xy)ndash Equal to the slope of the imagendash A steep slope is equal to an edge

                                120571120571119891119891 119909119909119910119910 = 119866(119892119892119909119909119892119892119910119910)

                                DTU Compute

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                                Edge filter kernel The Prewitt filter is a typical

                                edge filter Output image has high

                                values where there are edges

                                -1 0 1

                                -1 0 1

                                -1 0 1Vertical Prewitt filter

                                DTU Compute

                                2122018Introduction to Medical Image Analysis72 DTU Compute Technical University of Denmark

                                Prewitt filter

                                Original Prewitt Prewitt

                                Hot colormapSmooth 15x15

                                Smooth 15x15

                                Prewitt

                                DTU Compute

                                2122018Introduction to Medical Image Analysis73 DTU Compute Technical University of Denmark

                                Edge detection Edge filter

                                ndash Prewitt for example Thresholding

                                ndash Separate edges from non-edges

                                Output is binary imagendash Edges are white

                                DTU Compute

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                                Edge filtering

                                A) MeanB) Horizontal SobelC) Vertical PrewittD) Horisontal PrewittE) Median

                                Der udfoslashres en filtrering (correlation) med et filter paring billedet Der bruges ikke coefficient normalization Den filtrerede vaeligrdi i den markerede pixel bliver -119 Hvilket et 3x3 filter blev benyttet

                                0

                                8

                                1 10

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                                02511 - Niveau af dagens emne forelaeligsingA) Meget letB) LetC) PassendeD) SvaeligrtE) Meget svaeligrt

                                23

                                6

                                10

                                A B C D E

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                                02512 - Niveau af dagens emne forelaeligsingA) Meget letB) LetC) PassendeD) SvaeligrtE) Meget svaeligrt

                                0 0

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                                02511 - Mit eget udbytte af dagenA) Jeg har laeligrt meget lidtB) Lidt laeligringC) PassendeD) God laeligringE) Jeg har laeligrt meget

                                0 0

                                2

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                                02512 - Mit eget udbytte af dagenA) Jeg har laeligrt meget lidtB) Lidt laeligringC) PassendeD) God laeligringE) Jeg har laeligrt meget

                                2

                                1

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                                02511 - Sidste uges oslashvelser (pixelwiseoperations)A) Meget letteB) LetteC) PassendeD) SvaeligreE) Meget svaeligre

                                0 0

                                1

                                4

                                1

                                A B C D E

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                                1
                                4
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                                02512 - Sidste uges oslashvelser (pixelwiseoperations)A) Meget letteB) LetteC) PassendeD) SvaeligreE) Meget svaeligre

                                3

                                0

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                                Denne uges brug af clickersA) click click click ndash jeg bliver

                                sindssygB) For meget clickC) PassendeD) Jeg vil gerne have lidt mereE) Jeg kan ikrsquo faring nok

                                0 0

                                5

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                                6

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                                What can you do after today Describe the difference between point processing and neighbourhood

                                processing Compute a rank filtered image using the min max median and

                                difference rank filters Compute a mean filtered image Decide if median or average filtering should be used for noise removal Choose the appropriate image border handling based on a given input

                                image Implement and apply template matching Compute the normalised cross correlation and explain why it should be

                                used Apply given image filter kernels to images Use edge filters on images Describe finite difference approximation of image gradients Describe the concept of edge detection

                                DTU Compute

                                2122018Introduction to Medical Image Analysis84 DTU Compute Technical University of Denmark

                                Oslashvelsesrapport over oslashvelse 4 - 02511 Oslashvelser taeligller cirka 30 af karakteren Skal afleveres senest den 7 marts kl 2359 Kan afleveres af 1 eller 2 personer

                                ndash I skal skrive jeres egen oslashvelsesrapportndash Brug mindst et af jeres egne billeder

                                Afleveres som PDF Lad vaeligre med at kopiere opgaveteksten ind i jeres

                                opgave Put Matlab kode i et Appendix og henvis fra teksten Eksempel rapport over oslashvelse findes paring

                                hjemmesiden under eksamen

                                DTU Compute

                                2122018Introduction to Medical Image Analysis85 DTU Compute Technical University of Denmark

                                Exercises

                                • Introduction to Medical Image Analysis
                                • Lecture 4 ndash Neighbourhood Processing
                                • What can you do after today
                                • Point processing
                                • Point processing
                                • Neighbourhood processing
                                • Use of filtering
                                • Salt and pepper noise
                                • Salt and pepper noise
                                • What is so special about noise
                                • Noise ndash go away
                                • What is the median Value
                                • The median value
                                • Noise away ndash the median filter
                                • Noise removal ndash average filter
                                • Noise removal ndash median filter
                                • Image Filtering
                                • Median filter
                                • Rank filters
                                • Median filter
                                • Correlation
                                • Why do we need similarity
                                • Correlation (1D)
                                • Correlation (1D)
                                • Normalisation
                                • Normalisation
                                • Correlation on images
                                • Correlation on images
                                • Correlation on images
                                • Draw your filter
                                • Correlation on images ndash no normalisation
                                • Correlation on images ndash no normalisation 2
                                • Mathematics of 2D Correlation
                                • Mathematics of 2D Correlation
                                • Mathematics of 2D Correlation
                                • Slide Number 40
                                • 2D Kernel Normalisation
                                • Correlation
                                • Smoothing filters
                                • Use of smoothing
                                • Use of smoothing
                                • Mean filter
                                • Border handling
                                • Border handling ndash extend the input
                                • Correlation with zero padding
                                • Border handling ndash extend the input
                                • Template Matching
                                • Template Matching
                                • Template Matching
                                • Template Matching
                                • Problematic Correlation
                                • Normalised Cross Correlation
                                • Length of template
                                • Length of image patch
                                • Normalised Cross Correlation
                                • Normalised Cross Correlation
                                • Normalised Cross Correlation
                                • Edges
                                • Edges
                                • Finite Difference
                                • Edges
                                • Edges in 2D
                                • Edge filter kernel
                                • Prewitt filter
                                • Edge detection
                                • Edge filtering
                                • 02511 - Niveau af dagens emne forelaeligsing
                                • 02512 - Niveau af dagens emne forelaeligsing
                                • 02511 - Mit eget udbytte af dagen
                                • 02512 - Mit eget udbytte af dagen
                                • 02511 - Sidste uges oslashvelser (pixelwise operations)
                                • 02512 - Sidste uges oslashvelser (pixelwise operations)
                                • Denne uges brug af clickers
                                • What can you do after today
                                • Oslashvelsesrapport over oslashvelse 4 - 02511
                                • Exercises
                                  A0
                                  B0
                                  C5
                                  D0
                                  E6
                                  A
                                  B
                                  C
                                  D
                                  E
                                  A3
                                  B0
                                  C3
                                  D0
                                  E0
                                  A
                                  B
                                  C
                                  D
                                  E
                                  A0
                                  B0
                                  C1
                                  D4
                                  E1
                                  A
                                  B
                                  C
                                  D
                                  E
                                  A2
                                  B1
                                  C3
                                  D2
                                  E0
                                  A
                                  B
                                  C
                                  D
                                  E
                                  A0
                                  B0
                                  C2
                                  D6
                                  E0
                                  A
                                  B
                                  C
                                  D
                                  E
                                  A0
                                  B0
                                  C1
                                  D0
                                  E0
                                  A
                                  B
                                  C
                                  D
                                  E
                                  A2
                                  B3
                                  C6
                                  D1
                                  E0
                                  A
                                  B
                                  C
                                  D
                                  E
                                  A0
                                  B8
                                  C1
                                  D1
                                  E0
                                  A
                                  B
                                  C
                                  D
                                  E
                                  A1
                                  B2
                                  C2
                                  D3
                                  E2
                                  A
                                  B
                                  C
                                  D
                                  E
                                  A0
                                  B13
                                  C0
                                  D0
                                  E0
                                  A
                                  B
                                  C
                                  D
                                  E
                                  A12
                                  B0
                                  C0
                                  D0
                                  E0
                                  A
                                  B
                                  C
                                  D
                                  E
                                  A0
                                  B0
                                  C0
                                  D0
                                  E13
                                  A
                                  B
                                  C
                                  D
                                  E
                                  A13
                                  B0
                                  C0
                                  D0
                                  E0
                                  A
                                  B
                                  C
                                  D
                                  E
                                  A1
                                  B0
                                  C14
                                  D0
                                  E0
                                  A
                                  B
                                  C
                                  D
                                  E
                                  A0
                                  B12
                                  C1
                                  D0
                                  E0
                                  A
                                  B
                                  C
                                  D
                                  E
                                  A0
                                  B13
                                  C1
                                  D0
                                  E0
                                  A
                                  B
                                  C
                                  D
                                  E

                                  DTU Compute

                                  2122018Introduction to Medical Image Analysis15 DTU Compute Technical University of Denmark

                                  Noise removal ndash average filter

                                  Scanned X-ray with salt and pepper noise

                                  Average filter (3x3)

                                  DTU Compute

                                  2122018Introduction to Medical Image Analysis16 DTU Compute Technical University of Denmark

                                  Noise removal ndash median filter

                                  Scanned X-ray with salt and pepper noise

                                  Median filter (3x3)

                                  DTU Compute

                                  2122018Introduction to Medical Image Analysis17 DTU Compute Technical University of Denmark

                                  Image Filtering Creates a new filtered image Output pixel is computed based

                                  on a neighbourhood in the input image

                                  3 x 3 neighbourhoodndash Filter size 3 x 3ndash Kernel size 3 x 3ndash Mask size 3 x 3

                                  Larger filters often usedndash Size

                                  7 x 7ndash Number of elements

                                  49

                                  DTU Compute

                                  2122018Introduction to Medical Image Analysis18 DTU Compute Technical University of Denmark

                                  Median filterA) 25B) 90C) 198D) 86E) 103

                                  0

                                  13

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                                  A B C D E

                                  Chart1

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                                  Rank filters Based on sorting the pixel

                                  values in the neighbouring region

                                  Minimum rank filterndash Darker image Noise problems

                                  Maximum rank filterndash Lighter image Noise problems

                                  Difference filterndash Enhances changes (edges)

                                  0168 169 170 170 170172 172173

                                  -

                                  DTU Compute

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                                  Median filter

                                  A) 3B) 84C) 112D) 73E) 202

                                  0

                                  12

                                  10 0

                                  A B C D E

                                  Chart1

                                  0
                                  12
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                                  Correlation What is it Two measurements

                                  ndash Low correlationndash High correlation

                                  High correlation means that there is a relation between the values

                                  They look the same Correlation is a measure of

                                  similarity

                                  Low

                                  High

                                  Muscles

                                  Mat

                                  h Ski

                                  lls

                                  Muscles

                                  Ben

                                  ch P

                                  ress

                                  DTU Compute

                                  2122018Introduction to Medical Image Analysis24 DTU Compute Technical University of Denmark

                                  Why do we need similarity Image analysis is also about recognition of patterns Often an example pattern is used We need something to tell us if there is a high match

                                  between our pattern and a part of the image

                                  Example pattern

                                  Image

                                  Find matches

                                  DTU Compute

                                  2122018Introduction to Medical Image Analysis25 DTU Compute Technical University of Denmark

                                  Correlation (1D)

                                  1 1 2 2 1 1 2 2 1 1

                                  1 2 1

                                  45

                                  41

                                  1 1 + 2 1 + 1 2 = 5

                                  Normalise

                                  Kernel

                                  Signal (1D image)

                                  41

                                  DTU Compute

                                  2122018Introduction to Medical Image Analysis26 DTU Compute Technical University of Denmark

                                  Correlation (1D)

                                  1 1 2 2 1 1 2 2 1 1

                                  1 2 1

                                  45

                                  47

                                  47

                                  45

                                  45

                                  47

                                  47

                                  45

                                  41

                                  DTU Compute

                                  2122018Introduction to Medical Image Analysis27 DTU Compute Technical University of Denmark

                                  Normalisation

                                  1 1 2 2 1 1 2 2 1 1

                                  1 2 1

                                  45

                                  41

                                  1 1 + 2 1 + 1 2 = 5

                                  Normalise41

                                  bull The sum of the kernel elements is used

                                  bull Keep the values in the same range as the input image

                                  Sum is 4

                                  DTU Compute

                                  2122018Introduction to Medical Image Analysis28 DTU Compute Technical University of Denmark

                                  Normalisation Normalisation factor

                                  ndash Sum of kernel coefficients

                                  1 2 1h(x)

                                  119909119909

                                  ℎ 119909119909 = 1 + 2 + 1

                                  DTU Compute

                                  2122018Introduction to Medical Image Analysis29 DTU Compute Technical University of Denmark

                                  Correlation on images The filter is now 2D 1 1 1

                                  1 1 1

                                  1 1 1

                                  0 2 4

                                  1 2 2

                                  1 6 3

                                  1 2 12 5 3

                                  2 1 3

                                  1 3 1

                                  2 2 2

                                  0 1 3

                                  1 2 0

                                  2 1 4

                                  1 0 1

                                  912

                                  91

                                  Input OutputKernel

                                  Kernel coefficients

                                  DTU Compute

                                  2122018Introduction to Medical Image Analysis30 DTU Compute Technical University of Denmark

                                  Correlation on images

                                  1 1 11 1 11 1 1

                                  0 2 4

                                  1 2 2

                                  1 6 3

                                  1 2 0

                                  2 1 4

                                  1 0 1

                                  912

                                  911

                                  91

                                  Input Output

                                  1 3 1

                                  2 2 2

                                  0 1 3

                                  1 2 12 5 3

                                  2 1 3

                                  DTU Compute

                                  2122018Introduction to Medical Image Analysis31 DTU Compute Technical University of Denmark

                                  Correlation on images

                                  Input Output

                                  The mask is moved row by row

                                  No values at the border

                                  0 2 4

                                  1 2 2

                                  1 6 3

                                  1 2 0

                                  2 1 4

                                  1 0 1

                                  1 3 1

                                  2 2 2

                                  0 1 3

                                  1 2 12 5 3

                                  2 1 3

                                  DTU Compute

                                  2122018Introduction to Medical Image Analysis32 DTU Compute Technical University of Denmark

                                  1 2 1

                                  1 3 1

                                  1 2 1

                                  -1 -2 -1

                                  0 0 0

                                  1 2 1

                                  Draw your filter

                                  DTU Compute

                                  2122018Introduction to Medical Image Analysis33 DTU Compute Technical University of Denmark

                                  Correlation on images ndash no normalisationA) 4B) 7C) 16D) 23E) 25

                                  1 2 11 3 11 2 1

                                  0 2 41 2 2

                                  1 6 3

                                  1 2 12 5 3

                                  2 1 3

                                  1 3 1

                                  2 2 2

                                  0 1 3

                                  1 2 0

                                  2 1 4

                                  1 0 11 0

                                  14

                                  0 0

                                  A B C D E

                                  Chart1

                                  1
                                  0
                                  14
                                  0
                                  0

                                  Sheet1

                                  DTU Compute

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                                  Correlation on images ndash no normalisation 2A) 010B) 3 3C) 6 2D) 10 15E) 11 32

                                  13

                                  0 0 0 0

                                  A B C D E

                                  -1 -2 -10 0 01 2 1

                                  0 2 41 2 2

                                  1 6 3

                                  1 2 12 5 3

                                  2 1 3

                                  1 3 1

                                  2 2 2

                                  0 1 3

                                  1 2 0

                                  2 1 4

                                  1 0 1

                                  Chart1

                                  13
                                  0
                                  0
                                  0
                                  0

                                  Sheet1

                                  DTU Compute

                                  2122018Introduction to Medical Image Analysis37 DTU Compute Technical University of Denmark

                                  Mathematics of 2D Correlation

                                  h

                                  f

                                  Correlation operator

                                  1 2 11 3 11 2 1

                                  0 2 4

                                  1 2 2

                                  1 6 3

                                  1 2 1

                                  2 5 3

                                  2 1 3

                                  1 3 1

                                  2 2 2

                                  0 1 3

                                  1 2 0

                                  2 1 4

                                  1 0 1

                                  119892119892 119909119909119910119910 = 119891119891 119909119909119910119910 ∘ ℎ(119909119909119910119910)

                                  DTU Compute

                                  2122018Introduction to Medical Image Analysis38 DTU Compute Technical University of Denmark

                                  Mathematics of 2D Correlation

                                  1 2 11 3 11 2 1

                                  0 2 4

                                  1 2 2

                                  1 6 3

                                  1 2 1

                                  2 5 3

                                  2 1 3

                                  1 3 1

                                  2 2 2

                                  0 1 3

                                  1 2 0

                                  2 1 4

                                  1 0 1

                                  h

                                  fh(00)

                                  f(21)

                                  Example g(21)

                                  i = -1 j = -1

                                  i = 1 j = 0

                                  119892119892 119909119909119910119910 = 119895119895=minus119877119877

                                  119877119877

                                  119894119894=minus119877119877

                                  119877119877

                                  ℎ(119894119894 119895119895) 119891119891(119909119909 + 119894119894119910119910 + 119895119895)

                                  DTU Compute

                                  2122018Introduction to Medical Image Analysis39 DTU Compute Technical University of Denmark

                                  Mathematics of 2D Correlation

                                  1 2 11 3 11 2 1

                                  0 2 4

                                  1 2 2

                                  1 6 3

                                  1 2 1

                                  2 5 3

                                  2 1 3

                                  1 3 1

                                  2 2 2

                                  0 1 3

                                  1 2 0

                                  2 1 4

                                  1 0 1

                                  h

                                  f

                                  119892119892 119909119909119910119910 = 119895119895=minus119877119877

                                  119877119877

                                  119894119894=minus119877119877

                                  119877119877

                                  ℎ(119894119894 119895119895) 119891119891(119909119909 + 119894119894119910119910 + 119895119895)

                                  119892119892(119909119909119910119910 = 1 2 + 2 0 + 1 1 + 1 1 + 3 4 + 1 2 + 1 0 + 2 1 + 1 0

                                  DTU Compute

                                  2122018Introduction to Medical Image Analysis40 DTU Compute Technical University of Denmark

                                  119892119892 119909119909 119910119910 = 119895119895=minus119877119877

                                  119877119877

                                  119894119894=minus119877119877

                                  119877119877

                                  ℎ(119894119894 119895119895) 119891119891(119909119909 + 119894119894119910119910 + 119895119895)

                                  119892119892 22 =ℎ minus1minus1 sdot 119891119891 11 + ℎ 0minus1 sdot 119891119891 21 + ℎ 1minus1 sdot 119891119891 31 +ℎ minus10 sdot 119891119891 12 + ℎ 00 sdot 119891119891 22 + ℎ 10 sdot 119891119891 32 +ℎ minus11 sdot 119891119891 13 + ℎ 01 sdot 119891119891 23 + ℎ 11 sdot 119891119891 33

                                  DTU Compute

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                                  2D Kernel Normalisation

                                  1 2 11 3 11 2 1

                                  h

                                  Normalisation factor

                                  1 + 2 + 1 + 1 + 3 + 1 + 1 + 2 + 1 = 13

                                  119909119909

                                  119910119910

                                  ℎ(119909119909119910119910)

                                  DTU Compute

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                                  CorrelationA) 50122B) 123001C) 11233D) 2550E) 90454

                                  0 0 0 0

                                  13

                                  A B C D E

                                  Chart1

                                  0
                                  0
                                  0
                                  0
                                  13

                                  Sheet1

                                  DTU Compute

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                                  Smoothing filters

                                  Also know as ndash Smoothing kernel Mean filter Low pass filter blurring

                                  The simplest filter ndash Spatial low pass filterndash Removes high frequencies

                                  Another mask ndash Gaussian filter

                                  1 1 1

                                  1 1 1

                                  1 1 191

                                  1 2 1

                                  2 4 2

                                  1 2 1161

                                  Why Gaussian

                                  DTU Compute

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                                  Use of smoothing

                                  3x3 7x7 11x11 15x15

                                  DTU Compute

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                                  Use of smoothing Large kernels smooth more Removes high frequency information Good at enhancing big structures

                                  3x3 15x15

                                  DTU Compute

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                                  Mean filterA) 166B) 113C) 12D) 51E) 245

                                  0 0 0 0

                                  A B C D E

                                  Chart1

                                  12
                                  0
                                  0
                                  0
                                  0

                                  Sheet1

                                  DTU Compute

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                                  Border handling

                                  0 2 41 2 2

                                  1 6 3

                                  1 2 12 5 3

                                  2 1 3

                                  1 3 1

                                  2 2 2

                                  0 1 3

                                  1 2 0

                                  2 1 4

                                  1 0 1

                                  Input Output

                                  No values at the border

                                  DTU Compute

                                  2122018Introduction to Medical Image Analysis50 DTU Compute Technical University of Denmark

                                  Border handling ndash extend the input

                                  0 2 41 2 2

                                  1 6 3

                                  1 2 12 5 3

                                  2 1 3

                                  1 3 1

                                  2 2 2

                                  0 1 3

                                  1 2 0

                                  2 1 4

                                  1 0 1

                                  Input

                                  0 0 0 0 000000

                                  bull Zero padding ndash what happens

                                  bull Zero is black ndash creates dark border around the image

                                  DTU Compute

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                                  Correlation with zero paddingA) 5 8B) 12 16C) 13 3D) 15 21E) 17 12

                                  1 2 11 3 11 2 1

                                  0 2 41 2 2

                                  1 6 3

                                  1 2 12 5 3

                                  2 1 3

                                  1 3 1

                                  2 2 2

                                  0 1 3

                                  1 2 0

                                  2 1 4

                                  1 0 1

                                  0

                                  13

                                  0 0 0

                                  A B C D E

                                  Chart1

                                  0
                                  13
                                  0
                                  0
                                  0

                                  Sheet1

                                  DTU Compute

                                  2122018Introduction to Medical Image Analysis53 DTU Compute Technical University of Denmark

                                  Border handling ndash extend the input

                                  0 2 41 2 2

                                  1 6 3

                                  1 2 12 5 3

                                  2 1 3

                                  1 3 1

                                  2 2 2

                                  0 1 3

                                  1 2 0

                                  2 1 4

                                  1 0 1

                                  Input

                                  1 2 0 1 311211

                                  bull Reflection

                                  bull Normally better than zero padding

                                  DTU Compute

                                  2122018Introduction to Medical Image Analysis54 DTU Compute Technical University of Denmark

                                  Template Matching Template

                                  ndash Skabelon paring dansk Locates objects in images

                                  Input

                                  Template

                                  Output Correlation image

                                  DTU Compute

                                  2122018Introduction to Medical Image Analysis55 DTU Compute Technical University of Denmark

                                  Template Matching The correlation between the template and the input

                                  image is computed for each pixel

                                  Input

                                  Template

                                  Output Correlation image

                                  DTU Compute

                                  2122018Introduction to Medical Image Analysis56 DTU Compute Technical University of Denmark

                                  Template Matching The pixel with the highest value is found in the

                                  output imagendash Here is the highest correlation

                                  Input

                                  Template

                                  Output Correlation image

                                  DTU Compute

                                  2122018Introduction to Medical Image Analysis57 DTU Compute Technical University of Denmark

                                  Template Matching This corresponds to the found pattern in the input

                                  image

                                  Input

                                  Template

                                  Output Correlation image

                                  DTU Compute

                                  2122018Introduction to Medical Image Analysis58 DTU Compute Technical University of Denmark

                                  Problematic Correlation Correlation matching has problem with light areas ndash

                                  why

                                  Input (f)

                                  Template (h)

                                  Output Correlation imageFake max

                                  Real max

                                  Very High119892119892 119909119909119910119910 = 119895119895=minus119877119877

                                  119877119877

                                  119894119894=minus119877119877

                                  119877119877

                                  ℎ(119894119894 119895119895) 119891119891(119909119909 + 119894119894119910119910 + 119895119895)

                                  DTU Compute

                                  2122018Introduction to Medical Image Analysis59 DTU Compute Technical University of Denmark

                                  Normalised Cross Correlation

                                  Input (f)

                                  Template (h)

                                  Output Correlation image

                                  Real max

                                  NCC x y =Correlation

                                  Length of image patch sdot Length of template

                                  DTU Compute

                                  2122018Introduction to Medical Image Analysis60 DTU Compute Technical University of Denmark

                                  Length of template Vector length

                                  ndash Put all pixel values into a vectorndash Compute the length of this vector

                                  Describes the intensity of the templatendash Bright template has a large lengthndash Dark template has a small length

                                  Template (h)

                                  Length of template = 119895119895=minus119877119877

                                  119877119877

                                  119894119894=minus119877119877

                                  119877119877

                                  ℎ(119894119894 119895119895) ℎ(119894119894 119895119895)

                                  DTU Compute

                                  2122018Introduction to Medical Image Analysis61 DTU Compute Technical University of Denmark

                                  Length of image patch Vector length based on pixel values in image patch Describes the intensity of the image patch

                                  Template (h)

                                  Input (f) with patch

                                  DTU Compute

                                  2122018Introduction to Medical Image Analysis62 DTU Compute Technical University of Denmark

                                  Normalised Cross Correlation The length of the image patch and the length of

                                  template normalise the NCC If the image is very bright the NCC will be ldquopulled

                                  downrdquo

                                  NCC x y =Correlation

                                  Length of image patch sdot Length of template

                                  DTU Compute

                                  2122018Introduction to Medical Image Analysis63 DTU Compute Technical University of Denmark

                                  Normalised Cross Correlation NCC will be between

                                  ndash 0 No similarity between template and image patchndash 1 Template and image patch are identical

                                  Input (f)

                                  Template (h)

                                  Output Correlation image

                                  Real max

                                  NCC x y =Correlation

                                  Length of image patch sdot Length of template

                                  DTU Compute

                                  2122018Introduction to Medical Image Analysis64 DTU Compute Technical University of Denmark

                                  Normalised Cross Correlation

                                  A) 010B) 033C) 083D) 062E) 098

                                  Der udfoslashres template matching med og normalized crosscorrelation (NCC) beregnes Hvad bliver NNC i den markerede pixel

                                  1

                                  2 2

                                  3

                                  2

                                  A B C D E

                                  Chart1

                                  1
                                  2
                                  2
                                  3
                                  2

                                  Sheet1

                                  DTU Compute

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                                  Edges An edge is where there is a

                                  high change in gray level values

                                  Objects are often separated from the background by edgesGray level profile

                                  DTU Compute

                                  2122018Introduction to Medical Image Analysis67 DTU Compute Technical University of Denmark

                                  Edges The profile as a function f(d) What value is high when there

                                  is an edgendash The slope of fndash The slope of the tangent at d

                                  f(d)

                                  119891119891prime(119889119889)

                                  DTU Compute

                                  2122018Introduction to Medical Image Analysis68 DTU Compute Technical University of Denmark

                                  Finite Difference Definition of slope

                                  Approximation

                                  Simpler approximationh = 1

                                  119891119891prime 119889119889 = limℎrarr0

                                  119891119891 119889119889 + ℎ minus 119891119891(119889119889)ℎ

                                  119891119891prime 119889119889 asymp119891119891 119889119889 + ℎ minus 119891119891(119889119889)

                                  ℎ

                                  119891119891prime 119889119889 asymp 119891119891 119889119889 + 1 minus 119891119891(119889119889)

                                  DTU Compute

                                  2122018Introduction to Medical Image Analysis69 DTU Compute Technical University of Denmark

                                  Edges Discrete approximation of frsquo(d) Can be implemented as a filter

                                  -1 0 1

                                  f(d-2) f(d-1) f(d) f(d+1) f(d+2) f(d+3)

                                  f(d)

                                  119891119891prime 119889119889 asymp 119891119891 119889119889 + 1 minus 119891119891(119889119889)

                                  DTU Compute

                                  2122018Introduction to Medical Image Analysis70 DTU Compute Technical University of Denmark

                                  Edges in 2D Changes in gray level values

                                  ndash Image gradientndash Gradient is the 2D derivative of a 2D function f(xy)ndash Equal to the slope of the imagendash A steep slope is equal to an edge

                                  120571120571119891119891 119909119909119910119910 = 119866(119892119892119909119909119892119892119910119910)

                                  DTU Compute

                                  2122018Introduction to Medical Image Analysis71 DTU Compute Technical University of Denmark

                                  Edge filter kernel The Prewitt filter is a typical

                                  edge filter Output image has high

                                  values where there are edges

                                  -1 0 1

                                  -1 0 1

                                  -1 0 1Vertical Prewitt filter

                                  DTU Compute

                                  2122018Introduction to Medical Image Analysis72 DTU Compute Technical University of Denmark

                                  Prewitt filter

                                  Original Prewitt Prewitt

                                  Hot colormapSmooth 15x15

                                  Smooth 15x15

                                  Prewitt

                                  DTU Compute

                                  2122018Introduction to Medical Image Analysis73 DTU Compute Technical University of Denmark

                                  Edge detection Edge filter

                                  ndash Prewitt for example Thresholding

                                  ndash Separate edges from non-edges

                                  Output is binary imagendash Edges are white

                                  DTU Compute

                                  2122018Introduction to Medical Image Analysis74 DTU Compute Technical University of Denmark

                                  Edge filtering

                                  A) MeanB) Horizontal SobelC) Vertical PrewittD) Horisontal PrewittE) Median

                                  Der udfoslashres en filtrering (correlation) med et filter paring billedet Der bruges ikke coefficient normalization Den filtrerede vaeligrdi i den markerede pixel bliver -119 Hvilket et 3x3 filter blev benyttet

                                  0

                                  8

                                  1 10

                                  A B C D E

                                  Chart1

                                  0
                                  8
                                  1
                                  1
                                  0

                                  Sheet1

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                                  02511 - Niveau af dagens emne forelaeligsingA) Meget letB) LetC) PassendeD) SvaeligrtE) Meget svaeligrt

                                  23

                                  6

                                  10

                                  A B C D E

                                  Chart1

                                  2
                                  3
                                  6
                                  1
                                  0

                                  Sheet1

                                  DTU Compute

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                                  02512 - Niveau af dagens emne forelaeligsingA) Meget letB) LetC) PassendeD) SvaeligrtE) Meget svaeligrt

                                  0 0

                                  1

                                  0 0

                                  A B C D E

                                  Chart1

                                  0
                                  0
                                  1
                                  0
                                  0

                                  Sheet1

                                  DTU Compute

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                                  02511 - Mit eget udbytte af dagenA) Jeg har laeligrt meget lidtB) Lidt laeligringC) PassendeD) God laeligringE) Jeg har laeligrt meget

                                  0 0

                                  2

                                  6

                                  0

                                  A B C D E

                                  Chart1

                                  0
                                  0
                                  2
                                  6
                                  0

                                  Sheet1

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                                  02512 - Mit eget udbytte af dagenA) Jeg har laeligrt meget lidtB) Lidt laeligringC) PassendeD) God laeligringE) Jeg har laeligrt meget

                                  2

                                  1

                                  3

                                  2

                                  0

                                  A B C D E

                                  Chart1

                                  2
                                  1
                                  3
                                  2
                                  0

                                  Sheet1

                                  DTU Compute

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                                  02511 - Sidste uges oslashvelser (pixelwiseoperations)A) Meget letteB) LetteC) PassendeD) SvaeligreE) Meget svaeligre

                                  0 0

                                  1

                                  4

                                  1

                                  A B C D E

                                  Chart1

                                  0
                                  0
                                  1
                                  4
                                  1

                                  Sheet1

                                  DTU Compute

                                  2122018Introduction to Medical Image Analysis81 DTU Compute Technical University of Denmark

                                  02512 - Sidste uges oslashvelser (pixelwiseoperations)A) Meget letteB) LetteC) PassendeD) SvaeligreE) Meget svaeligre

                                  3

                                  0

                                  3

                                  0 0

                                  A B C D E

                                  Chart1

                                  3
                                  0
                                  3
                                  0
                                  0

                                  Sheet1

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                                  2122018Introduction to Medical Image Analysis82 DTU Compute Technical University of Denmark

                                  Denne uges brug af clickersA) click click click ndash jeg bliver

                                  sindssygB) For meget clickC) PassendeD) Jeg vil gerne have lidt mereE) Jeg kan ikrsquo faring nok

                                  0 0

                                  5

                                  0

                                  6

                                  A B C D E

                                  Chart1

                                  0
                                  0
                                  5
                                  0
                                  6

                                  Sheet1

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                                  What can you do after today Describe the difference between point processing and neighbourhood

                                  processing Compute a rank filtered image using the min max median and

                                  difference rank filters Compute a mean filtered image Decide if median or average filtering should be used for noise removal Choose the appropriate image border handling based on a given input

                                  image Implement and apply template matching Compute the normalised cross correlation and explain why it should be

                                  used Apply given image filter kernels to images Use edge filters on images Describe finite difference approximation of image gradients Describe the concept of edge detection

                                  DTU Compute

                                  2122018Introduction to Medical Image Analysis84 DTU Compute Technical University of Denmark

                                  Oslashvelsesrapport over oslashvelse 4 - 02511 Oslashvelser taeligller cirka 30 af karakteren Skal afleveres senest den 7 marts kl 2359 Kan afleveres af 1 eller 2 personer

                                  ndash I skal skrive jeres egen oslashvelsesrapportndash Brug mindst et af jeres egne billeder

                                  Afleveres som PDF Lad vaeligre med at kopiere opgaveteksten ind i jeres

                                  opgave Put Matlab kode i et Appendix og henvis fra teksten Eksempel rapport over oslashvelse findes paring

                                  hjemmesiden under eksamen

                                  DTU Compute

                                  2122018Introduction to Medical Image Analysis85 DTU Compute Technical University of Denmark

                                  Exercises

                                  • Introduction to Medical Image Analysis
                                  • Lecture 4 ndash Neighbourhood Processing
                                  • What can you do after today
                                  • Point processing
                                  • Point processing
                                  • Neighbourhood processing
                                  • Use of filtering
                                  • Salt and pepper noise
                                  • Salt and pepper noise
                                  • What is so special about noise
                                  • Noise ndash go away
                                  • What is the median Value
                                  • The median value
                                  • Noise away ndash the median filter
                                  • Noise removal ndash average filter
                                  • Noise removal ndash median filter
                                  • Image Filtering
                                  • Median filter
                                  • Rank filters
                                  • Median filter
                                  • Correlation
                                  • Why do we need similarity
                                  • Correlation (1D)
                                  • Correlation (1D)
                                  • Normalisation
                                  • Normalisation
                                  • Correlation on images
                                  • Correlation on images
                                  • Correlation on images
                                  • Draw your filter
                                  • Correlation on images ndash no normalisation
                                  • Correlation on images ndash no normalisation 2
                                  • Mathematics of 2D Correlation
                                  • Mathematics of 2D Correlation
                                  • Mathematics of 2D Correlation
                                  • Slide Number 40
                                  • 2D Kernel Normalisation
                                  • Correlation
                                  • Smoothing filters
                                  • Use of smoothing
                                  • Use of smoothing
                                  • Mean filter
                                  • Border handling
                                  • Border handling ndash extend the input
                                  • Correlation with zero padding
                                  • Border handling ndash extend the input
                                  • Template Matching
                                  • Template Matching
                                  • Template Matching
                                  • Template Matching
                                  • Problematic Correlation
                                  • Normalised Cross Correlation
                                  • Length of template
                                  • Length of image patch
                                  • Normalised Cross Correlation
                                  • Normalised Cross Correlation
                                  • Normalised Cross Correlation
                                  • Edges
                                  • Edges
                                  • Finite Difference
                                  • Edges
                                  • Edges in 2D
                                  • Edge filter kernel
                                  • Prewitt filter
                                  • Edge detection
                                  • Edge filtering
                                  • 02511 - Niveau af dagens emne forelaeligsing
                                  • 02512 - Niveau af dagens emne forelaeligsing
                                  • 02511 - Mit eget udbytte af dagen
                                  • 02512 - Mit eget udbytte af dagen
                                  • 02511 - Sidste uges oslashvelser (pixelwise operations)
                                  • 02512 - Sidste uges oslashvelser (pixelwise operations)
                                  • Denne uges brug af clickers
                                  • What can you do after today
                                  • Oslashvelsesrapport over oslashvelse 4 - 02511
                                  • Exercises
                                    A0
                                    B0
                                    C5
                                    D0
                                    E6
                                    A
                                    B
                                    C
                                    D
                                    E
                                    A3
                                    B0
                                    C3
                                    D0
                                    E0
                                    A
                                    B
                                    C
                                    D
                                    E
                                    A0
                                    B0
                                    C1
                                    D4
                                    E1
                                    A
                                    B
                                    C
                                    D
                                    E
                                    A2
                                    B1
                                    C3
                                    D2
                                    E0
                                    A
                                    B
                                    C
                                    D
                                    E
                                    A0
                                    B0
                                    C2
                                    D6
                                    E0
                                    A
                                    B
                                    C
                                    D
                                    E
                                    A0
                                    B0
                                    C1
                                    D0
                                    E0
                                    A
                                    B
                                    C
                                    D
                                    E
                                    A2
                                    B3
                                    C6
                                    D1
                                    E0
                                    A
                                    B
                                    C
                                    D
                                    E
                                    A0
                                    B8
                                    C1
                                    D1
                                    E0
                                    A
                                    B
                                    C
                                    D
                                    E
                                    A1
                                    B2
                                    C2
                                    D3
                                    E2
                                    A
                                    B
                                    C
                                    D
                                    E
                                    A0
                                    B13
                                    C0
                                    D0
                                    E0
                                    A
                                    B
                                    C
                                    D
                                    E
                                    A12
                                    B0
                                    C0
                                    D0
                                    E0
                                    A
                                    B
                                    C
                                    D
                                    E
                                    A0
                                    B0
                                    C0
                                    D0
                                    E13
                                    A
                                    B
                                    C
                                    D
                                    E
                                    A13
                                    B0
                                    C0
                                    D0
                                    E0
                                    A
                                    B
                                    C
                                    D
                                    E
                                    A1
                                    B0
                                    C14
                                    D0
                                    E0
                                    A
                                    B
                                    C
                                    D
                                    E
                                    A0
                                    B12
                                    C1
                                    D0
                                    E0
                                    A
                                    B
                                    C
                                    D
                                    E
                                    A0
                                    B13
                                    C1
                                    D0
                                    E0
                                    A
                                    B
                                    C
                                    D
                                    E

                                    DTU Compute

                                    2122018Introduction to Medical Image Analysis16 DTU Compute Technical University of Denmark

                                    Noise removal ndash median filter

                                    Scanned X-ray with salt and pepper noise

                                    Median filter (3x3)

                                    DTU Compute

                                    2122018Introduction to Medical Image Analysis17 DTU Compute Technical University of Denmark

                                    Image Filtering Creates a new filtered image Output pixel is computed based

                                    on a neighbourhood in the input image

                                    3 x 3 neighbourhoodndash Filter size 3 x 3ndash Kernel size 3 x 3ndash Mask size 3 x 3

                                    Larger filters often usedndash Size

                                    7 x 7ndash Number of elements

                                    49

                                    DTU Compute

                                    2122018Introduction to Medical Image Analysis18 DTU Compute Technical University of Denmark

                                    Median filterA) 25B) 90C) 198D) 86E) 103

                                    0

                                    13

                                    1 0 0

                                    A B C D E

                                    Chart1

                                    0
                                    13
                                    1
                                    0
                                    0

                                    Sheet1

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                                    Rank filters Based on sorting the pixel

                                    values in the neighbouring region

                                    Minimum rank filterndash Darker image Noise problems

                                    Maximum rank filterndash Lighter image Noise problems

                                    Difference filterndash Enhances changes (edges)

                                    0168 169 170 170 170172 172173

                                    -

                                    DTU Compute

                                    2122018Introduction to Medical Image Analysis21 DTU Compute Technical University of Denmark

                                    Median filter

                                    A) 3B) 84C) 112D) 73E) 202

                                    0

                                    12

                                    10 0

                                    A B C D E

                                    Chart1

                                    0
                                    12
                                    1
                                    0
                                    0

                                    Sheet1

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                                    2122018Introduction to Medical Image Analysis23 DTU Compute Technical University of Denmark

                                    Correlation What is it Two measurements

                                    ndash Low correlationndash High correlation

                                    High correlation means that there is a relation between the values

                                    They look the same Correlation is a measure of

                                    similarity

                                    Low

                                    High

                                    Muscles

                                    Mat

                                    h Ski

                                    lls

                                    Muscles

                                    Ben

                                    ch P

                                    ress

                                    DTU Compute

                                    2122018Introduction to Medical Image Analysis24 DTU Compute Technical University of Denmark

                                    Why do we need similarity Image analysis is also about recognition of patterns Often an example pattern is used We need something to tell us if there is a high match

                                    between our pattern and a part of the image

                                    Example pattern

                                    Image

                                    Find matches

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                                    2122018Introduction to Medical Image Analysis25 DTU Compute Technical University of Denmark

                                    Correlation (1D)

                                    1 1 2 2 1 1 2 2 1 1

                                    1 2 1

                                    45

                                    41

                                    1 1 + 2 1 + 1 2 = 5

                                    Normalise

                                    Kernel

                                    Signal (1D image)

                                    41

                                    DTU Compute

                                    2122018Introduction to Medical Image Analysis26 DTU Compute Technical University of Denmark

                                    Correlation (1D)

                                    1 1 2 2 1 1 2 2 1 1

                                    1 2 1

                                    45

                                    47

                                    47

                                    45

                                    45

                                    47

                                    47

                                    45

                                    41

                                    DTU Compute

                                    2122018Introduction to Medical Image Analysis27 DTU Compute Technical University of Denmark

                                    Normalisation

                                    1 1 2 2 1 1 2 2 1 1

                                    1 2 1

                                    45

                                    41

                                    1 1 + 2 1 + 1 2 = 5

                                    Normalise41

                                    bull The sum of the kernel elements is used

                                    bull Keep the values in the same range as the input image

                                    Sum is 4

                                    DTU Compute

                                    2122018Introduction to Medical Image Analysis28 DTU Compute Technical University of Denmark

                                    Normalisation Normalisation factor

                                    ndash Sum of kernel coefficients

                                    1 2 1h(x)

                                    119909119909

                                    ℎ 119909119909 = 1 + 2 + 1

                                    DTU Compute

                                    2122018Introduction to Medical Image Analysis29 DTU Compute Technical University of Denmark

                                    Correlation on images The filter is now 2D 1 1 1

                                    1 1 1

                                    1 1 1

                                    0 2 4

                                    1 2 2

                                    1 6 3

                                    1 2 12 5 3

                                    2 1 3

                                    1 3 1

                                    2 2 2

                                    0 1 3

                                    1 2 0

                                    2 1 4

                                    1 0 1

                                    912

                                    91

                                    Input OutputKernel

                                    Kernel coefficients

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                                    2122018Introduction to Medical Image Analysis30 DTU Compute Technical University of Denmark

                                    Correlation on images

                                    1 1 11 1 11 1 1

                                    0 2 4

                                    1 2 2

                                    1 6 3

                                    1 2 0

                                    2 1 4

                                    1 0 1

                                    912

                                    911

                                    91

                                    Input Output

                                    1 3 1

                                    2 2 2

                                    0 1 3

                                    1 2 12 5 3

                                    2 1 3

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                                    Correlation on images

                                    Input Output

                                    The mask is moved row by row

                                    No values at the border

                                    0 2 4

                                    1 2 2

                                    1 6 3

                                    1 2 0

                                    2 1 4

                                    1 0 1

                                    1 3 1

                                    2 2 2

                                    0 1 3

                                    1 2 12 5 3

                                    2 1 3

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                                    1 2 1

                                    1 3 1

                                    1 2 1

                                    -1 -2 -1

                                    0 0 0

                                    1 2 1

                                    Draw your filter

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                                    Correlation on images ndash no normalisationA) 4B) 7C) 16D) 23E) 25

                                    1 2 11 3 11 2 1

                                    0 2 41 2 2

                                    1 6 3

                                    1 2 12 5 3

                                    2 1 3

                                    1 3 1

                                    2 2 2

                                    0 1 3

                                    1 2 0

                                    2 1 4

                                    1 0 11 0

                                    14

                                    0 0

                                    A B C D E

                                    Chart1

                                    1
                                    0
                                    14
                                    0
                                    0

                                    Sheet1

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                                    Correlation on images ndash no normalisation 2A) 010B) 3 3C) 6 2D) 10 15E) 11 32

                                    13

                                    0 0 0 0

                                    A B C D E

                                    -1 -2 -10 0 01 2 1

                                    0 2 41 2 2

                                    1 6 3

                                    1 2 12 5 3

                                    2 1 3

                                    1 3 1

                                    2 2 2

                                    0 1 3

                                    1 2 0

                                    2 1 4

                                    1 0 1

                                    Chart1

                                    13
                                    0
                                    0
                                    0
                                    0

                                    Sheet1

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                                    Mathematics of 2D Correlation

                                    h

                                    f

                                    Correlation operator

                                    1 2 11 3 11 2 1

                                    0 2 4

                                    1 2 2

                                    1 6 3

                                    1 2 1

                                    2 5 3

                                    2 1 3

                                    1 3 1

                                    2 2 2

                                    0 1 3

                                    1 2 0

                                    2 1 4

                                    1 0 1

                                    119892119892 119909119909119910119910 = 119891119891 119909119909119910119910 ∘ ℎ(119909119909119910119910)

                                    DTU Compute

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                                    Mathematics of 2D Correlation

                                    1 2 11 3 11 2 1

                                    0 2 4

                                    1 2 2

                                    1 6 3

                                    1 2 1

                                    2 5 3

                                    2 1 3

                                    1 3 1

                                    2 2 2

                                    0 1 3

                                    1 2 0

                                    2 1 4

                                    1 0 1

                                    h

                                    fh(00)

                                    f(21)

                                    Example g(21)

                                    i = -1 j = -1

                                    i = 1 j = 0

                                    119892119892 119909119909119910119910 = 119895119895=minus119877119877

                                    119877119877

                                    119894119894=minus119877119877

                                    119877119877

                                    ℎ(119894119894 119895119895) 119891119891(119909119909 + 119894119894119910119910 + 119895119895)

                                    DTU Compute

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                                    Mathematics of 2D Correlation

                                    1 2 11 3 11 2 1

                                    0 2 4

                                    1 2 2

                                    1 6 3

                                    1 2 1

                                    2 5 3

                                    2 1 3

                                    1 3 1

                                    2 2 2

                                    0 1 3

                                    1 2 0

                                    2 1 4

                                    1 0 1

                                    h

                                    f

                                    119892119892 119909119909119910119910 = 119895119895=minus119877119877

                                    119877119877

                                    119894119894=minus119877119877

                                    119877119877

                                    ℎ(119894119894 119895119895) 119891119891(119909119909 + 119894119894119910119910 + 119895119895)

                                    119892119892(119909119909119910119910 = 1 2 + 2 0 + 1 1 + 1 1 + 3 4 + 1 2 + 1 0 + 2 1 + 1 0

                                    DTU Compute

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                                    119892119892 119909119909 119910119910 = 119895119895=minus119877119877

                                    119877119877

                                    119894119894=minus119877119877

                                    119877119877

                                    ℎ(119894119894 119895119895) 119891119891(119909119909 + 119894119894119910119910 + 119895119895)

                                    119892119892 22 =ℎ minus1minus1 sdot 119891119891 11 + ℎ 0minus1 sdot 119891119891 21 + ℎ 1minus1 sdot 119891119891 31 +ℎ minus10 sdot 119891119891 12 + ℎ 00 sdot 119891119891 22 + ℎ 10 sdot 119891119891 32 +ℎ minus11 sdot 119891119891 13 + ℎ 01 sdot 119891119891 23 + ℎ 11 sdot 119891119891 33

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                                    2D Kernel Normalisation

                                    1 2 11 3 11 2 1

                                    h

                                    Normalisation factor

                                    1 + 2 + 1 + 1 + 3 + 1 + 1 + 2 + 1 = 13

                                    119909119909

                                    119910119910

                                    ℎ(119909119909119910119910)

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                                    CorrelationA) 50122B) 123001C) 11233D) 2550E) 90454

                                    0 0 0 0

                                    13

                                    A B C D E

                                    Chart1

                                    0
                                    0
                                    0
                                    0
                                    13

                                    Sheet1

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                                    Smoothing filters

                                    Also know as ndash Smoothing kernel Mean filter Low pass filter blurring

                                    The simplest filter ndash Spatial low pass filterndash Removes high frequencies

                                    Another mask ndash Gaussian filter

                                    1 1 1

                                    1 1 1

                                    1 1 191

                                    1 2 1

                                    2 4 2

                                    1 2 1161

                                    Why Gaussian

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                                    Use of smoothing

                                    3x3 7x7 11x11 15x15

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                                    Use of smoothing Large kernels smooth more Removes high frequency information Good at enhancing big structures

                                    3x3 15x15

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                                    Mean filterA) 166B) 113C) 12D) 51E) 245

                                    0 0 0 0

                                    A B C D E

                                    Chart1

                                    12
                                    0
                                    0
                                    0
                                    0

                                    Sheet1

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                                    Border handling

                                    0 2 41 2 2

                                    1 6 3

                                    1 2 12 5 3

                                    2 1 3

                                    1 3 1

                                    2 2 2

                                    0 1 3

                                    1 2 0

                                    2 1 4

                                    1 0 1

                                    Input Output

                                    No values at the border

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                                    Border handling ndash extend the input

                                    0 2 41 2 2

                                    1 6 3

                                    1 2 12 5 3

                                    2 1 3

                                    1 3 1

                                    2 2 2

                                    0 1 3

                                    1 2 0

                                    2 1 4

                                    1 0 1

                                    Input

                                    0 0 0 0 000000

                                    bull Zero padding ndash what happens

                                    bull Zero is black ndash creates dark border around the image

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                                    Correlation with zero paddingA) 5 8B) 12 16C) 13 3D) 15 21E) 17 12

                                    1 2 11 3 11 2 1

                                    0 2 41 2 2

                                    1 6 3

                                    1 2 12 5 3

                                    2 1 3

                                    1 3 1

                                    2 2 2

                                    0 1 3

                                    1 2 0

                                    2 1 4

                                    1 0 1

                                    0

                                    13

                                    0 0 0

                                    A B C D E

                                    Chart1

                                    0
                                    13
                                    0
                                    0
                                    0

                                    Sheet1

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                                    Border handling ndash extend the input

                                    0 2 41 2 2

                                    1 6 3

                                    1 2 12 5 3

                                    2 1 3

                                    1 3 1

                                    2 2 2

                                    0 1 3

                                    1 2 0

                                    2 1 4

                                    1 0 1

                                    Input

                                    1 2 0 1 311211

                                    bull Reflection

                                    bull Normally better than zero padding

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                                    2122018Introduction to Medical Image Analysis54 DTU Compute Technical University of Denmark

                                    Template Matching Template

                                    ndash Skabelon paring dansk Locates objects in images

                                    Input

                                    Template

                                    Output Correlation image

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                                    2122018Introduction to Medical Image Analysis55 DTU Compute Technical University of Denmark

                                    Template Matching The correlation between the template and the input

                                    image is computed for each pixel

                                    Input

                                    Template

                                    Output Correlation image

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                                    2122018Introduction to Medical Image Analysis56 DTU Compute Technical University of Denmark

                                    Template Matching The pixel with the highest value is found in the

                                    output imagendash Here is the highest correlation

                                    Input

                                    Template

                                    Output Correlation image

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                                    Template Matching This corresponds to the found pattern in the input

                                    image

                                    Input

                                    Template

                                    Output Correlation image

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                                    2122018Introduction to Medical Image Analysis58 DTU Compute Technical University of Denmark

                                    Problematic Correlation Correlation matching has problem with light areas ndash

                                    why

                                    Input (f)

                                    Template (h)

                                    Output Correlation imageFake max

                                    Real max

                                    Very High119892119892 119909119909119910119910 = 119895119895=minus119877119877

                                    119877119877

                                    119894119894=minus119877119877

                                    119877119877

                                    ℎ(119894119894 119895119895) 119891119891(119909119909 + 119894119894119910119910 + 119895119895)

                                    DTU Compute

                                    2122018Introduction to Medical Image Analysis59 DTU Compute Technical University of Denmark

                                    Normalised Cross Correlation

                                    Input (f)

                                    Template (h)

                                    Output Correlation image

                                    Real max

                                    NCC x y =Correlation

                                    Length of image patch sdot Length of template

                                    DTU Compute

                                    2122018Introduction to Medical Image Analysis60 DTU Compute Technical University of Denmark

                                    Length of template Vector length

                                    ndash Put all pixel values into a vectorndash Compute the length of this vector

                                    Describes the intensity of the templatendash Bright template has a large lengthndash Dark template has a small length

                                    Template (h)

                                    Length of template = 119895119895=minus119877119877

                                    119877119877

                                    119894119894=minus119877119877

                                    119877119877

                                    ℎ(119894119894 119895119895) ℎ(119894119894 119895119895)

                                    DTU Compute

                                    2122018Introduction to Medical Image Analysis61 DTU Compute Technical University of Denmark

                                    Length of image patch Vector length based on pixel values in image patch Describes the intensity of the image patch

                                    Template (h)

                                    Input (f) with patch

                                    DTU Compute

                                    2122018Introduction to Medical Image Analysis62 DTU Compute Technical University of Denmark

                                    Normalised Cross Correlation The length of the image patch and the length of

                                    template normalise the NCC If the image is very bright the NCC will be ldquopulled

                                    downrdquo

                                    NCC x y =Correlation

                                    Length of image patch sdot Length of template

                                    DTU Compute

                                    2122018Introduction to Medical Image Analysis63 DTU Compute Technical University of Denmark

                                    Normalised Cross Correlation NCC will be between

                                    ndash 0 No similarity between template and image patchndash 1 Template and image patch are identical

                                    Input (f)

                                    Template (h)

                                    Output Correlation image

                                    Real max

                                    NCC x y =Correlation

                                    Length of image patch sdot Length of template

                                    DTU Compute

                                    2122018Introduction to Medical Image Analysis64 DTU Compute Technical University of Denmark

                                    Normalised Cross Correlation

                                    A) 010B) 033C) 083D) 062E) 098

                                    Der udfoslashres template matching med og normalized crosscorrelation (NCC) beregnes Hvad bliver NNC i den markerede pixel

                                    1

                                    2 2

                                    3

                                    2

                                    A B C D E

                                    Chart1

                                    1
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                                    3
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                                    Sheet1

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                                    Edges An edge is where there is a

                                    high change in gray level values

                                    Objects are often separated from the background by edgesGray level profile

                                    DTU Compute

                                    2122018Introduction to Medical Image Analysis67 DTU Compute Technical University of Denmark

                                    Edges The profile as a function f(d) What value is high when there

                                    is an edgendash The slope of fndash The slope of the tangent at d

                                    f(d)

                                    119891119891prime(119889119889)

                                    DTU Compute

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                                    Finite Difference Definition of slope

                                    Approximation

                                    Simpler approximationh = 1

                                    119891119891prime 119889119889 = limℎrarr0

                                    119891119891 119889119889 + ℎ minus 119891119891(119889119889)ℎ

                                    119891119891prime 119889119889 asymp119891119891 119889119889 + ℎ minus 119891119891(119889119889)

                                    ℎ

                                    119891119891prime 119889119889 asymp 119891119891 119889119889 + 1 minus 119891119891(119889119889)

                                    DTU Compute

                                    2122018Introduction to Medical Image Analysis69 DTU Compute Technical University of Denmark

                                    Edges Discrete approximation of frsquo(d) Can be implemented as a filter

                                    -1 0 1

                                    f(d-2) f(d-1) f(d) f(d+1) f(d+2) f(d+3)

                                    f(d)

                                    119891119891prime 119889119889 asymp 119891119891 119889119889 + 1 minus 119891119891(119889119889)

                                    DTU Compute

                                    2122018Introduction to Medical Image Analysis70 DTU Compute Technical University of Denmark

                                    Edges in 2D Changes in gray level values

                                    ndash Image gradientndash Gradient is the 2D derivative of a 2D function f(xy)ndash Equal to the slope of the imagendash A steep slope is equal to an edge

                                    120571120571119891119891 119909119909119910119910 = 119866(119892119892119909119909119892119892119910119910)

                                    DTU Compute

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                                    Edge filter kernel The Prewitt filter is a typical

                                    edge filter Output image has high

                                    values where there are edges

                                    -1 0 1

                                    -1 0 1

                                    -1 0 1Vertical Prewitt filter

                                    DTU Compute

                                    2122018Introduction to Medical Image Analysis72 DTU Compute Technical University of Denmark

                                    Prewitt filter

                                    Original Prewitt Prewitt

                                    Hot colormapSmooth 15x15

                                    Smooth 15x15

                                    Prewitt

                                    DTU Compute

                                    2122018Introduction to Medical Image Analysis73 DTU Compute Technical University of Denmark

                                    Edge detection Edge filter

                                    ndash Prewitt for example Thresholding

                                    ndash Separate edges from non-edges

                                    Output is binary imagendash Edges are white

                                    DTU Compute

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                                    Edge filtering

                                    A) MeanB) Horizontal SobelC) Vertical PrewittD) Horisontal PrewittE) Median

                                    Der udfoslashres en filtrering (correlation) med et filter paring billedet Der bruges ikke coefficient normalization Den filtrerede vaeligrdi i den markerede pixel bliver -119 Hvilket et 3x3 filter blev benyttet

                                    0

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                                    02511 - Niveau af dagens emne forelaeligsingA) Meget letB) LetC) PassendeD) SvaeligrtE) Meget svaeligrt

                                    23

                                    6

                                    10

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                                    02512 - Niveau af dagens emne forelaeligsingA) Meget letB) LetC) PassendeD) SvaeligrtE) Meget svaeligrt

                                    0 0

                                    1

                                    0 0

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                                    02511 - Mit eget udbytte af dagenA) Jeg har laeligrt meget lidtB) Lidt laeligringC) PassendeD) God laeligringE) Jeg har laeligrt meget

                                    0 0

                                    2

                                    6

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                                    02512 - Mit eget udbytte af dagenA) Jeg har laeligrt meget lidtB) Lidt laeligringC) PassendeD) God laeligringE) Jeg har laeligrt meget

                                    2

                                    1

                                    3

                                    2

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                                    A B C D E

                                    Chart1

                                    2
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                                    02511 - Sidste uges oslashvelser (pixelwiseoperations)A) Meget letteB) LetteC) PassendeD) SvaeligreE) Meget svaeligre

                                    0 0

                                    1

                                    4

                                    1

                                    A B C D E

                                    Chart1

                                    0
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                                    1
                                    4
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                                    02512 - Sidste uges oslashvelser (pixelwiseoperations)A) Meget letteB) LetteC) PassendeD) SvaeligreE) Meget svaeligre

                                    3

                                    0

                                    3

                                    0 0

                                    A B C D E

                                    Chart1

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                                    Denne uges brug af clickersA) click click click ndash jeg bliver

                                    sindssygB) For meget clickC) PassendeD) Jeg vil gerne have lidt mereE) Jeg kan ikrsquo faring nok

                                    0 0

                                    5

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                                    What can you do after today Describe the difference between point processing and neighbourhood

                                    processing Compute a rank filtered image using the min max median and

                                    difference rank filters Compute a mean filtered image Decide if median or average filtering should be used for noise removal Choose the appropriate image border handling based on a given input

                                    image Implement and apply template matching Compute the normalised cross correlation and explain why it should be

                                    used Apply given image filter kernels to images Use edge filters on images Describe finite difference approximation of image gradients Describe the concept of edge detection

                                    DTU Compute

                                    2122018Introduction to Medical Image Analysis84 DTU Compute Technical University of Denmark

                                    Oslashvelsesrapport over oslashvelse 4 - 02511 Oslashvelser taeligller cirka 30 af karakteren Skal afleveres senest den 7 marts kl 2359 Kan afleveres af 1 eller 2 personer

                                    ndash I skal skrive jeres egen oslashvelsesrapportndash Brug mindst et af jeres egne billeder

                                    Afleveres som PDF Lad vaeligre med at kopiere opgaveteksten ind i jeres

                                    opgave Put Matlab kode i et Appendix og henvis fra teksten Eksempel rapport over oslashvelse findes paring

                                    hjemmesiden under eksamen

                                    DTU Compute

                                    2122018Introduction to Medical Image Analysis85 DTU Compute Technical University of Denmark

                                    Exercises

                                    • Introduction to Medical Image Analysis
                                    • Lecture 4 ndash Neighbourhood Processing
                                    • What can you do after today
                                    • Point processing
                                    • Point processing
                                    • Neighbourhood processing
                                    • Use of filtering
                                    • Salt and pepper noise
                                    • Salt and pepper noise
                                    • What is so special about noise
                                    • Noise ndash go away
                                    • What is the median Value
                                    • The median value
                                    • Noise away ndash the median filter
                                    • Noise removal ndash average filter
                                    • Noise removal ndash median filter
                                    • Image Filtering
                                    • Median filter
                                    • Rank filters
                                    • Median filter
                                    • Correlation
                                    • Why do we need similarity
                                    • Correlation (1D)
                                    • Correlation (1D)
                                    • Normalisation
                                    • Normalisation
                                    • Correlation on images
                                    • Correlation on images
                                    • Correlation on images
                                    • Draw your filter
                                    • Correlation on images ndash no normalisation
                                    • Correlation on images ndash no normalisation 2
                                    • Mathematics of 2D Correlation
                                    • Mathematics of 2D Correlation
                                    • Mathematics of 2D Correlation
                                    • Slide Number 40
                                    • 2D Kernel Normalisation
                                    • Correlation
                                    • Smoothing filters
                                    • Use of smoothing
                                    • Use of smoothing
                                    • Mean filter
                                    • Border handling
                                    • Border handling ndash extend the input
                                    • Correlation with zero padding
                                    • Border handling ndash extend the input
                                    • Template Matching
                                    • Template Matching
                                    • Template Matching
                                    • Template Matching
                                    • Problematic Correlation
                                    • Normalised Cross Correlation
                                    • Length of template
                                    • Length of image patch
                                    • Normalised Cross Correlation
                                    • Normalised Cross Correlation
                                    • Normalised Cross Correlation
                                    • Edges
                                    • Edges
                                    • Finite Difference
                                    • Edges
                                    • Edges in 2D
                                    • Edge filter kernel
                                    • Prewitt filter
                                    • Edge detection
                                    • Edge filtering
                                    • 02511 - Niveau af dagens emne forelaeligsing
                                    • 02512 - Niveau af dagens emne forelaeligsing
                                    • 02511 - Mit eget udbytte af dagen
                                    • 02512 - Mit eget udbytte af dagen
                                    • 02511 - Sidste uges oslashvelser (pixelwise operations)
                                    • 02512 - Sidste uges oslashvelser (pixelwise operations)
                                    • Denne uges brug af clickers
                                    • What can you do after today
                                    • Oslashvelsesrapport over oslashvelse 4 - 02511
                                    • Exercises
                                      A0
                                      B0
                                      C5
                                      D0
                                      E6
                                      A
                                      B
                                      C
                                      D
                                      E
                                      A3
                                      B0
                                      C3
                                      D0
                                      E0
                                      A
                                      B
                                      C
                                      D
                                      E
                                      A0
                                      B0
                                      C1
                                      D4
                                      E1
                                      A
                                      B
                                      C
                                      D
                                      E
                                      A2
                                      B1
                                      C3
                                      D2
                                      E0
                                      A
                                      B
                                      C
                                      D
                                      E
                                      A0
                                      B0
                                      C2
                                      D6
                                      E0
                                      A
                                      B
                                      C
                                      D
                                      E
                                      A0
                                      B0
                                      C1
                                      D0
                                      E0
                                      A
                                      B
                                      C
                                      D
                                      E
                                      A2
                                      B3
                                      C6
                                      D1
                                      E0
                                      A
                                      B
                                      C
                                      D
                                      E
                                      A0
                                      B8
                                      C1
                                      D1
                                      E0
                                      A
                                      B
                                      C
                                      D
                                      E
                                      A1
                                      B2
                                      C2
                                      D3
                                      E2
                                      A
                                      B
                                      C
                                      D
                                      E
                                      A0
                                      B13
                                      C0
                                      D0
                                      E0
                                      A
                                      B
                                      C
                                      D
                                      E
                                      A12
                                      B0
                                      C0
                                      D0
                                      E0
                                      A
                                      B
                                      C
                                      D
                                      E
                                      A0
                                      B0
                                      C0
                                      D0
                                      E13
                                      A
                                      B
                                      C
                                      D
                                      E
                                      A13
                                      B0
                                      C0
                                      D0
                                      E0
                                      A
                                      B
                                      C
                                      D
                                      E
                                      A1
                                      B0
                                      C14
                                      D0
                                      E0
                                      A
                                      B
                                      C
                                      D
                                      E
                                      A0
                                      B12
                                      C1
                                      D0
                                      E0
                                      A
                                      B
                                      C
                                      D
                                      E
                                      A0
                                      B13
                                      C1
                                      D0
                                      E0
                                      A
                                      B
                                      C
                                      D
                                      E

                                      DTU Compute

                                      2122018Introduction to Medical Image Analysis17 DTU Compute Technical University of Denmark

                                      Image Filtering Creates a new filtered image Output pixel is computed based

                                      on a neighbourhood in the input image

                                      3 x 3 neighbourhoodndash Filter size 3 x 3ndash Kernel size 3 x 3ndash Mask size 3 x 3

                                      Larger filters often usedndash Size

                                      7 x 7ndash Number of elements

                                      49

                                      DTU Compute

                                      2122018Introduction to Medical Image Analysis18 DTU Compute Technical University of Denmark

                                      Median filterA) 25B) 90C) 198D) 86E) 103

                                      0

                                      13

                                      1 0 0

                                      A B C D E

                                      Chart1

                                      0
                                      13
                                      1
                                      0
                                      0

                                      Sheet1

                                      DTU Compute

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                                      Rank filters Based on sorting the pixel

                                      values in the neighbouring region

                                      Minimum rank filterndash Darker image Noise problems

                                      Maximum rank filterndash Lighter image Noise problems

                                      Difference filterndash Enhances changes (edges)

                                      0168 169 170 170 170172 172173

                                      -

                                      DTU Compute

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                                      Median filter

                                      A) 3B) 84C) 112D) 73E) 202

                                      0

                                      12

                                      10 0

                                      A B C D E

                                      Chart1

                                      0
                                      12
                                      1
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                                      Correlation What is it Two measurements

                                      ndash Low correlationndash High correlation

                                      High correlation means that there is a relation between the values

                                      They look the same Correlation is a measure of

                                      similarity

                                      Low

                                      High

                                      Muscles

                                      Mat

                                      h Ski

                                      lls

                                      Muscles

                                      Ben

                                      ch P

                                      ress

                                      DTU Compute

                                      2122018Introduction to Medical Image Analysis24 DTU Compute Technical University of Denmark

                                      Why do we need similarity Image analysis is also about recognition of patterns Often an example pattern is used We need something to tell us if there is a high match

                                      between our pattern and a part of the image

                                      Example pattern

                                      Image

                                      Find matches

                                      DTU Compute

                                      2122018Introduction to Medical Image Analysis25 DTU Compute Technical University of Denmark

                                      Correlation (1D)

                                      1 1 2 2 1 1 2 2 1 1

                                      1 2 1

                                      45

                                      41

                                      1 1 + 2 1 + 1 2 = 5

                                      Normalise

                                      Kernel

                                      Signal (1D image)

                                      41

                                      DTU Compute

                                      2122018Introduction to Medical Image Analysis26 DTU Compute Technical University of Denmark

                                      Correlation (1D)

                                      1 1 2 2 1 1 2 2 1 1

                                      1 2 1

                                      45

                                      47

                                      47

                                      45

                                      45

                                      47

                                      47

                                      45

                                      41

                                      DTU Compute

                                      2122018Introduction to Medical Image Analysis27 DTU Compute Technical University of Denmark

                                      Normalisation

                                      1 1 2 2 1 1 2 2 1 1

                                      1 2 1

                                      45

                                      41

                                      1 1 + 2 1 + 1 2 = 5

                                      Normalise41

                                      bull The sum of the kernel elements is used

                                      bull Keep the values in the same range as the input image

                                      Sum is 4

                                      DTU Compute

                                      2122018Introduction to Medical Image Analysis28 DTU Compute Technical University of Denmark

                                      Normalisation Normalisation factor

                                      ndash Sum of kernel coefficients

                                      1 2 1h(x)

                                      119909119909

                                      ℎ 119909119909 = 1 + 2 + 1

                                      DTU Compute

                                      2122018Introduction to Medical Image Analysis29 DTU Compute Technical University of Denmark

                                      Correlation on images The filter is now 2D 1 1 1

                                      1 1 1

                                      1 1 1

                                      0 2 4

                                      1 2 2

                                      1 6 3

                                      1 2 12 5 3

                                      2 1 3

                                      1 3 1

                                      2 2 2

                                      0 1 3

                                      1 2 0

                                      2 1 4

                                      1 0 1

                                      912

                                      91

                                      Input OutputKernel

                                      Kernel coefficients

                                      DTU Compute

                                      2122018Introduction to Medical Image Analysis30 DTU Compute Technical University of Denmark

                                      Correlation on images

                                      1 1 11 1 11 1 1

                                      0 2 4

                                      1 2 2

                                      1 6 3

                                      1 2 0

                                      2 1 4

                                      1 0 1

                                      912

                                      911

                                      91

                                      Input Output

                                      1 3 1

                                      2 2 2

                                      0 1 3

                                      1 2 12 5 3

                                      2 1 3

                                      DTU Compute

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                                      Correlation on images

                                      Input Output

                                      The mask is moved row by row

                                      No values at the border

                                      0 2 4

                                      1 2 2

                                      1 6 3

                                      1 2 0

                                      2 1 4

                                      1 0 1

                                      1 3 1

                                      2 2 2

                                      0 1 3

                                      1 2 12 5 3

                                      2 1 3

                                      DTU Compute

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                                      1 2 1

                                      1 3 1

                                      1 2 1

                                      -1 -2 -1

                                      0 0 0

                                      1 2 1

                                      Draw your filter

                                      DTU Compute

                                      2122018Introduction to Medical Image Analysis33 DTU Compute Technical University of Denmark

                                      Correlation on images ndash no normalisationA) 4B) 7C) 16D) 23E) 25

                                      1 2 11 3 11 2 1

                                      0 2 41 2 2

                                      1 6 3

                                      1 2 12 5 3

                                      2 1 3

                                      1 3 1

                                      2 2 2

                                      0 1 3

                                      1 2 0

                                      2 1 4

                                      1 0 11 0

                                      14

                                      0 0

                                      A B C D E

                                      Chart1

                                      1
                                      0
                                      14
                                      0
                                      0

                                      Sheet1

                                      DTU Compute

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                                      Correlation on images ndash no normalisation 2A) 010B) 3 3C) 6 2D) 10 15E) 11 32

                                      13

                                      0 0 0 0

                                      A B C D E

                                      -1 -2 -10 0 01 2 1

                                      0 2 41 2 2

                                      1 6 3

                                      1 2 12 5 3

                                      2 1 3

                                      1 3 1

                                      2 2 2

                                      0 1 3

                                      1 2 0

                                      2 1 4

                                      1 0 1

                                      Chart1

                                      13
                                      0
                                      0
                                      0
                                      0

                                      Sheet1

                                      DTU Compute

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                                      Mathematics of 2D Correlation

                                      h

                                      f

                                      Correlation operator

                                      1 2 11 3 11 2 1

                                      0 2 4

                                      1 2 2

                                      1 6 3

                                      1 2 1

                                      2 5 3

                                      2 1 3

                                      1 3 1

                                      2 2 2

                                      0 1 3

                                      1 2 0

                                      2 1 4

                                      1 0 1

                                      119892119892 119909119909119910119910 = 119891119891 119909119909119910119910 ∘ ℎ(119909119909119910119910)

                                      DTU Compute

                                      2122018Introduction to Medical Image Analysis38 DTU Compute Technical University of Denmark

                                      Mathematics of 2D Correlation

                                      1 2 11 3 11 2 1

                                      0 2 4

                                      1 2 2

                                      1 6 3

                                      1 2 1

                                      2 5 3

                                      2 1 3

                                      1 3 1

                                      2 2 2

                                      0 1 3

                                      1 2 0

                                      2 1 4

                                      1 0 1

                                      h

                                      fh(00)

                                      f(21)

                                      Example g(21)

                                      i = -1 j = -1

                                      i = 1 j = 0

                                      119892119892 119909119909119910119910 = 119895119895=minus119877119877

                                      119877119877

                                      119894119894=minus119877119877

                                      119877119877

                                      ℎ(119894119894 119895119895) 119891119891(119909119909 + 119894119894119910119910 + 119895119895)

                                      DTU Compute

                                      2122018Introduction to Medical Image Analysis39 DTU Compute Technical University of Denmark

                                      Mathematics of 2D Correlation

                                      1 2 11 3 11 2 1

                                      0 2 4

                                      1 2 2

                                      1 6 3

                                      1 2 1

                                      2 5 3

                                      2 1 3

                                      1 3 1

                                      2 2 2

                                      0 1 3

                                      1 2 0

                                      2 1 4

                                      1 0 1

                                      h

                                      f

                                      119892119892 119909119909119910119910 = 119895119895=minus119877119877

                                      119877119877

                                      119894119894=minus119877119877

                                      119877119877

                                      ℎ(119894119894 119895119895) 119891119891(119909119909 + 119894119894119910119910 + 119895119895)

                                      119892119892(119909119909119910119910 = 1 2 + 2 0 + 1 1 + 1 1 + 3 4 + 1 2 + 1 0 + 2 1 + 1 0

                                      DTU Compute

                                      2122018Introduction to Medical Image Analysis40 DTU Compute Technical University of Denmark

                                      119892119892 119909119909 119910119910 = 119895119895=minus119877119877

                                      119877119877

                                      119894119894=minus119877119877

                                      119877119877

                                      ℎ(119894119894 119895119895) 119891119891(119909119909 + 119894119894119910119910 + 119895119895)

                                      119892119892 22 =ℎ minus1minus1 sdot 119891119891 11 + ℎ 0minus1 sdot 119891119891 21 + ℎ 1minus1 sdot 119891119891 31 +ℎ minus10 sdot 119891119891 12 + ℎ 00 sdot 119891119891 22 + ℎ 10 sdot 119891119891 32 +ℎ minus11 sdot 119891119891 13 + ℎ 01 sdot 119891119891 23 + ℎ 11 sdot 119891119891 33

                                      DTU Compute

                                      2122018Introduction to Medical Image Analysis41 DTU Compute Technical University of Denmark

                                      2D Kernel Normalisation

                                      1 2 11 3 11 2 1

                                      h

                                      Normalisation factor

                                      1 + 2 + 1 + 1 + 3 + 1 + 1 + 2 + 1 = 13

                                      119909119909

                                      119910119910

                                      ℎ(119909119909119910119910)

                                      DTU Compute

                                      2122018Introduction to Medical Image Analysis42 DTU Compute Technical University of Denmark

                                      CorrelationA) 50122B) 123001C) 11233D) 2550E) 90454

                                      0 0 0 0

                                      13

                                      A B C D E

                                      Chart1

                                      0
                                      0
                                      0
                                      0
                                      13

                                      Sheet1

                                      DTU Compute

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                                      Smoothing filters

                                      Also know as ndash Smoothing kernel Mean filter Low pass filter blurring

                                      The simplest filter ndash Spatial low pass filterndash Removes high frequencies

                                      Another mask ndash Gaussian filter

                                      1 1 1

                                      1 1 1

                                      1 1 191

                                      1 2 1

                                      2 4 2

                                      1 2 1161

                                      Why Gaussian

                                      DTU Compute

                                      2122018Introduction to Medical Image Analysis45 DTU Compute Technical University of Denmark

                                      Use of smoothing

                                      3x3 7x7 11x11 15x15

                                      DTU Compute

                                      2122018Introduction to Medical Image Analysis46 DTU Compute Technical University of Denmark

                                      Use of smoothing Large kernels smooth more Removes high frequency information Good at enhancing big structures

                                      3x3 15x15

                                      DTU Compute

                                      2122018Introduction to Medical Image Analysis47 DTU Compute Technical University of Denmark

                                      Mean filterA) 166B) 113C) 12D) 51E) 245

                                      0 0 0 0

                                      A B C D E

                                      Chart1

                                      12
                                      0
                                      0
                                      0
                                      0

                                      Sheet1

                                      DTU Compute

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                                      Border handling

                                      0 2 41 2 2

                                      1 6 3

                                      1 2 12 5 3

                                      2 1 3

                                      1 3 1

                                      2 2 2

                                      0 1 3

                                      1 2 0

                                      2 1 4

                                      1 0 1

                                      Input Output

                                      No values at the border

                                      DTU Compute

                                      2122018Introduction to Medical Image Analysis50 DTU Compute Technical University of Denmark

                                      Border handling ndash extend the input

                                      0 2 41 2 2

                                      1 6 3

                                      1 2 12 5 3

                                      2 1 3

                                      1 3 1

                                      2 2 2

                                      0 1 3

                                      1 2 0

                                      2 1 4

                                      1 0 1

                                      Input

                                      0 0 0 0 000000

                                      bull Zero padding ndash what happens

                                      bull Zero is black ndash creates dark border around the image

                                      DTU Compute

                                      2122018Introduction to Medical Image Analysis51 DTU Compute Technical University of Denmark

                                      Correlation with zero paddingA) 5 8B) 12 16C) 13 3D) 15 21E) 17 12

                                      1 2 11 3 11 2 1

                                      0 2 41 2 2

                                      1 6 3

                                      1 2 12 5 3

                                      2 1 3

                                      1 3 1

                                      2 2 2

                                      0 1 3

                                      1 2 0

                                      2 1 4

                                      1 0 1

                                      0

                                      13

                                      0 0 0

                                      A B C D E

                                      Chart1

                                      0
                                      13
                                      0
                                      0
                                      0

                                      Sheet1

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                                      Border handling ndash extend the input

                                      0 2 41 2 2

                                      1 6 3

                                      1 2 12 5 3

                                      2 1 3

                                      1 3 1

                                      2 2 2

                                      0 1 3

                                      1 2 0

                                      2 1 4

                                      1 0 1

                                      Input

                                      1 2 0 1 311211

                                      bull Reflection

                                      bull Normally better than zero padding

                                      DTU Compute

                                      2122018Introduction to Medical Image Analysis54 DTU Compute Technical University of Denmark

                                      Template Matching Template

                                      ndash Skabelon paring dansk Locates objects in images

                                      Input

                                      Template

                                      Output Correlation image

                                      DTU Compute

                                      2122018Introduction to Medical Image Analysis55 DTU Compute Technical University of Denmark

                                      Template Matching The correlation between the template and the input

                                      image is computed for each pixel

                                      Input

                                      Template

                                      Output Correlation image

                                      DTU Compute

                                      2122018Introduction to Medical Image Analysis56 DTU Compute Technical University of Denmark

                                      Template Matching The pixel with the highest value is found in the

                                      output imagendash Here is the highest correlation

                                      Input

                                      Template

                                      Output Correlation image

                                      DTU Compute

                                      2122018Introduction to Medical Image Analysis57 DTU Compute Technical University of Denmark

                                      Template Matching This corresponds to the found pattern in the input

                                      image

                                      Input

                                      Template

                                      Output Correlation image

                                      DTU Compute

                                      2122018Introduction to Medical Image Analysis58 DTU Compute Technical University of Denmark

                                      Problematic Correlation Correlation matching has problem with light areas ndash

                                      why

                                      Input (f)

                                      Template (h)

                                      Output Correlation imageFake max

                                      Real max

                                      Very High119892119892 119909119909119910119910 = 119895119895=minus119877119877

                                      119877119877

                                      119894119894=minus119877119877

                                      119877119877

                                      ℎ(119894119894 119895119895) 119891119891(119909119909 + 119894119894119910119910 + 119895119895)

                                      DTU Compute

                                      2122018Introduction to Medical Image Analysis59 DTU Compute Technical University of Denmark

                                      Normalised Cross Correlation

                                      Input (f)

                                      Template (h)

                                      Output Correlation image

                                      Real max

                                      NCC x y =Correlation

                                      Length of image patch sdot Length of template

                                      DTU Compute

                                      2122018Introduction to Medical Image Analysis60 DTU Compute Technical University of Denmark

                                      Length of template Vector length

                                      ndash Put all pixel values into a vectorndash Compute the length of this vector

                                      Describes the intensity of the templatendash Bright template has a large lengthndash Dark template has a small length

                                      Template (h)

                                      Length of template = 119895119895=minus119877119877

                                      119877119877

                                      119894119894=minus119877119877

                                      119877119877

                                      ℎ(119894119894 119895119895) ℎ(119894119894 119895119895)

                                      DTU Compute

                                      2122018Introduction to Medical Image Analysis61 DTU Compute Technical University of Denmark

                                      Length of image patch Vector length based on pixel values in image patch Describes the intensity of the image patch

                                      Template (h)

                                      Input (f) with patch

                                      DTU Compute

                                      2122018Introduction to Medical Image Analysis62 DTU Compute Technical University of Denmark

                                      Normalised Cross Correlation The length of the image patch and the length of

                                      template normalise the NCC If the image is very bright the NCC will be ldquopulled

                                      downrdquo

                                      NCC x y =Correlation

                                      Length of image patch sdot Length of template

                                      DTU Compute

                                      2122018Introduction to Medical Image Analysis63 DTU Compute Technical University of Denmark

                                      Normalised Cross Correlation NCC will be between

                                      ndash 0 No similarity between template and image patchndash 1 Template and image patch are identical

                                      Input (f)

                                      Template (h)

                                      Output Correlation image

                                      Real max

                                      NCC x y =Correlation

                                      Length of image patch sdot Length of template

                                      DTU Compute

                                      2122018Introduction to Medical Image Analysis64 DTU Compute Technical University of Denmark

                                      Normalised Cross Correlation

                                      A) 010B) 033C) 083D) 062E) 098

                                      Der udfoslashres template matching med og normalized crosscorrelation (NCC) beregnes Hvad bliver NNC i den markerede pixel

                                      1

                                      2 2

                                      3

                                      2

                                      A B C D E

                                      Chart1

                                      1
                                      2
                                      2
                                      3
                                      2

                                      Sheet1

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                                      Edges An edge is where there is a

                                      high change in gray level values

                                      Objects are often separated from the background by edgesGray level profile

                                      DTU Compute

                                      2122018Introduction to Medical Image Analysis67 DTU Compute Technical University of Denmark

                                      Edges The profile as a function f(d) What value is high when there

                                      is an edgendash The slope of fndash The slope of the tangent at d

                                      f(d)

                                      119891119891prime(119889119889)

                                      DTU Compute

                                      2122018Introduction to Medical Image Analysis68 DTU Compute Technical University of Denmark

                                      Finite Difference Definition of slope

                                      Approximation

                                      Simpler approximationh = 1

                                      119891119891prime 119889119889 = limℎrarr0

                                      119891119891 119889119889 + ℎ minus 119891119891(119889119889)ℎ

                                      119891119891prime 119889119889 asymp119891119891 119889119889 + ℎ minus 119891119891(119889119889)

                                      ℎ

                                      119891119891prime 119889119889 asymp 119891119891 119889119889 + 1 minus 119891119891(119889119889)

                                      DTU Compute

                                      2122018Introduction to Medical Image Analysis69 DTU Compute Technical University of Denmark

                                      Edges Discrete approximation of frsquo(d) Can be implemented as a filter

                                      -1 0 1

                                      f(d-2) f(d-1) f(d) f(d+1) f(d+2) f(d+3)

                                      f(d)

                                      119891119891prime 119889119889 asymp 119891119891 119889119889 + 1 minus 119891119891(119889119889)

                                      DTU Compute

                                      2122018Introduction to Medical Image Analysis70 DTU Compute Technical University of Denmark

                                      Edges in 2D Changes in gray level values

                                      ndash Image gradientndash Gradient is the 2D derivative of a 2D function f(xy)ndash Equal to the slope of the imagendash A steep slope is equal to an edge

                                      120571120571119891119891 119909119909119910119910 = 119866(119892119892119909119909119892119892119910119910)

                                      DTU Compute

                                      2122018Introduction to Medical Image Analysis71 DTU Compute Technical University of Denmark

                                      Edge filter kernel The Prewitt filter is a typical

                                      edge filter Output image has high

                                      values where there are edges

                                      -1 0 1

                                      -1 0 1

                                      -1 0 1Vertical Prewitt filter

                                      DTU Compute

                                      2122018Introduction to Medical Image Analysis72 DTU Compute Technical University of Denmark

                                      Prewitt filter

                                      Original Prewitt Prewitt

                                      Hot colormapSmooth 15x15

                                      Smooth 15x15

                                      Prewitt

                                      DTU Compute

                                      2122018Introduction to Medical Image Analysis73 DTU Compute Technical University of Denmark

                                      Edge detection Edge filter

                                      ndash Prewitt for example Thresholding

                                      ndash Separate edges from non-edges

                                      Output is binary imagendash Edges are white

                                      DTU Compute

                                      2122018Introduction to Medical Image Analysis74 DTU Compute Technical University of Denmark

                                      Edge filtering

                                      A) MeanB) Horizontal SobelC) Vertical PrewittD) Horisontal PrewittE) Median

                                      Der udfoslashres en filtrering (correlation) med et filter paring billedet Der bruges ikke coefficient normalization Den filtrerede vaeligrdi i den markerede pixel bliver -119 Hvilket et 3x3 filter blev benyttet

                                      0

                                      8

                                      1 10

                                      A B C D E

                                      Chart1

                                      0
                                      8
                                      1
                                      1
                                      0

                                      Sheet1

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                                      02511 - Niveau af dagens emne forelaeligsingA) Meget letB) LetC) PassendeD) SvaeligrtE) Meget svaeligrt

                                      23

                                      6

                                      10

                                      A B C D E

                                      Chart1

                                      2
                                      3
                                      6
                                      1
                                      0

                                      Sheet1

                                      DTU Compute

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                                      02512 - Niveau af dagens emne forelaeligsingA) Meget letB) LetC) PassendeD) SvaeligrtE) Meget svaeligrt

                                      0 0

                                      1

                                      0 0

                                      A B C D E

                                      Chart1

                                      0
                                      0
                                      1
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                                      2122018Introduction to Medical Image Analysis78 DTU Compute Technical University of Denmark

                                      02511 - Mit eget udbytte af dagenA) Jeg har laeligrt meget lidtB) Lidt laeligringC) PassendeD) God laeligringE) Jeg har laeligrt meget

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                                      02512 - Mit eget udbytte af dagenA) Jeg har laeligrt meget lidtB) Lidt laeligringC) PassendeD) God laeligringE) Jeg har laeligrt meget

                                      2

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                                      02511 - Sidste uges oslashvelser (pixelwiseoperations)A) Meget letteB) LetteC) PassendeD) SvaeligreE) Meget svaeligre

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                                      02512 - Sidste uges oslashvelser (pixelwiseoperations)A) Meget letteB) LetteC) PassendeD) SvaeligreE) Meget svaeligre

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                                      Denne uges brug af clickersA) click click click ndash jeg bliver

                                      sindssygB) For meget clickC) PassendeD) Jeg vil gerne have lidt mereE) Jeg kan ikrsquo faring nok

                                      0 0

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                                      What can you do after today Describe the difference between point processing and neighbourhood

                                      processing Compute a rank filtered image using the min max median and

                                      difference rank filters Compute a mean filtered image Decide if median or average filtering should be used for noise removal Choose the appropriate image border handling based on a given input

                                      image Implement and apply template matching Compute the normalised cross correlation and explain why it should be

                                      used Apply given image filter kernels to images Use edge filters on images Describe finite difference approximation of image gradients Describe the concept of edge detection

                                      DTU Compute

                                      2122018Introduction to Medical Image Analysis84 DTU Compute Technical University of Denmark

                                      Oslashvelsesrapport over oslashvelse 4 - 02511 Oslashvelser taeligller cirka 30 af karakteren Skal afleveres senest den 7 marts kl 2359 Kan afleveres af 1 eller 2 personer

                                      ndash I skal skrive jeres egen oslashvelsesrapportndash Brug mindst et af jeres egne billeder

                                      Afleveres som PDF Lad vaeligre med at kopiere opgaveteksten ind i jeres

                                      opgave Put Matlab kode i et Appendix og henvis fra teksten Eksempel rapport over oslashvelse findes paring

                                      hjemmesiden under eksamen

                                      DTU Compute

                                      2122018Introduction to Medical Image Analysis85 DTU Compute Technical University of Denmark

                                      Exercises

                                      • Introduction to Medical Image Analysis
                                      • Lecture 4 ndash Neighbourhood Processing
                                      • What can you do after today
                                      • Point processing
                                      • Point processing
                                      • Neighbourhood processing
                                      • Use of filtering
                                      • Salt and pepper noise
                                      • Salt and pepper noise
                                      • What is so special about noise
                                      • Noise ndash go away
                                      • What is the median Value
                                      • The median value
                                      • Noise away ndash the median filter
                                      • Noise removal ndash average filter
                                      • Noise removal ndash median filter
                                      • Image Filtering
                                      • Median filter
                                      • Rank filters
                                      • Median filter
                                      • Correlation
                                      • Why do we need similarity
                                      • Correlation (1D)
                                      • Correlation (1D)
                                      • Normalisation
                                      • Normalisation
                                      • Correlation on images
                                      • Correlation on images
                                      • Correlation on images
                                      • Draw your filter
                                      • Correlation on images ndash no normalisation
                                      • Correlation on images ndash no normalisation 2
                                      • Mathematics of 2D Correlation
                                      • Mathematics of 2D Correlation
                                      • Mathematics of 2D Correlation
                                      • Slide Number 40
                                      • 2D Kernel Normalisation
                                      • Correlation
                                      • Smoothing filters
                                      • Use of smoothing
                                      • Use of smoothing
                                      • Mean filter
                                      • Border handling
                                      • Border handling ndash extend the input
                                      • Correlation with zero padding
                                      • Border handling ndash extend the input
                                      • Template Matching
                                      • Template Matching
                                      • Template Matching
                                      • Template Matching
                                      • Problematic Correlation
                                      • Normalised Cross Correlation
                                      • Length of template
                                      • Length of image patch
                                      • Normalised Cross Correlation
                                      • Normalised Cross Correlation
                                      • Normalised Cross Correlation
                                      • Edges
                                      • Edges
                                      • Finite Difference
                                      • Edges
                                      • Edges in 2D
                                      • Edge filter kernel
                                      • Prewitt filter
                                      • Edge detection
                                      • Edge filtering
                                      • 02511 - Niveau af dagens emne forelaeligsing
                                      • 02512 - Niveau af dagens emne forelaeligsing
                                      • 02511 - Mit eget udbytte af dagen
                                      • 02512 - Mit eget udbytte af dagen
                                      • 02511 - Sidste uges oslashvelser (pixelwise operations)
                                      • 02512 - Sidste uges oslashvelser (pixelwise operations)
                                      • Denne uges brug af clickers
                                      • What can you do after today
                                      • Oslashvelsesrapport over oslashvelse 4 - 02511
                                      • Exercises
                                        A0
                                        B0
                                        C5
                                        D0
                                        E6
                                        A
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                                        C
                                        D
                                        E
                                        A3
                                        B0
                                        C3
                                        D0
                                        E0
                                        A
                                        B
                                        C
                                        D
                                        E
                                        A0
                                        B0
                                        C1
                                        D4
                                        E1
                                        A
                                        B
                                        C
                                        D
                                        E
                                        A2
                                        B1
                                        C3
                                        D2
                                        E0
                                        A
                                        B
                                        C
                                        D
                                        E
                                        A0
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                                        D6
                                        E0
                                        A
                                        B
                                        C
                                        D
                                        E
                                        A0
                                        B0
                                        C1
                                        D0
                                        E0
                                        A
                                        B
                                        C
                                        D
                                        E
                                        A2
                                        B3
                                        C6
                                        D1
                                        E0
                                        A
                                        B
                                        C
                                        D
                                        E
                                        A0
                                        B8
                                        C1
                                        D1
                                        E0
                                        A
                                        B
                                        C
                                        D
                                        E
                                        A1
                                        B2
                                        C2
                                        D3
                                        E2
                                        A
                                        B
                                        C
                                        D
                                        E
                                        A0
                                        B13
                                        C0
                                        D0
                                        E0
                                        A
                                        B
                                        C
                                        D
                                        E
                                        A12
                                        B0
                                        C0
                                        D0
                                        E0
                                        A
                                        B
                                        C
                                        D
                                        E
                                        A0
                                        B0
                                        C0
                                        D0
                                        E13
                                        A
                                        B
                                        C
                                        D
                                        E
                                        A13
                                        B0
                                        C0
                                        D0
                                        E0
                                        A
                                        B
                                        C
                                        D
                                        E
                                        A1
                                        B0
                                        C14
                                        D0
                                        E0
                                        A
                                        B
                                        C
                                        D
                                        E
                                        A0
                                        B12
                                        C1
                                        D0
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                                        A
                                        B
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                                        A0
                                        B13
                                        C1
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                                        E0
                                        A
                                        B
                                        C
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                                        E

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                                        Median filterA) 25B) 90C) 198D) 86E) 103

                                        0

                                        13

                                        1 0 0

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                                        Rank filters Based on sorting the pixel

                                        values in the neighbouring region

                                        Minimum rank filterndash Darker image Noise problems

                                        Maximum rank filterndash Lighter image Noise problems

                                        Difference filterndash Enhances changes (edges)

                                        0168 169 170 170 170172 172173

                                        -

                                        DTU Compute

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                                        Median filter

                                        A) 3B) 84C) 112D) 73E) 202

                                        0

                                        12

                                        10 0

                                        A B C D E

                                        Chart1

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                                        Correlation What is it Two measurements

                                        ndash Low correlationndash High correlation

                                        High correlation means that there is a relation between the values

                                        They look the same Correlation is a measure of

                                        similarity

                                        Low

                                        High

                                        Muscles

                                        Mat

                                        h Ski

                                        lls

                                        Muscles

                                        Ben

                                        ch P

                                        ress

                                        DTU Compute

                                        2122018Introduction to Medical Image Analysis24 DTU Compute Technical University of Denmark

                                        Why do we need similarity Image analysis is also about recognition of patterns Often an example pattern is used We need something to tell us if there is a high match

                                        between our pattern and a part of the image

                                        Example pattern

                                        Image

                                        Find matches

                                        DTU Compute

                                        2122018Introduction to Medical Image Analysis25 DTU Compute Technical University of Denmark

                                        Correlation (1D)

                                        1 1 2 2 1 1 2 2 1 1

                                        1 2 1

                                        45

                                        41

                                        1 1 + 2 1 + 1 2 = 5

                                        Normalise

                                        Kernel

                                        Signal (1D image)

                                        41

                                        DTU Compute

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                                        Correlation (1D)

                                        1 1 2 2 1 1 2 2 1 1

                                        1 2 1

                                        45

                                        47

                                        47

                                        45

                                        45

                                        47

                                        47

                                        45

                                        41

                                        DTU Compute

                                        2122018Introduction to Medical Image Analysis27 DTU Compute Technical University of Denmark

                                        Normalisation

                                        1 1 2 2 1 1 2 2 1 1

                                        1 2 1

                                        45

                                        41

                                        1 1 + 2 1 + 1 2 = 5

                                        Normalise41

                                        bull The sum of the kernel elements is used

                                        bull Keep the values in the same range as the input image

                                        Sum is 4

                                        DTU Compute

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                                        Normalisation Normalisation factor

                                        ndash Sum of kernel coefficients

                                        1 2 1h(x)

                                        119909119909

                                        ℎ 119909119909 = 1 + 2 + 1

                                        DTU Compute

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                                        Correlation on images The filter is now 2D 1 1 1

                                        1 1 1

                                        1 1 1

                                        0 2 4

                                        1 2 2

                                        1 6 3

                                        1 2 12 5 3

                                        2 1 3

                                        1 3 1

                                        2 2 2

                                        0 1 3

                                        1 2 0

                                        2 1 4

                                        1 0 1

                                        912

                                        91

                                        Input OutputKernel

                                        Kernel coefficients

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                                        Correlation on images

                                        1 1 11 1 11 1 1

                                        0 2 4

                                        1 2 2

                                        1 6 3

                                        1 2 0

                                        2 1 4

                                        1 0 1

                                        912

                                        911

                                        91

                                        Input Output

                                        1 3 1

                                        2 2 2

                                        0 1 3

                                        1 2 12 5 3

                                        2 1 3

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                                        Correlation on images

                                        Input Output

                                        The mask is moved row by row

                                        No values at the border

                                        0 2 4

                                        1 2 2

                                        1 6 3

                                        1 2 0

                                        2 1 4

                                        1 0 1

                                        1 3 1

                                        2 2 2

                                        0 1 3

                                        1 2 12 5 3

                                        2 1 3

                                        DTU Compute

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                                        1 2 1

                                        1 3 1

                                        1 2 1

                                        -1 -2 -1

                                        0 0 0

                                        1 2 1

                                        Draw your filter

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                                        Correlation on images ndash no normalisationA) 4B) 7C) 16D) 23E) 25

                                        1 2 11 3 11 2 1

                                        0 2 41 2 2

                                        1 6 3

                                        1 2 12 5 3

                                        2 1 3

                                        1 3 1

                                        2 2 2

                                        0 1 3

                                        1 2 0

                                        2 1 4

                                        1 0 11 0

                                        14

                                        0 0

                                        A B C D E

                                        Chart1

                                        1
                                        0
                                        14
                                        0
                                        0

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                                        Correlation on images ndash no normalisation 2A) 010B) 3 3C) 6 2D) 10 15E) 11 32

                                        13

                                        0 0 0 0

                                        A B C D E

                                        -1 -2 -10 0 01 2 1

                                        0 2 41 2 2

                                        1 6 3

                                        1 2 12 5 3

                                        2 1 3

                                        1 3 1

                                        2 2 2

                                        0 1 3

                                        1 2 0

                                        2 1 4

                                        1 0 1

                                        Chart1

                                        13
                                        0
                                        0
                                        0
                                        0

                                        Sheet1

                                        DTU Compute

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                                        Mathematics of 2D Correlation

                                        h

                                        f

                                        Correlation operator

                                        1 2 11 3 11 2 1

                                        0 2 4

                                        1 2 2

                                        1 6 3

                                        1 2 1

                                        2 5 3

                                        2 1 3

                                        1 3 1

                                        2 2 2

                                        0 1 3

                                        1 2 0

                                        2 1 4

                                        1 0 1

                                        119892119892 119909119909119910119910 = 119891119891 119909119909119910119910 ∘ ℎ(119909119909119910119910)

                                        DTU Compute

                                        2122018Introduction to Medical Image Analysis38 DTU Compute Technical University of Denmark

                                        Mathematics of 2D Correlation

                                        1 2 11 3 11 2 1

                                        0 2 4

                                        1 2 2

                                        1 6 3

                                        1 2 1

                                        2 5 3

                                        2 1 3

                                        1 3 1

                                        2 2 2

                                        0 1 3

                                        1 2 0

                                        2 1 4

                                        1 0 1

                                        h

                                        fh(00)

                                        f(21)

                                        Example g(21)

                                        i = -1 j = -1

                                        i = 1 j = 0

                                        119892119892 119909119909119910119910 = 119895119895=minus119877119877

                                        119877119877

                                        119894119894=minus119877119877

                                        119877119877

                                        ℎ(119894119894 119895119895) 119891119891(119909119909 + 119894119894119910119910 + 119895119895)

                                        DTU Compute

                                        2122018Introduction to Medical Image Analysis39 DTU Compute Technical University of Denmark

                                        Mathematics of 2D Correlation

                                        1 2 11 3 11 2 1

                                        0 2 4

                                        1 2 2

                                        1 6 3

                                        1 2 1

                                        2 5 3

                                        2 1 3

                                        1 3 1

                                        2 2 2

                                        0 1 3

                                        1 2 0

                                        2 1 4

                                        1 0 1

                                        h

                                        f

                                        119892119892 119909119909119910119910 = 119895119895=minus119877119877

                                        119877119877

                                        119894119894=minus119877119877

                                        119877119877

                                        ℎ(119894119894 119895119895) 119891119891(119909119909 + 119894119894119910119910 + 119895119895)

                                        119892119892(119909119909119910119910 = 1 2 + 2 0 + 1 1 + 1 1 + 3 4 + 1 2 + 1 0 + 2 1 + 1 0

                                        DTU Compute

                                        2122018Introduction to Medical Image Analysis40 DTU Compute Technical University of Denmark

                                        119892119892 119909119909 119910119910 = 119895119895=minus119877119877

                                        119877119877

                                        119894119894=minus119877119877

                                        119877119877

                                        ℎ(119894119894 119895119895) 119891119891(119909119909 + 119894119894119910119910 + 119895119895)

                                        119892119892 22 =ℎ minus1minus1 sdot 119891119891 11 + ℎ 0minus1 sdot 119891119891 21 + ℎ 1minus1 sdot 119891119891 31 +ℎ minus10 sdot 119891119891 12 + ℎ 00 sdot 119891119891 22 + ℎ 10 sdot 119891119891 32 +ℎ minus11 sdot 119891119891 13 + ℎ 01 sdot 119891119891 23 + ℎ 11 sdot 119891119891 33

                                        DTU Compute

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                                        2D Kernel Normalisation

                                        1 2 11 3 11 2 1

                                        h

                                        Normalisation factor

                                        1 + 2 + 1 + 1 + 3 + 1 + 1 + 2 + 1 = 13

                                        119909119909

                                        119910119910

                                        ℎ(119909119909119910119910)

                                        DTU Compute

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                                        CorrelationA) 50122B) 123001C) 11233D) 2550E) 90454

                                        0 0 0 0

                                        13

                                        A B C D E

                                        Chart1

                                        0
                                        0
                                        0
                                        0
                                        13

                                        Sheet1

                                        DTU Compute

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                                        Smoothing filters

                                        Also know as ndash Smoothing kernel Mean filter Low pass filter blurring

                                        The simplest filter ndash Spatial low pass filterndash Removes high frequencies

                                        Another mask ndash Gaussian filter

                                        1 1 1

                                        1 1 1

                                        1 1 191

                                        1 2 1

                                        2 4 2

                                        1 2 1161

                                        Why Gaussian

                                        DTU Compute

                                        2122018Introduction to Medical Image Analysis45 DTU Compute Technical University of Denmark

                                        Use of smoothing

                                        3x3 7x7 11x11 15x15

                                        DTU Compute

                                        2122018Introduction to Medical Image Analysis46 DTU Compute Technical University of Denmark

                                        Use of smoothing Large kernels smooth more Removes high frequency information Good at enhancing big structures

                                        3x3 15x15

                                        DTU Compute

                                        2122018Introduction to Medical Image Analysis47 DTU Compute Technical University of Denmark

                                        Mean filterA) 166B) 113C) 12D) 51E) 245

                                        0 0 0 0

                                        A B C D E

                                        Chart1

                                        12
                                        0
                                        0
                                        0
                                        0

                                        Sheet1

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                                        Border handling

                                        0 2 41 2 2

                                        1 6 3

                                        1 2 12 5 3

                                        2 1 3

                                        1 3 1

                                        2 2 2

                                        0 1 3

                                        1 2 0

                                        2 1 4

                                        1 0 1

                                        Input Output

                                        No values at the border

                                        DTU Compute

                                        2122018Introduction to Medical Image Analysis50 DTU Compute Technical University of Denmark

                                        Border handling ndash extend the input

                                        0 2 41 2 2

                                        1 6 3

                                        1 2 12 5 3

                                        2 1 3

                                        1 3 1

                                        2 2 2

                                        0 1 3

                                        1 2 0

                                        2 1 4

                                        1 0 1

                                        Input

                                        0 0 0 0 000000

                                        bull Zero padding ndash what happens

                                        bull Zero is black ndash creates dark border around the image

                                        DTU Compute

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                                        Correlation with zero paddingA) 5 8B) 12 16C) 13 3D) 15 21E) 17 12

                                        1 2 11 3 11 2 1

                                        0 2 41 2 2

                                        1 6 3

                                        1 2 12 5 3

                                        2 1 3

                                        1 3 1

                                        2 2 2

                                        0 1 3

                                        1 2 0

                                        2 1 4

                                        1 0 1

                                        0

                                        13

                                        0 0 0

                                        A B C D E

                                        Chart1

                                        0
                                        13
                                        0
                                        0
                                        0

                                        Sheet1

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                                        Border handling ndash extend the input

                                        0 2 41 2 2

                                        1 6 3

                                        1 2 12 5 3

                                        2 1 3

                                        1 3 1

                                        2 2 2

                                        0 1 3

                                        1 2 0

                                        2 1 4

                                        1 0 1

                                        Input

                                        1 2 0 1 311211

                                        bull Reflection

                                        bull Normally better than zero padding

                                        DTU Compute

                                        2122018Introduction to Medical Image Analysis54 DTU Compute Technical University of Denmark

                                        Template Matching Template

                                        ndash Skabelon paring dansk Locates objects in images

                                        Input

                                        Template

                                        Output Correlation image

                                        DTU Compute

                                        2122018Introduction to Medical Image Analysis55 DTU Compute Technical University of Denmark

                                        Template Matching The correlation between the template and the input

                                        image is computed for each pixel

                                        Input

                                        Template

                                        Output Correlation image

                                        DTU Compute

                                        2122018Introduction to Medical Image Analysis56 DTU Compute Technical University of Denmark

                                        Template Matching The pixel with the highest value is found in the

                                        output imagendash Here is the highest correlation

                                        Input

                                        Template

                                        Output Correlation image

                                        DTU Compute

                                        2122018Introduction to Medical Image Analysis57 DTU Compute Technical University of Denmark

                                        Template Matching This corresponds to the found pattern in the input

                                        image

                                        Input

                                        Template

                                        Output Correlation image

                                        DTU Compute

                                        2122018Introduction to Medical Image Analysis58 DTU Compute Technical University of Denmark

                                        Problematic Correlation Correlation matching has problem with light areas ndash

                                        why

                                        Input (f)

                                        Template (h)

                                        Output Correlation imageFake max

                                        Real max

                                        Very High119892119892 119909119909119910119910 = 119895119895=minus119877119877

                                        119877119877

                                        119894119894=minus119877119877

                                        119877119877

                                        ℎ(119894119894 119895119895) 119891119891(119909119909 + 119894119894119910119910 + 119895119895)

                                        DTU Compute

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                                        Normalised Cross Correlation

                                        Input (f)

                                        Template (h)

                                        Output Correlation image

                                        Real max

                                        NCC x y =Correlation

                                        Length of image patch sdot Length of template

                                        DTU Compute

                                        2122018Introduction to Medical Image Analysis60 DTU Compute Technical University of Denmark

                                        Length of template Vector length

                                        ndash Put all pixel values into a vectorndash Compute the length of this vector

                                        Describes the intensity of the templatendash Bright template has a large lengthndash Dark template has a small length

                                        Template (h)

                                        Length of template = 119895119895=minus119877119877

                                        119877119877

                                        119894119894=minus119877119877

                                        119877119877

                                        ℎ(119894119894 119895119895) ℎ(119894119894 119895119895)

                                        DTU Compute

                                        2122018Introduction to Medical Image Analysis61 DTU Compute Technical University of Denmark

                                        Length of image patch Vector length based on pixel values in image patch Describes the intensity of the image patch

                                        Template (h)

                                        Input (f) with patch

                                        DTU Compute

                                        2122018Introduction to Medical Image Analysis62 DTU Compute Technical University of Denmark

                                        Normalised Cross Correlation The length of the image patch and the length of

                                        template normalise the NCC If the image is very bright the NCC will be ldquopulled

                                        downrdquo

                                        NCC x y =Correlation

                                        Length of image patch sdot Length of template

                                        DTU Compute

                                        2122018Introduction to Medical Image Analysis63 DTU Compute Technical University of Denmark

                                        Normalised Cross Correlation NCC will be between

                                        ndash 0 No similarity between template and image patchndash 1 Template and image patch are identical

                                        Input (f)

                                        Template (h)

                                        Output Correlation image

                                        Real max

                                        NCC x y =Correlation

                                        Length of image patch sdot Length of template

                                        DTU Compute

                                        2122018Introduction to Medical Image Analysis64 DTU Compute Technical University of Denmark

                                        Normalised Cross Correlation

                                        A) 010B) 033C) 083D) 062E) 098

                                        Der udfoslashres template matching med og normalized crosscorrelation (NCC) beregnes Hvad bliver NNC i den markerede pixel

                                        1

                                        2 2

                                        3

                                        2

                                        A B C D E

                                        Chart1

                                        1
                                        2
                                        2
                                        3
                                        2

                                        Sheet1

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                                        Edges An edge is where there is a

                                        high change in gray level values

                                        Objects are often separated from the background by edgesGray level profile

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                                        2122018Introduction to Medical Image Analysis67 DTU Compute Technical University of Denmark

                                        Edges The profile as a function f(d) What value is high when there

                                        is an edgendash The slope of fndash The slope of the tangent at d

                                        f(d)

                                        119891119891prime(119889119889)

                                        DTU Compute

                                        2122018Introduction to Medical Image Analysis68 DTU Compute Technical University of Denmark

                                        Finite Difference Definition of slope

                                        Approximation

                                        Simpler approximationh = 1

                                        119891119891prime 119889119889 = limℎrarr0

                                        119891119891 119889119889 + ℎ minus 119891119891(119889119889)ℎ

                                        119891119891prime 119889119889 asymp119891119891 119889119889 + ℎ minus 119891119891(119889119889)

                                        ℎ

                                        119891119891prime 119889119889 asymp 119891119891 119889119889 + 1 minus 119891119891(119889119889)

                                        DTU Compute

                                        2122018Introduction to Medical Image Analysis69 DTU Compute Technical University of Denmark

                                        Edges Discrete approximation of frsquo(d) Can be implemented as a filter

                                        -1 0 1

                                        f(d-2) f(d-1) f(d) f(d+1) f(d+2) f(d+3)

                                        f(d)

                                        119891119891prime 119889119889 asymp 119891119891 119889119889 + 1 minus 119891119891(119889119889)

                                        DTU Compute

                                        2122018Introduction to Medical Image Analysis70 DTU Compute Technical University of Denmark

                                        Edges in 2D Changes in gray level values

                                        ndash Image gradientndash Gradient is the 2D derivative of a 2D function f(xy)ndash Equal to the slope of the imagendash A steep slope is equal to an edge

                                        120571120571119891119891 119909119909119910119910 = 119866(119892119892119909119909119892119892119910119910)

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                                        2122018Introduction to Medical Image Analysis71 DTU Compute Technical University of Denmark

                                        Edge filter kernel The Prewitt filter is a typical

                                        edge filter Output image has high

                                        values where there are edges

                                        -1 0 1

                                        -1 0 1

                                        -1 0 1Vertical Prewitt filter

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                                        2122018Introduction to Medical Image Analysis72 DTU Compute Technical University of Denmark

                                        Prewitt filter

                                        Original Prewitt Prewitt

                                        Hot colormapSmooth 15x15

                                        Smooth 15x15

                                        Prewitt

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                                        2122018Introduction to Medical Image Analysis73 DTU Compute Technical University of Denmark

                                        Edge detection Edge filter

                                        ndash Prewitt for example Thresholding

                                        ndash Separate edges from non-edges

                                        Output is binary imagendash Edges are white

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                                        2122018Introduction to Medical Image Analysis74 DTU Compute Technical University of Denmark

                                        Edge filtering

                                        A) MeanB) Horizontal SobelC) Vertical PrewittD) Horisontal PrewittE) Median

                                        Der udfoslashres en filtrering (correlation) med et filter paring billedet Der bruges ikke coefficient normalization Den filtrerede vaeligrdi i den markerede pixel bliver -119 Hvilket et 3x3 filter blev benyttet

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                                        02511 - Niveau af dagens emne forelaeligsingA) Meget letB) LetC) PassendeD) SvaeligrtE) Meget svaeligrt

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                                        02512 - Niveau af dagens emne forelaeligsingA) Meget letB) LetC) PassendeD) SvaeligrtE) Meget svaeligrt

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                                        02511 - Mit eget udbytte af dagenA) Jeg har laeligrt meget lidtB) Lidt laeligringC) PassendeD) God laeligringE) Jeg har laeligrt meget

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                                        02512 - Mit eget udbytte af dagenA) Jeg har laeligrt meget lidtB) Lidt laeligringC) PassendeD) God laeligringE) Jeg har laeligrt meget

                                        2

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                                        02511 - Sidste uges oslashvelser (pixelwiseoperations)A) Meget letteB) LetteC) PassendeD) SvaeligreE) Meget svaeligre

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                                        02512 - Sidste uges oslashvelser (pixelwiseoperations)A) Meget letteB) LetteC) PassendeD) SvaeligreE) Meget svaeligre

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                                        Denne uges brug af clickersA) click click click ndash jeg bliver

                                        sindssygB) For meget clickC) PassendeD) Jeg vil gerne have lidt mereE) Jeg kan ikrsquo faring nok

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                                        What can you do after today Describe the difference between point processing and neighbourhood

                                        processing Compute a rank filtered image using the min max median and

                                        difference rank filters Compute a mean filtered image Decide if median or average filtering should be used for noise removal Choose the appropriate image border handling based on a given input

                                        image Implement and apply template matching Compute the normalised cross correlation and explain why it should be

                                        used Apply given image filter kernels to images Use edge filters on images Describe finite difference approximation of image gradients Describe the concept of edge detection

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                                        2122018Introduction to Medical Image Analysis84 DTU Compute Technical University of Denmark

                                        Oslashvelsesrapport over oslashvelse 4 - 02511 Oslashvelser taeligller cirka 30 af karakteren Skal afleveres senest den 7 marts kl 2359 Kan afleveres af 1 eller 2 personer

                                        ndash I skal skrive jeres egen oslashvelsesrapportndash Brug mindst et af jeres egne billeder

                                        Afleveres som PDF Lad vaeligre med at kopiere opgaveteksten ind i jeres

                                        opgave Put Matlab kode i et Appendix og henvis fra teksten Eksempel rapport over oslashvelse findes paring

                                        hjemmesiden under eksamen

                                        DTU Compute

                                        2122018Introduction to Medical Image Analysis85 DTU Compute Technical University of Denmark

                                        Exercises

                                        • Introduction to Medical Image Analysis
                                        • Lecture 4 ndash Neighbourhood Processing
                                        • What can you do after today
                                        • Point processing
                                        • Point processing
                                        • Neighbourhood processing
                                        • Use of filtering
                                        • Salt and pepper noise
                                        • Salt and pepper noise
                                        • What is so special about noise
                                        • Noise ndash go away
                                        • What is the median Value
                                        • The median value
                                        • Noise away ndash the median filter
                                        • Noise removal ndash average filter
                                        • Noise removal ndash median filter
                                        • Image Filtering
                                        • Median filter
                                        • Rank filters
                                        • Median filter
                                        • Correlation
                                        • Why do we need similarity
                                        • Correlation (1D)
                                        • Correlation (1D)
                                        • Normalisation
                                        • Normalisation
                                        • Correlation on images
                                        • Correlation on images
                                        • Correlation on images
                                        • Draw your filter
                                        • Correlation on images ndash no normalisation
                                        • Correlation on images ndash no normalisation 2
                                        • Mathematics of 2D Correlation
                                        • Mathematics of 2D Correlation
                                        • Mathematics of 2D Correlation
                                        • Slide Number 40
                                        • 2D Kernel Normalisation
                                        • Correlation
                                        • Smoothing filters
                                        • Use of smoothing
                                        • Use of smoothing
                                        • Mean filter
                                        • Border handling
                                        • Border handling ndash extend the input
                                        • Correlation with zero padding
                                        • Border handling ndash extend the input
                                        • Template Matching
                                        • Template Matching
                                        • Template Matching
                                        • Template Matching
                                        • Problematic Correlation
                                        • Normalised Cross Correlation
                                        • Length of template
                                        • Length of image patch
                                        • Normalised Cross Correlation
                                        • Normalised Cross Correlation
                                        • Normalised Cross Correlation
                                        • Edges
                                        • Edges
                                        • Finite Difference
                                        • Edges
                                        • Edges in 2D
                                        • Edge filter kernel
                                        • Prewitt filter
                                        • Edge detection
                                        • Edge filtering
                                        • 02511 - Niveau af dagens emne forelaeligsing
                                        • 02512 - Niveau af dagens emne forelaeligsing
                                        • 02511 - Mit eget udbytte af dagen
                                        • 02512 - Mit eget udbytte af dagen
                                        • 02511 - Sidste uges oslashvelser (pixelwise operations)
                                        • 02512 - Sidste uges oslashvelser (pixelwise operations)
                                        • Denne uges brug af clickers
                                        • What can you do after today
                                        • Oslashvelsesrapport over oslashvelse 4 - 02511
                                        • Exercises
                                          A0
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                                          Rank filters Based on sorting the pixel

                                          values in the neighbouring region

                                          Minimum rank filterndash Darker image Noise problems

                                          Maximum rank filterndash Lighter image Noise problems

                                          Difference filterndash Enhances changes (edges)

                                          0168 169 170 170 170172 172173

                                          -

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                                          Median filter

                                          A) 3B) 84C) 112D) 73E) 202

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                                          Correlation What is it Two measurements

                                          ndash Low correlationndash High correlation

                                          High correlation means that there is a relation between the values

                                          They look the same Correlation is a measure of

                                          similarity

                                          Low

                                          High

                                          Muscles

                                          Mat

                                          h Ski

                                          lls

                                          Muscles

                                          Ben

                                          ch P

                                          ress

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                                          2122018Introduction to Medical Image Analysis24 DTU Compute Technical University of Denmark

                                          Why do we need similarity Image analysis is also about recognition of patterns Often an example pattern is used We need something to tell us if there is a high match

                                          between our pattern and a part of the image

                                          Example pattern

                                          Image

                                          Find matches

                                          DTU Compute

                                          2122018Introduction to Medical Image Analysis25 DTU Compute Technical University of Denmark

                                          Correlation (1D)

                                          1 1 2 2 1 1 2 2 1 1

                                          1 2 1

                                          45

                                          41

                                          1 1 + 2 1 + 1 2 = 5

                                          Normalise

                                          Kernel

                                          Signal (1D image)

                                          41

                                          DTU Compute

                                          2122018Introduction to Medical Image Analysis26 DTU Compute Technical University of Denmark

                                          Correlation (1D)

                                          1 1 2 2 1 1 2 2 1 1

                                          1 2 1

                                          45

                                          47

                                          47

                                          45

                                          45

                                          47

                                          47

                                          45

                                          41

                                          DTU Compute

                                          2122018Introduction to Medical Image Analysis27 DTU Compute Technical University of Denmark

                                          Normalisation

                                          1 1 2 2 1 1 2 2 1 1

                                          1 2 1

                                          45

                                          41

                                          1 1 + 2 1 + 1 2 = 5

                                          Normalise41

                                          bull The sum of the kernel elements is used

                                          bull Keep the values in the same range as the input image

                                          Sum is 4

                                          DTU Compute

                                          2122018Introduction to Medical Image Analysis28 DTU Compute Technical University of Denmark

                                          Normalisation Normalisation factor

                                          ndash Sum of kernel coefficients

                                          1 2 1h(x)

                                          119909119909

                                          ℎ 119909119909 = 1 + 2 + 1

                                          DTU Compute

                                          2122018Introduction to Medical Image Analysis29 DTU Compute Technical University of Denmark

                                          Correlation on images The filter is now 2D 1 1 1

                                          1 1 1

                                          1 1 1

                                          0 2 4

                                          1 2 2

                                          1 6 3

                                          1 2 12 5 3

                                          2 1 3

                                          1 3 1

                                          2 2 2

                                          0 1 3

                                          1 2 0

                                          2 1 4

                                          1 0 1

                                          912

                                          91

                                          Input OutputKernel

                                          Kernel coefficients

                                          DTU Compute

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                                          Correlation on images

                                          1 1 11 1 11 1 1

                                          0 2 4

                                          1 2 2

                                          1 6 3

                                          1 2 0

                                          2 1 4

                                          1 0 1

                                          912

                                          911

                                          91

                                          Input Output

                                          1 3 1

                                          2 2 2

                                          0 1 3

                                          1 2 12 5 3

                                          2 1 3

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                                          Correlation on images

                                          Input Output

                                          The mask is moved row by row

                                          No values at the border

                                          0 2 4

                                          1 2 2

                                          1 6 3

                                          1 2 0

                                          2 1 4

                                          1 0 1

                                          1 3 1

                                          2 2 2

                                          0 1 3

                                          1 2 12 5 3

                                          2 1 3

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                                          1 2 1

                                          1 3 1

                                          1 2 1

                                          -1 -2 -1

                                          0 0 0

                                          1 2 1

                                          Draw your filter

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                                          2122018Introduction to Medical Image Analysis33 DTU Compute Technical University of Denmark

                                          Correlation on images ndash no normalisationA) 4B) 7C) 16D) 23E) 25

                                          1 2 11 3 11 2 1

                                          0 2 41 2 2

                                          1 6 3

                                          1 2 12 5 3

                                          2 1 3

                                          1 3 1

                                          2 2 2

                                          0 1 3

                                          1 2 0

                                          2 1 4

                                          1 0 11 0

                                          14

                                          0 0

                                          A B C D E

                                          Chart1

                                          1
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                                          0
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                                          Correlation on images ndash no normalisation 2A) 010B) 3 3C) 6 2D) 10 15E) 11 32

                                          13

                                          0 0 0 0

                                          A B C D E

                                          -1 -2 -10 0 01 2 1

                                          0 2 41 2 2

                                          1 6 3

                                          1 2 12 5 3

                                          2 1 3

                                          1 3 1

                                          2 2 2

                                          0 1 3

                                          1 2 0

                                          2 1 4

                                          1 0 1

                                          Chart1

                                          13
                                          0
                                          0
                                          0
                                          0

                                          Sheet1

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                                          Mathematics of 2D Correlation

                                          h

                                          f

                                          Correlation operator

                                          1 2 11 3 11 2 1

                                          0 2 4

                                          1 2 2

                                          1 6 3

                                          1 2 1

                                          2 5 3

                                          2 1 3

                                          1 3 1

                                          2 2 2

                                          0 1 3

                                          1 2 0

                                          2 1 4

                                          1 0 1

                                          119892119892 119909119909119910119910 = 119891119891 119909119909119910119910 ∘ ℎ(119909119909119910119910)

                                          DTU Compute

                                          2122018Introduction to Medical Image Analysis38 DTU Compute Technical University of Denmark

                                          Mathematics of 2D Correlation

                                          1 2 11 3 11 2 1

                                          0 2 4

                                          1 2 2

                                          1 6 3

                                          1 2 1

                                          2 5 3

                                          2 1 3

                                          1 3 1

                                          2 2 2

                                          0 1 3

                                          1 2 0

                                          2 1 4

                                          1 0 1

                                          h

                                          fh(00)

                                          f(21)

                                          Example g(21)

                                          i = -1 j = -1

                                          i = 1 j = 0

                                          119892119892 119909119909119910119910 = 119895119895=minus119877119877

                                          119877119877

                                          119894119894=minus119877119877

                                          119877119877

                                          ℎ(119894119894 119895119895) 119891119891(119909119909 + 119894119894119910119910 + 119895119895)

                                          DTU Compute

                                          2122018Introduction to Medical Image Analysis39 DTU Compute Technical University of Denmark

                                          Mathematics of 2D Correlation

                                          1 2 11 3 11 2 1

                                          0 2 4

                                          1 2 2

                                          1 6 3

                                          1 2 1

                                          2 5 3

                                          2 1 3

                                          1 3 1

                                          2 2 2

                                          0 1 3

                                          1 2 0

                                          2 1 4

                                          1 0 1

                                          h

                                          f

                                          119892119892 119909119909119910119910 = 119895119895=minus119877119877

                                          119877119877

                                          119894119894=minus119877119877

                                          119877119877

                                          ℎ(119894119894 119895119895) 119891119891(119909119909 + 119894119894119910119910 + 119895119895)

                                          119892119892(119909119909119910119910 = 1 2 + 2 0 + 1 1 + 1 1 + 3 4 + 1 2 + 1 0 + 2 1 + 1 0

                                          DTU Compute

                                          2122018Introduction to Medical Image Analysis40 DTU Compute Technical University of Denmark

                                          119892119892 119909119909 119910119910 = 119895119895=minus119877119877

                                          119877119877

                                          119894119894=minus119877119877

                                          119877119877

                                          ℎ(119894119894 119895119895) 119891119891(119909119909 + 119894119894119910119910 + 119895119895)

                                          119892119892 22 =ℎ minus1minus1 sdot 119891119891 11 + ℎ 0minus1 sdot 119891119891 21 + ℎ 1minus1 sdot 119891119891 31 +ℎ minus10 sdot 119891119891 12 + ℎ 00 sdot 119891119891 22 + ℎ 10 sdot 119891119891 32 +ℎ minus11 sdot 119891119891 13 + ℎ 01 sdot 119891119891 23 + ℎ 11 sdot 119891119891 33

                                          DTU Compute

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                                          2D Kernel Normalisation

                                          1 2 11 3 11 2 1

                                          h

                                          Normalisation factor

                                          1 + 2 + 1 + 1 + 3 + 1 + 1 + 2 + 1 = 13

                                          119909119909

                                          119910119910

                                          ℎ(119909119909119910119910)

                                          DTU Compute

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                                          CorrelationA) 50122B) 123001C) 11233D) 2550E) 90454

                                          0 0 0 0

                                          13

                                          A B C D E

                                          Chart1

                                          0
                                          0
                                          0
                                          0
                                          13

                                          Sheet1

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                                          Smoothing filters

                                          Also know as ndash Smoothing kernel Mean filter Low pass filter blurring

                                          The simplest filter ndash Spatial low pass filterndash Removes high frequencies

                                          Another mask ndash Gaussian filter

                                          1 1 1

                                          1 1 1

                                          1 1 191

                                          1 2 1

                                          2 4 2

                                          1 2 1161

                                          Why Gaussian

                                          DTU Compute

                                          2122018Introduction to Medical Image Analysis45 DTU Compute Technical University of Denmark

                                          Use of smoothing

                                          3x3 7x7 11x11 15x15

                                          DTU Compute

                                          2122018Introduction to Medical Image Analysis46 DTU Compute Technical University of Denmark

                                          Use of smoothing Large kernels smooth more Removes high frequency information Good at enhancing big structures

                                          3x3 15x15

                                          DTU Compute

                                          2122018Introduction to Medical Image Analysis47 DTU Compute Technical University of Denmark

                                          Mean filterA) 166B) 113C) 12D) 51E) 245

                                          0 0 0 0

                                          A B C D E

                                          Chart1

                                          12
                                          0
                                          0
                                          0
                                          0

                                          Sheet1

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                                          Border handling

                                          0 2 41 2 2

                                          1 6 3

                                          1 2 12 5 3

                                          2 1 3

                                          1 3 1

                                          2 2 2

                                          0 1 3

                                          1 2 0

                                          2 1 4

                                          1 0 1

                                          Input Output

                                          No values at the border

                                          DTU Compute

                                          2122018Introduction to Medical Image Analysis50 DTU Compute Technical University of Denmark

                                          Border handling ndash extend the input

                                          0 2 41 2 2

                                          1 6 3

                                          1 2 12 5 3

                                          2 1 3

                                          1 3 1

                                          2 2 2

                                          0 1 3

                                          1 2 0

                                          2 1 4

                                          1 0 1

                                          Input

                                          0 0 0 0 000000

                                          bull Zero padding ndash what happens

                                          bull Zero is black ndash creates dark border around the image

                                          DTU Compute

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                                          Correlation with zero paddingA) 5 8B) 12 16C) 13 3D) 15 21E) 17 12

                                          1 2 11 3 11 2 1

                                          0 2 41 2 2

                                          1 6 3

                                          1 2 12 5 3

                                          2 1 3

                                          1 3 1

                                          2 2 2

                                          0 1 3

                                          1 2 0

                                          2 1 4

                                          1 0 1

                                          0

                                          13

                                          0 0 0

                                          A B C D E

                                          Chart1

                                          0
                                          13
                                          0
                                          0
                                          0

                                          Sheet1

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                                          Border handling ndash extend the input

                                          0 2 41 2 2

                                          1 6 3

                                          1 2 12 5 3

                                          2 1 3

                                          1 3 1

                                          2 2 2

                                          0 1 3

                                          1 2 0

                                          2 1 4

                                          1 0 1

                                          Input

                                          1 2 0 1 311211

                                          bull Reflection

                                          bull Normally better than zero padding

                                          DTU Compute

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                                          Template Matching Template

                                          ndash Skabelon paring dansk Locates objects in images

                                          Input

                                          Template

                                          Output Correlation image

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                                          Template Matching The correlation between the template and the input

                                          image is computed for each pixel

                                          Input

                                          Template

                                          Output Correlation image

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                                          Template Matching The pixel with the highest value is found in the

                                          output imagendash Here is the highest correlation

                                          Input

                                          Template

                                          Output Correlation image

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                                          Template Matching This corresponds to the found pattern in the input

                                          image

                                          Input

                                          Template

                                          Output Correlation image

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                                          Problematic Correlation Correlation matching has problem with light areas ndash

                                          why

                                          Input (f)

                                          Template (h)

                                          Output Correlation imageFake max

                                          Real max

                                          Very High119892119892 119909119909119910119910 = 119895119895=minus119877119877

                                          119877119877

                                          119894119894=minus119877119877

                                          119877119877

                                          ℎ(119894119894 119895119895) 119891119891(119909119909 + 119894119894119910119910 + 119895119895)

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                                          Normalised Cross Correlation

                                          Input (f)

                                          Template (h)

                                          Output Correlation image

                                          Real max

                                          NCC x y =Correlation

                                          Length of image patch sdot Length of template

                                          DTU Compute

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                                          Length of template Vector length

                                          ndash Put all pixel values into a vectorndash Compute the length of this vector

                                          Describes the intensity of the templatendash Bright template has a large lengthndash Dark template has a small length

                                          Template (h)

                                          Length of template = 119895119895=minus119877119877

                                          119877119877

                                          119894119894=minus119877119877

                                          119877119877

                                          ℎ(119894119894 119895119895) ℎ(119894119894 119895119895)

                                          DTU Compute

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                                          Length of image patch Vector length based on pixel values in image patch Describes the intensity of the image patch

                                          Template (h)

                                          Input (f) with patch

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                                          Normalised Cross Correlation The length of the image patch and the length of

                                          template normalise the NCC If the image is very bright the NCC will be ldquopulled

                                          downrdquo

                                          NCC x y =Correlation

                                          Length of image patch sdot Length of template

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                                          Normalised Cross Correlation NCC will be between

                                          ndash 0 No similarity between template and image patchndash 1 Template and image patch are identical

                                          Input (f)

                                          Template (h)

                                          Output Correlation image

                                          Real max

                                          NCC x y =Correlation

                                          Length of image patch sdot Length of template

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                                          Normalised Cross Correlation

                                          A) 010B) 033C) 083D) 062E) 098

                                          Der udfoslashres template matching med og normalized crosscorrelation (NCC) beregnes Hvad bliver NNC i den markerede pixel

                                          1

                                          2 2

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                                          A B C D E

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                                          Edges An edge is where there is a

                                          high change in gray level values

                                          Objects are often separated from the background by edgesGray level profile

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                                          2122018Introduction to Medical Image Analysis67 DTU Compute Technical University of Denmark

                                          Edges The profile as a function f(d) What value is high when there

                                          is an edgendash The slope of fndash The slope of the tangent at d

                                          f(d)

                                          119891119891prime(119889119889)

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                                          Finite Difference Definition of slope

                                          Approximation

                                          Simpler approximationh = 1

                                          119891119891prime 119889119889 = limℎrarr0

                                          119891119891 119889119889 + ℎ minus 119891119891(119889119889)ℎ

                                          119891119891prime 119889119889 asymp119891119891 119889119889 + ℎ minus 119891119891(119889119889)

                                          ℎ

                                          119891119891prime 119889119889 asymp 119891119891 119889119889 + 1 minus 119891119891(119889119889)

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                                          Edges Discrete approximation of frsquo(d) Can be implemented as a filter

                                          -1 0 1

                                          f(d-2) f(d-1) f(d) f(d+1) f(d+2) f(d+3)

                                          f(d)

                                          119891119891prime 119889119889 asymp 119891119891 119889119889 + 1 minus 119891119891(119889119889)

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                                          Edges in 2D Changes in gray level values

                                          ndash Image gradientndash Gradient is the 2D derivative of a 2D function f(xy)ndash Equal to the slope of the imagendash A steep slope is equal to an edge

                                          120571120571119891119891 119909119909119910119910 = 119866(119892119892119909119909119892119892119910119910)

                                          DTU Compute

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                                          Edge filter kernel The Prewitt filter is a typical

                                          edge filter Output image has high

                                          values where there are edges

                                          -1 0 1

                                          -1 0 1

                                          -1 0 1Vertical Prewitt filter

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                                          Prewitt filter

                                          Original Prewitt Prewitt

                                          Hot colormapSmooth 15x15

                                          Smooth 15x15

                                          Prewitt

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                                          Edge detection Edge filter

                                          ndash Prewitt for example Thresholding

                                          ndash Separate edges from non-edges

                                          Output is binary imagendash Edges are white

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                                          Edge filtering

                                          A) MeanB) Horizontal SobelC) Vertical PrewittD) Horisontal PrewittE) Median

                                          Der udfoslashres en filtrering (correlation) med et filter paring billedet Der bruges ikke coefficient normalization Den filtrerede vaeligrdi i den markerede pixel bliver -119 Hvilket et 3x3 filter blev benyttet

                                          0

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                                          02511 - Niveau af dagens emne forelaeligsingA) Meget letB) LetC) PassendeD) SvaeligrtE) Meget svaeligrt

                                          23

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                                          02512 - Niveau af dagens emne forelaeligsingA) Meget letB) LetC) PassendeD) SvaeligrtE) Meget svaeligrt

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                                          02511 - Mit eget udbytte af dagenA) Jeg har laeligrt meget lidtB) Lidt laeligringC) PassendeD) God laeligringE) Jeg har laeligrt meget

                                          0 0

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                                          02512 - Mit eget udbytte af dagenA) Jeg har laeligrt meget lidtB) Lidt laeligringC) PassendeD) God laeligringE) Jeg har laeligrt meget

                                          2

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                                          02511 - Sidste uges oslashvelser (pixelwiseoperations)A) Meget letteB) LetteC) PassendeD) SvaeligreE) Meget svaeligre

                                          0 0

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                                          02512 - Sidste uges oslashvelser (pixelwiseoperations)A) Meget letteB) LetteC) PassendeD) SvaeligreE) Meget svaeligre

                                          3

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                                          Denne uges brug af clickersA) click click click ndash jeg bliver

                                          sindssygB) For meget clickC) PassendeD) Jeg vil gerne have lidt mereE) Jeg kan ikrsquo faring nok

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                                          What can you do after today Describe the difference between point processing and neighbourhood

                                          processing Compute a rank filtered image using the min max median and

                                          difference rank filters Compute a mean filtered image Decide if median or average filtering should be used for noise removal Choose the appropriate image border handling based on a given input

                                          image Implement and apply template matching Compute the normalised cross correlation and explain why it should be

                                          used Apply given image filter kernels to images Use edge filters on images Describe finite difference approximation of image gradients Describe the concept of edge detection

                                          DTU Compute

                                          2122018Introduction to Medical Image Analysis84 DTU Compute Technical University of Denmark

                                          Oslashvelsesrapport over oslashvelse 4 - 02511 Oslashvelser taeligller cirka 30 af karakteren Skal afleveres senest den 7 marts kl 2359 Kan afleveres af 1 eller 2 personer

                                          ndash I skal skrive jeres egen oslashvelsesrapportndash Brug mindst et af jeres egne billeder

                                          Afleveres som PDF Lad vaeligre med at kopiere opgaveteksten ind i jeres

                                          opgave Put Matlab kode i et Appendix og henvis fra teksten Eksempel rapport over oslashvelse findes paring

                                          hjemmesiden under eksamen

                                          DTU Compute

                                          2122018Introduction to Medical Image Analysis85 DTU Compute Technical University of Denmark

                                          Exercises

                                          • Introduction to Medical Image Analysis
                                          • Lecture 4 ndash Neighbourhood Processing
                                          • What can you do after today
                                          • Point processing
                                          • Point processing
                                          • Neighbourhood processing
                                          • Use of filtering
                                          • Salt and pepper noise
                                          • Salt and pepper noise
                                          • What is so special about noise
                                          • Noise ndash go away
                                          • What is the median Value
                                          • The median value
                                          • Noise away ndash the median filter
                                          • Noise removal ndash average filter
                                          • Noise removal ndash median filter
                                          • Image Filtering
                                          • Median filter
                                          • Rank filters
                                          • Median filter
                                          • Correlation
                                          • Why do we need similarity
                                          • Correlation (1D)
                                          • Correlation (1D)
                                          • Normalisation
                                          • Normalisation
                                          • Correlation on images
                                          • Correlation on images
                                          • Correlation on images
                                          • Draw your filter
                                          • Correlation on images ndash no normalisation
                                          • Correlation on images ndash no normalisation 2
                                          • Mathematics of 2D Correlation
                                          • Mathematics of 2D Correlation
                                          • Mathematics of 2D Correlation
                                          • Slide Number 40
                                          • 2D Kernel Normalisation
                                          • Correlation
                                          • Smoothing filters
                                          • Use of smoothing
                                          • Use of smoothing
                                          • Mean filter
                                          • Border handling
                                          • Border handling ndash extend the input
                                          • Correlation with zero padding
                                          • Border handling ndash extend the input
                                          • Template Matching
                                          • Template Matching
                                          • Template Matching
                                          • Template Matching
                                          • Problematic Correlation
                                          • Normalised Cross Correlation
                                          • Length of template
                                          • Length of image patch
                                          • Normalised Cross Correlation
                                          • Normalised Cross Correlation
                                          • Normalised Cross Correlation
                                          • Edges
                                          • Edges
                                          • Finite Difference
                                          • Edges
                                          • Edges in 2D
                                          • Edge filter kernel
                                          • Prewitt filter
                                          • Edge detection
                                          • Edge filtering
                                          • 02511 - Niveau af dagens emne forelaeligsing
                                          • 02512 - Niveau af dagens emne forelaeligsing
                                          • 02511 - Mit eget udbytte af dagen
                                          • 02512 - Mit eget udbytte af dagen
                                          • 02511 - Sidste uges oslashvelser (pixelwise operations)
                                          • 02512 - Sidste uges oslashvelser (pixelwise operations)
                                          • Denne uges brug af clickers
                                          • What can you do after today
                                          • Oslashvelsesrapport over oslashvelse 4 - 02511
                                          • Exercises
                                            A0
                                            B0
                                            C5
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                                            E6
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                                            C14
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                                            C1
                                            D0
                                            E0
                                            A
                                            B
                                            C
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                                            C1
                                            D0
                                            E0
                                            A
                                            B
                                            C
                                            D
                                            E

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                                            Rank filters Based on sorting the pixel

                                            values in the neighbouring region

                                            Minimum rank filterndash Darker image Noise problems

                                            Maximum rank filterndash Lighter image Noise problems

                                            Difference filterndash Enhances changes (edges)

                                            0168 169 170 170 170172 172173

                                            -

                                            DTU Compute

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                                            Median filter

                                            A) 3B) 84C) 112D) 73E) 202

                                            0

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                                            Correlation What is it Two measurements

                                            ndash Low correlationndash High correlation

                                            High correlation means that there is a relation between the values

                                            They look the same Correlation is a measure of

                                            similarity

                                            Low

                                            High

                                            Muscles

                                            Mat

                                            h Ski

                                            lls

                                            Muscles

                                            Ben

                                            ch P

                                            ress

                                            DTU Compute

                                            2122018Introduction to Medical Image Analysis24 DTU Compute Technical University of Denmark

                                            Why do we need similarity Image analysis is also about recognition of patterns Often an example pattern is used We need something to tell us if there is a high match

                                            between our pattern and a part of the image

                                            Example pattern

                                            Image

                                            Find matches

                                            DTU Compute

                                            2122018Introduction to Medical Image Analysis25 DTU Compute Technical University of Denmark

                                            Correlation (1D)

                                            1 1 2 2 1 1 2 2 1 1

                                            1 2 1

                                            45

                                            41

                                            1 1 + 2 1 + 1 2 = 5

                                            Normalise

                                            Kernel

                                            Signal (1D image)

                                            41

                                            DTU Compute

                                            2122018Introduction to Medical Image Analysis26 DTU Compute Technical University of Denmark

                                            Correlation (1D)

                                            1 1 2 2 1 1 2 2 1 1

                                            1 2 1

                                            45

                                            47

                                            47

                                            45

                                            45

                                            47

                                            47

                                            45

                                            41

                                            DTU Compute

                                            2122018Introduction to Medical Image Analysis27 DTU Compute Technical University of Denmark

                                            Normalisation

                                            1 1 2 2 1 1 2 2 1 1

                                            1 2 1

                                            45

                                            41

                                            1 1 + 2 1 + 1 2 = 5

                                            Normalise41

                                            bull The sum of the kernel elements is used

                                            bull Keep the values in the same range as the input image

                                            Sum is 4

                                            DTU Compute

                                            2122018Introduction to Medical Image Analysis28 DTU Compute Technical University of Denmark

                                            Normalisation Normalisation factor

                                            ndash Sum of kernel coefficients

                                            1 2 1h(x)

                                            119909119909

                                            ℎ 119909119909 = 1 + 2 + 1

                                            DTU Compute

                                            2122018Introduction to Medical Image Analysis29 DTU Compute Technical University of Denmark

                                            Correlation on images The filter is now 2D 1 1 1

                                            1 1 1

                                            1 1 1

                                            0 2 4

                                            1 2 2

                                            1 6 3

                                            1 2 12 5 3

                                            2 1 3

                                            1 3 1

                                            2 2 2

                                            0 1 3

                                            1 2 0

                                            2 1 4

                                            1 0 1

                                            912

                                            91

                                            Input OutputKernel

                                            Kernel coefficients

                                            DTU Compute

                                            2122018Introduction to Medical Image Analysis30 DTU Compute Technical University of Denmark

                                            Correlation on images

                                            1 1 11 1 11 1 1

                                            0 2 4

                                            1 2 2

                                            1 6 3

                                            1 2 0

                                            2 1 4

                                            1 0 1

                                            912

                                            911

                                            91

                                            Input Output

                                            1 3 1

                                            2 2 2

                                            0 1 3

                                            1 2 12 5 3

                                            2 1 3

                                            DTU Compute

                                            2122018Introduction to Medical Image Analysis31 DTU Compute Technical University of Denmark

                                            Correlation on images

                                            Input Output

                                            The mask is moved row by row

                                            No values at the border

                                            0 2 4

                                            1 2 2

                                            1 6 3

                                            1 2 0

                                            2 1 4

                                            1 0 1

                                            1 3 1

                                            2 2 2

                                            0 1 3

                                            1 2 12 5 3

                                            2 1 3

                                            DTU Compute

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                                            1 2 1

                                            1 3 1

                                            1 2 1

                                            -1 -2 -1

                                            0 0 0

                                            1 2 1

                                            Draw your filter

                                            DTU Compute

                                            2122018Introduction to Medical Image Analysis33 DTU Compute Technical University of Denmark

                                            Correlation on images ndash no normalisationA) 4B) 7C) 16D) 23E) 25

                                            1 2 11 3 11 2 1

                                            0 2 41 2 2

                                            1 6 3

                                            1 2 12 5 3

                                            2 1 3

                                            1 3 1

                                            2 2 2

                                            0 1 3

                                            1 2 0

                                            2 1 4

                                            1 0 11 0

                                            14

                                            0 0

                                            A B C D E

                                            Chart1

                                            1
                                            0
                                            14
                                            0
                                            0

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                                            Correlation on images ndash no normalisation 2A) 010B) 3 3C) 6 2D) 10 15E) 11 32

                                            13

                                            0 0 0 0

                                            A B C D E

                                            -1 -2 -10 0 01 2 1

                                            0 2 41 2 2

                                            1 6 3

                                            1 2 12 5 3

                                            2 1 3

                                            1 3 1

                                            2 2 2

                                            0 1 3

                                            1 2 0

                                            2 1 4

                                            1 0 1

                                            Chart1

                                            13
                                            0
                                            0
                                            0
                                            0

                                            Sheet1

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                                            Mathematics of 2D Correlation

                                            h

                                            f

                                            Correlation operator

                                            1 2 11 3 11 2 1

                                            0 2 4

                                            1 2 2

                                            1 6 3

                                            1 2 1

                                            2 5 3

                                            2 1 3

                                            1 3 1

                                            2 2 2

                                            0 1 3

                                            1 2 0

                                            2 1 4

                                            1 0 1

                                            119892119892 119909119909119910119910 = 119891119891 119909119909119910119910 ∘ ℎ(119909119909119910119910)

                                            DTU Compute

                                            2122018Introduction to Medical Image Analysis38 DTU Compute Technical University of Denmark

                                            Mathematics of 2D Correlation

                                            1 2 11 3 11 2 1

                                            0 2 4

                                            1 2 2

                                            1 6 3

                                            1 2 1

                                            2 5 3

                                            2 1 3

                                            1 3 1

                                            2 2 2

                                            0 1 3

                                            1 2 0

                                            2 1 4

                                            1 0 1

                                            h

                                            fh(00)

                                            f(21)

                                            Example g(21)

                                            i = -1 j = -1

                                            i = 1 j = 0

                                            119892119892 119909119909119910119910 = 119895119895=minus119877119877

                                            119877119877

                                            119894119894=minus119877119877

                                            119877119877

                                            ℎ(119894119894 119895119895) 119891119891(119909119909 + 119894119894119910119910 + 119895119895)

                                            DTU Compute

                                            2122018Introduction to Medical Image Analysis39 DTU Compute Technical University of Denmark

                                            Mathematics of 2D Correlation

                                            1 2 11 3 11 2 1

                                            0 2 4

                                            1 2 2

                                            1 6 3

                                            1 2 1

                                            2 5 3

                                            2 1 3

                                            1 3 1

                                            2 2 2

                                            0 1 3

                                            1 2 0

                                            2 1 4

                                            1 0 1

                                            h

                                            f

                                            119892119892 119909119909119910119910 = 119895119895=minus119877119877

                                            119877119877

                                            119894119894=minus119877119877

                                            119877119877

                                            ℎ(119894119894 119895119895) 119891119891(119909119909 + 119894119894119910119910 + 119895119895)

                                            119892119892(119909119909119910119910 = 1 2 + 2 0 + 1 1 + 1 1 + 3 4 + 1 2 + 1 0 + 2 1 + 1 0

                                            DTU Compute

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                                            119892119892 119909119909 119910119910 = 119895119895=minus119877119877

                                            119877119877

                                            119894119894=minus119877119877

                                            119877119877

                                            ℎ(119894119894 119895119895) 119891119891(119909119909 + 119894119894119910119910 + 119895119895)

                                            119892119892 22 =ℎ minus1minus1 sdot 119891119891 11 + ℎ 0minus1 sdot 119891119891 21 + ℎ 1minus1 sdot 119891119891 31 +ℎ minus10 sdot 119891119891 12 + ℎ 00 sdot 119891119891 22 + ℎ 10 sdot 119891119891 32 +ℎ minus11 sdot 119891119891 13 + ℎ 01 sdot 119891119891 23 + ℎ 11 sdot 119891119891 33

                                            DTU Compute

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                                            2D Kernel Normalisation

                                            1 2 11 3 11 2 1

                                            h

                                            Normalisation factor

                                            1 + 2 + 1 + 1 + 3 + 1 + 1 + 2 + 1 = 13

                                            119909119909

                                            119910119910

                                            ℎ(119909119909119910119910)

                                            DTU Compute

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                                            CorrelationA) 50122B) 123001C) 11233D) 2550E) 90454

                                            0 0 0 0

                                            13

                                            A B C D E

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                                            0
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                                            0
                                            0
                                            13

                                            Sheet1

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                                            Smoothing filters

                                            Also know as ndash Smoothing kernel Mean filter Low pass filter blurring

                                            The simplest filter ndash Spatial low pass filterndash Removes high frequencies

                                            Another mask ndash Gaussian filter

                                            1 1 1

                                            1 1 1

                                            1 1 191

                                            1 2 1

                                            2 4 2

                                            1 2 1161

                                            Why Gaussian

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                                            Use of smoothing

                                            3x3 7x7 11x11 15x15

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                                            Use of smoothing Large kernels smooth more Removes high frequency information Good at enhancing big structures

                                            3x3 15x15

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                                            Mean filterA) 166B) 113C) 12D) 51E) 245

                                            0 0 0 0

                                            A B C D E

                                            Chart1

                                            12
                                            0
                                            0
                                            0
                                            0

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                                            Border handling

                                            0 2 41 2 2

                                            1 6 3

                                            1 2 12 5 3

                                            2 1 3

                                            1 3 1

                                            2 2 2

                                            0 1 3

                                            1 2 0

                                            2 1 4

                                            1 0 1

                                            Input Output

                                            No values at the border

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                                            Border handling ndash extend the input

                                            0 2 41 2 2

                                            1 6 3

                                            1 2 12 5 3

                                            2 1 3

                                            1 3 1

                                            2 2 2

                                            0 1 3

                                            1 2 0

                                            2 1 4

                                            1 0 1

                                            Input

                                            0 0 0 0 000000

                                            bull Zero padding ndash what happens

                                            bull Zero is black ndash creates dark border around the image

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                                            Correlation with zero paddingA) 5 8B) 12 16C) 13 3D) 15 21E) 17 12

                                            1 2 11 3 11 2 1

                                            0 2 41 2 2

                                            1 6 3

                                            1 2 12 5 3

                                            2 1 3

                                            1 3 1

                                            2 2 2

                                            0 1 3

                                            1 2 0

                                            2 1 4

                                            1 0 1

                                            0

                                            13

                                            0 0 0

                                            A B C D E

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                                            0
                                            13
                                            0
                                            0
                                            0

                                            Sheet1

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                                            Border handling ndash extend the input

                                            0 2 41 2 2

                                            1 6 3

                                            1 2 12 5 3

                                            2 1 3

                                            1 3 1

                                            2 2 2

                                            0 1 3

                                            1 2 0

                                            2 1 4

                                            1 0 1

                                            Input

                                            1 2 0 1 311211

                                            bull Reflection

                                            bull Normally better than zero padding

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                                            Template Matching Template

                                            ndash Skabelon paring dansk Locates objects in images

                                            Input

                                            Template

                                            Output Correlation image

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                                            Template Matching The correlation between the template and the input

                                            image is computed for each pixel

                                            Input

                                            Template

                                            Output Correlation image

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                                            Template Matching The pixel with the highest value is found in the

                                            output imagendash Here is the highest correlation

                                            Input

                                            Template

                                            Output Correlation image

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                                            Template Matching This corresponds to the found pattern in the input

                                            image

                                            Input

                                            Template

                                            Output Correlation image

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                                            Problematic Correlation Correlation matching has problem with light areas ndash

                                            why

                                            Input (f)

                                            Template (h)

                                            Output Correlation imageFake max

                                            Real max

                                            Very High119892119892 119909119909119910119910 = 119895119895=minus119877119877

                                            119877119877

                                            119894119894=minus119877119877

                                            119877119877

                                            ℎ(119894119894 119895119895) 119891119891(119909119909 + 119894119894119910119910 + 119895119895)

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                                            Normalised Cross Correlation

                                            Input (f)

                                            Template (h)

                                            Output Correlation image

                                            Real max

                                            NCC x y =Correlation

                                            Length of image patch sdot Length of template

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                                            Length of template Vector length

                                            ndash Put all pixel values into a vectorndash Compute the length of this vector

                                            Describes the intensity of the templatendash Bright template has a large lengthndash Dark template has a small length

                                            Template (h)

                                            Length of template = 119895119895=minus119877119877

                                            119877119877

                                            119894119894=minus119877119877

                                            119877119877

                                            ℎ(119894119894 119895119895) ℎ(119894119894 119895119895)

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                                            Length of image patch Vector length based on pixel values in image patch Describes the intensity of the image patch

                                            Template (h)

                                            Input (f) with patch

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                                            Normalised Cross Correlation The length of the image patch and the length of

                                            template normalise the NCC If the image is very bright the NCC will be ldquopulled

                                            downrdquo

                                            NCC x y =Correlation

                                            Length of image patch sdot Length of template

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                                            Normalised Cross Correlation NCC will be between

                                            ndash 0 No similarity between template and image patchndash 1 Template and image patch are identical

                                            Input (f)

                                            Template (h)

                                            Output Correlation image

                                            Real max

                                            NCC x y =Correlation

                                            Length of image patch sdot Length of template

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                                            Normalised Cross Correlation

                                            A) 010B) 033C) 083D) 062E) 098

                                            Der udfoslashres template matching med og normalized crosscorrelation (NCC) beregnes Hvad bliver NNC i den markerede pixel

                                            1

                                            2 2

                                            3

                                            2

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                                            Edges An edge is where there is a

                                            high change in gray level values

                                            Objects are often separated from the background by edgesGray level profile

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                                            Edges The profile as a function f(d) What value is high when there

                                            is an edgendash The slope of fndash The slope of the tangent at d

                                            f(d)

                                            119891119891prime(119889119889)

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                                            Finite Difference Definition of slope

                                            Approximation

                                            Simpler approximationh = 1

                                            119891119891prime 119889119889 = limℎrarr0

                                            119891119891 119889119889 + ℎ minus 119891119891(119889119889)ℎ

                                            119891119891prime 119889119889 asymp119891119891 119889119889 + ℎ minus 119891119891(119889119889)

                                            ℎ

                                            119891119891prime 119889119889 asymp 119891119891 119889119889 + 1 minus 119891119891(119889119889)

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                                            Edges Discrete approximation of frsquo(d) Can be implemented as a filter

                                            -1 0 1

                                            f(d-2) f(d-1) f(d) f(d+1) f(d+2) f(d+3)

                                            f(d)

                                            119891119891prime 119889119889 asymp 119891119891 119889119889 + 1 minus 119891119891(119889119889)

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                                            Edges in 2D Changes in gray level values

                                            ndash Image gradientndash Gradient is the 2D derivative of a 2D function f(xy)ndash Equal to the slope of the imagendash A steep slope is equal to an edge

                                            120571120571119891119891 119909119909119910119910 = 119866(119892119892119909119909119892119892119910119910)

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                                            Edge filter kernel The Prewitt filter is a typical

                                            edge filter Output image has high

                                            values where there are edges

                                            -1 0 1

                                            -1 0 1

                                            -1 0 1Vertical Prewitt filter

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                                            Prewitt filter

                                            Original Prewitt Prewitt

                                            Hot colormapSmooth 15x15

                                            Smooth 15x15

                                            Prewitt

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                                            Edge detection Edge filter

                                            ndash Prewitt for example Thresholding

                                            ndash Separate edges from non-edges

                                            Output is binary imagendash Edges are white

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                                            Edge filtering

                                            A) MeanB) Horizontal SobelC) Vertical PrewittD) Horisontal PrewittE) Median

                                            Der udfoslashres en filtrering (correlation) med et filter paring billedet Der bruges ikke coefficient normalization Den filtrerede vaeligrdi i den markerede pixel bliver -119 Hvilket et 3x3 filter blev benyttet

                                            0

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                                            02511 - Niveau af dagens emne forelaeligsingA) Meget letB) LetC) PassendeD) SvaeligrtE) Meget svaeligrt

                                            23

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                                            02512 - Niveau af dagens emne forelaeligsingA) Meget letB) LetC) PassendeD) SvaeligrtE) Meget svaeligrt

                                            0 0

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                                            02511 - Mit eget udbytte af dagenA) Jeg har laeligrt meget lidtB) Lidt laeligringC) PassendeD) God laeligringE) Jeg har laeligrt meget

                                            0 0

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                                            02512 - Mit eget udbytte af dagenA) Jeg har laeligrt meget lidtB) Lidt laeligringC) PassendeD) God laeligringE) Jeg har laeligrt meget

                                            2

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                                            02511 - Sidste uges oslashvelser (pixelwiseoperations)A) Meget letteB) LetteC) PassendeD) SvaeligreE) Meget svaeligre

                                            0 0

                                            1

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                                            1

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                                            02512 - Sidste uges oslashvelser (pixelwiseoperations)A) Meget letteB) LetteC) PassendeD) SvaeligreE) Meget svaeligre

                                            3

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                                            Denne uges brug af clickersA) click click click ndash jeg bliver

                                            sindssygB) For meget clickC) PassendeD) Jeg vil gerne have lidt mereE) Jeg kan ikrsquo faring nok

                                            0 0

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                                            What can you do after today Describe the difference between point processing and neighbourhood

                                            processing Compute a rank filtered image using the min max median and

                                            difference rank filters Compute a mean filtered image Decide if median or average filtering should be used for noise removal Choose the appropriate image border handling based on a given input

                                            image Implement and apply template matching Compute the normalised cross correlation and explain why it should be

                                            used Apply given image filter kernels to images Use edge filters on images Describe finite difference approximation of image gradients Describe the concept of edge detection

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                                            Oslashvelsesrapport over oslashvelse 4 - 02511 Oslashvelser taeligller cirka 30 af karakteren Skal afleveres senest den 7 marts kl 2359 Kan afleveres af 1 eller 2 personer

                                            ndash I skal skrive jeres egen oslashvelsesrapportndash Brug mindst et af jeres egne billeder

                                            Afleveres som PDF Lad vaeligre med at kopiere opgaveteksten ind i jeres

                                            opgave Put Matlab kode i et Appendix og henvis fra teksten Eksempel rapport over oslashvelse findes paring

                                            hjemmesiden under eksamen

                                            DTU Compute

                                            2122018Introduction to Medical Image Analysis85 DTU Compute Technical University of Denmark

                                            Exercises

                                            • Introduction to Medical Image Analysis
                                            • Lecture 4 ndash Neighbourhood Processing
                                            • What can you do after today
                                            • Point processing
                                            • Point processing
                                            • Neighbourhood processing
                                            • Use of filtering
                                            • Salt and pepper noise
                                            • Salt and pepper noise
                                            • What is so special about noise
                                            • Noise ndash go away
                                            • What is the median Value
                                            • The median value
                                            • Noise away ndash the median filter
                                            • Noise removal ndash average filter
                                            • Noise removal ndash median filter
                                            • Image Filtering
                                            • Median filter
                                            • Rank filters
                                            • Median filter
                                            • Correlation
                                            • Why do we need similarity
                                            • Correlation (1D)
                                            • Correlation (1D)
                                            • Normalisation
                                            • Normalisation
                                            • Correlation on images
                                            • Correlation on images
                                            • Correlation on images
                                            • Draw your filter
                                            • Correlation on images ndash no normalisation
                                            • Correlation on images ndash no normalisation 2
                                            • Mathematics of 2D Correlation
                                            • Mathematics of 2D Correlation
                                            • Mathematics of 2D Correlation
                                            • Slide Number 40
                                            • 2D Kernel Normalisation
                                            • Correlation
                                            • Smoothing filters
                                            • Use of smoothing
                                            • Use of smoothing
                                            • Mean filter
                                            • Border handling
                                            • Border handling ndash extend the input
                                            • Correlation with zero padding
                                            • Border handling ndash extend the input
                                            • Template Matching
                                            • Template Matching
                                            • Template Matching
                                            • Template Matching
                                            • Problematic Correlation
                                            • Normalised Cross Correlation
                                            • Length of template
                                            • Length of image patch
                                            • Normalised Cross Correlation
                                            • Normalised Cross Correlation
                                            • Normalised Cross Correlation
                                            • Edges
                                            • Edges
                                            • Finite Difference
                                            • Edges
                                            • Edges in 2D
                                            • Edge filter kernel
                                            • Prewitt filter
                                            • Edge detection
                                            • Edge filtering
                                            • 02511 - Niveau af dagens emne forelaeligsing
                                            • 02512 - Niveau af dagens emne forelaeligsing
                                            • 02511 - Mit eget udbytte af dagen
                                            • 02512 - Mit eget udbytte af dagen
                                            • 02511 - Sidste uges oslashvelser (pixelwise operations)
                                            • 02512 - Sidste uges oslashvelser (pixelwise operations)
                                            • Denne uges brug af clickers
                                            • What can you do after today
                                            • Oslashvelsesrapport over oslashvelse 4 - 02511
                                            • Exercises
                                              A0
                                              B0
                                              C5
                                              D0
                                              E6
                                              A
                                              B
                                              C
                                              D
                                              E
                                              A3
                                              B0
                                              C3
                                              D0
                                              E0
                                              A
                                              B
                                              C
                                              D
                                              E
                                              A0
                                              B0
                                              C1
                                              D4
                                              E1
                                              A
                                              B
                                              C
                                              D
                                              E
                                              A2
                                              B1
                                              C3
                                              D2
                                              E0
                                              A
                                              B
                                              C
                                              D
                                              E
                                              A0
                                              B0
                                              C2
                                              D6
                                              E0
                                              A
                                              B
                                              C
                                              D
                                              E
                                              A0
                                              B0
                                              C1
                                              D0
                                              E0
                                              A
                                              B
                                              C
                                              D
                                              E
                                              A2
                                              B3
                                              C6
                                              D1
                                              E0
                                              A
                                              B
                                              C
                                              D
                                              E
                                              A0
                                              B8
                                              C1
                                              D1
                                              E0
                                              A
                                              B
                                              C
                                              D
                                              E
                                              A1
                                              B2
                                              C2
                                              D3
                                              E2
                                              A
                                              B
                                              C
                                              D
                                              E
                                              A0
                                              B13
                                              C0
                                              D0
                                              E0
                                              A
                                              B
                                              C
                                              D
                                              E
                                              A12
                                              B0
                                              C0
                                              D0
                                              E0
                                              A
                                              B
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                                              A0
                                              B0
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                                              E13
                                              A
                                              B
                                              C
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                                              A13
                                              B0
                                              C0
                                              D0
                                              E0
                                              A
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                                              C
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                                              E
                                              A1
                                              B0
                                              C14
                                              D0
                                              E0
                                              A
                                              B
                                              C
                                              D
                                              E
                                              A0
                                              B12
                                              C1
                                              D0
                                              E0
                                              A
                                              B
                                              C
                                              D
                                              E
                                              A0
                                              B13
                                              C1
                                              D0
                                              E0

                                              DTU Compute

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                                              Rank filters Based on sorting the pixel

                                              values in the neighbouring region

                                              Minimum rank filterndash Darker image Noise problems

                                              Maximum rank filterndash Lighter image Noise problems

                                              Difference filterndash Enhances changes (edges)

                                              0168 169 170 170 170172 172173

                                              -

                                              DTU Compute

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                                              Median filter

                                              A) 3B) 84C) 112D) 73E) 202

                                              0

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                                              Correlation What is it Two measurements

                                              ndash Low correlationndash High correlation

                                              High correlation means that there is a relation between the values

                                              They look the same Correlation is a measure of

                                              similarity

                                              Low

                                              High

                                              Muscles

                                              Mat

                                              h Ski

                                              lls

                                              Muscles

                                              Ben

                                              ch P

                                              ress

                                              DTU Compute

                                              2122018Introduction to Medical Image Analysis24 DTU Compute Technical University of Denmark

                                              Why do we need similarity Image analysis is also about recognition of patterns Often an example pattern is used We need something to tell us if there is a high match

                                              between our pattern and a part of the image

                                              Example pattern

                                              Image

                                              Find matches

                                              DTU Compute

                                              2122018Introduction to Medical Image Analysis25 DTU Compute Technical University of Denmark

                                              Correlation (1D)

                                              1 1 2 2 1 1 2 2 1 1

                                              1 2 1

                                              45

                                              41

                                              1 1 + 2 1 + 1 2 = 5

                                              Normalise

                                              Kernel

                                              Signal (1D image)

                                              41

                                              DTU Compute

                                              2122018Introduction to Medical Image Analysis26 DTU Compute Technical University of Denmark

                                              Correlation (1D)

                                              1 1 2 2 1 1 2 2 1 1

                                              1 2 1

                                              45

                                              47

                                              47

                                              45

                                              45

                                              47

                                              47

                                              45

                                              41

                                              DTU Compute

                                              2122018Introduction to Medical Image Analysis27 DTU Compute Technical University of Denmark

                                              Normalisation

                                              1 1 2 2 1 1 2 2 1 1

                                              1 2 1

                                              45

                                              41

                                              1 1 + 2 1 + 1 2 = 5

                                              Normalise41

                                              bull The sum of the kernel elements is used

                                              bull Keep the values in the same range as the input image

                                              Sum is 4

                                              DTU Compute

                                              2122018Introduction to Medical Image Analysis28 DTU Compute Technical University of Denmark

                                              Normalisation Normalisation factor

                                              ndash Sum of kernel coefficients

                                              1 2 1h(x)

                                              119909119909

                                              ℎ 119909119909 = 1 + 2 + 1

                                              DTU Compute

                                              2122018Introduction to Medical Image Analysis29 DTU Compute Technical University of Denmark

                                              Correlation on images The filter is now 2D 1 1 1

                                              1 1 1

                                              1 1 1

                                              0 2 4

                                              1 2 2

                                              1 6 3

                                              1 2 12 5 3

                                              2 1 3

                                              1 3 1

                                              2 2 2

                                              0 1 3

                                              1 2 0

                                              2 1 4

                                              1 0 1

                                              912

                                              91

                                              Input OutputKernel

                                              Kernel coefficients

                                              DTU Compute

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                                              Correlation on images

                                              1 1 11 1 11 1 1

                                              0 2 4

                                              1 2 2

                                              1 6 3

                                              1 2 0

                                              2 1 4

                                              1 0 1

                                              912

                                              911

                                              91

                                              Input Output

                                              1 3 1

                                              2 2 2

                                              0 1 3

                                              1 2 12 5 3

                                              2 1 3

                                              DTU Compute

                                              2122018Introduction to Medical Image Analysis31 DTU Compute Technical University of Denmark

                                              Correlation on images

                                              Input Output

                                              The mask is moved row by row

                                              No values at the border

                                              0 2 4

                                              1 2 2

                                              1 6 3

                                              1 2 0

                                              2 1 4

                                              1 0 1

                                              1 3 1

                                              2 2 2

                                              0 1 3

                                              1 2 12 5 3

                                              2 1 3

                                              DTU Compute

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                                              1 2 1

                                              1 3 1

                                              1 2 1

                                              -1 -2 -1

                                              0 0 0

                                              1 2 1

                                              Draw your filter

                                              DTU Compute

                                              2122018Introduction to Medical Image Analysis33 DTU Compute Technical University of Denmark

                                              Correlation on images ndash no normalisationA) 4B) 7C) 16D) 23E) 25

                                              1 2 11 3 11 2 1

                                              0 2 41 2 2

                                              1 6 3

                                              1 2 12 5 3

                                              2 1 3

                                              1 3 1

                                              2 2 2

                                              0 1 3

                                              1 2 0

                                              2 1 4

                                              1 0 11 0

                                              14

                                              0 0

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                                              Correlation on images ndash no normalisation 2A) 010B) 3 3C) 6 2D) 10 15E) 11 32

                                              13

                                              0 0 0 0

                                              A B C D E

                                              -1 -2 -10 0 01 2 1

                                              0 2 41 2 2

                                              1 6 3

                                              1 2 12 5 3

                                              2 1 3

                                              1 3 1

                                              2 2 2

                                              0 1 3

                                              1 2 0

                                              2 1 4

                                              1 0 1

                                              Chart1

                                              13
                                              0
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                                              Sheet1

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                                              Mathematics of 2D Correlation

                                              h

                                              f

                                              Correlation operator

                                              1 2 11 3 11 2 1

                                              0 2 4

                                              1 2 2

                                              1 6 3

                                              1 2 1

                                              2 5 3

                                              2 1 3

                                              1 3 1

                                              2 2 2

                                              0 1 3

                                              1 2 0

                                              2 1 4

                                              1 0 1

                                              119892119892 119909119909119910119910 = 119891119891 119909119909119910119910 ∘ ℎ(119909119909119910119910)

                                              DTU Compute

                                              2122018Introduction to Medical Image Analysis38 DTU Compute Technical University of Denmark

                                              Mathematics of 2D Correlation

                                              1 2 11 3 11 2 1

                                              0 2 4

                                              1 2 2

                                              1 6 3

                                              1 2 1

                                              2 5 3

                                              2 1 3

                                              1 3 1

                                              2 2 2

                                              0 1 3

                                              1 2 0

                                              2 1 4

                                              1 0 1

                                              h

                                              fh(00)

                                              f(21)

                                              Example g(21)

                                              i = -1 j = -1

                                              i = 1 j = 0

                                              119892119892 119909119909119910119910 = 119895119895=minus119877119877

                                              119877119877

                                              119894119894=minus119877119877

                                              119877119877

                                              ℎ(119894119894 119895119895) 119891119891(119909119909 + 119894119894119910119910 + 119895119895)

                                              DTU Compute

                                              2122018Introduction to Medical Image Analysis39 DTU Compute Technical University of Denmark

                                              Mathematics of 2D Correlation

                                              1 2 11 3 11 2 1

                                              0 2 4

                                              1 2 2

                                              1 6 3

                                              1 2 1

                                              2 5 3

                                              2 1 3

                                              1 3 1

                                              2 2 2

                                              0 1 3

                                              1 2 0

                                              2 1 4

                                              1 0 1

                                              h

                                              f

                                              119892119892 119909119909119910119910 = 119895119895=minus119877119877

                                              119877119877

                                              119894119894=minus119877119877

                                              119877119877

                                              ℎ(119894119894 119895119895) 119891119891(119909119909 + 119894119894119910119910 + 119895119895)

                                              119892119892(119909119909119910119910 = 1 2 + 2 0 + 1 1 + 1 1 + 3 4 + 1 2 + 1 0 + 2 1 + 1 0

                                              DTU Compute

                                              2122018Introduction to Medical Image Analysis40 DTU Compute Technical University of Denmark

                                              119892119892 119909119909 119910119910 = 119895119895=minus119877119877

                                              119877119877

                                              119894119894=minus119877119877

                                              119877119877

                                              ℎ(119894119894 119895119895) 119891119891(119909119909 + 119894119894119910119910 + 119895119895)

                                              119892119892 22 =ℎ minus1minus1 sdot 119891119891 11 + ℎ 0minus1 sdot 119891119891 21 + ℎ 1minus1 sdot 119891119891 31 +ℎ minus10 sdot 119891119891 12 + ℎ 00 sdot 119891119891 22 + ℎ 10 sdot 119891119891 32 +ℎ minus11 sdot 119891119891 13 + ℎ 01 sdot 119891119891 23 + ℎ 11 sdot 119891119891 33

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                                              2D Kernel Normalisation

                                              1 2 11 3 11 2 1

                                              h

                                              Normalisation factor

                                              1 + 2 + 1 + 1 + 3 + 1 + 1 + 2 + 1 = 13

                                              119909119909

                                              119910119910

                                              ℎ(119909119909119910119910)

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                                              CorrelationA) 50122B) 123001C) 11233D) 2550E) 90454

                                              0 0 0 0

                                              13

                                              A B C D E

                                              Chart1

                                              0
                                              0
                                              0
                                              0
                                              13

                                              Sheet1

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                                              Smoothing filters

                                              Also know as ndash Smoothing kernel Mean filter Low pass filter blurring

                                              The simplest filter ndash Spatial low pass filterndash Removes high frequencies

                                              Another mask ndash Gaussian filter

                                              1 1 1

                                              1 1 1

                                              1 1 191

                                              1 2 1

                                              2 4 2

                                              1 2 1161

                                              Why Gaussian

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                                              Use of smoothing

                                              3x3 7x7 11x11 15x15

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                                              Use of smoothing Large kernels smooth more Removes high frequency information Good at enhancing big structures

                                              3x3 15x15

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                                              Mean filterA) 166B) 113C) 12D) 51E) 245

                                              0 0 0 0

                                              A B C D E

                                              Chart1

                                              12
                                              0
                                              0
                                              0
                                              0

                                              Sheet1

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                                              Border handling

                                              0 2 41 2 2

                                              1 6 3

                                              1 2 12 5 3

                                              2 1 3

                                              1 3 1

                                              2 2 2

                                              0 1 3

                                              1 2 0

                                              2 1 4

                                              1 0 1

                                              Input Output

                                              No values at the border

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                                              Border handling ndash extend the input

                                              0 2 41 2 2

                                              1 6 3

                                              1 2 12 5 3

                                              2 1 3

                                              1 3 1

                                              2 2 2

                                              0 1 3

                                              1 2 0

                                              2 1 4

                                              1 0 1

                                              Input

                                              0 0 0 0 000000

                                              bull Zero padding ndash what happens

                                              bull Zero is black ndash creates dark border around the image

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                                              Correlation with zero paddingA) 5 8B) 12 16C) 13 3D) 15 21E) 17 12

                                              1 2 11 3 11 2 1

                                              0 2 41 2 2

                                              1 6 3

                                              1 2 12 5 3

                                              2 1 3

                                              1 3 1

                                              2 2 2

                                              0 1 3

                                              1 2 0

                                              2 1 4

                                              1 0 1

                                              0

                                              13

                                              0 0 0

                                              A B C D E

                                              Chart1

                                              0
                                              13
                                              0
                                              0
                                              0

                                              Sheet1

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                                              Border handling ndash extend the input

                                              0 2 41 2 2

                                              1 6 3

                                              1 2 12 5 3

                                              2 1 3

                                              1 3 1

                                              2 2 2

                                              0 1 3

                                              1 2 0

                                              2 1 4

                                              1 0 1

                                              Input

                                              1 2 0 1 311211

                                              bull Reflection

                                              bull Normally better than zero padding

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                                              2122018Introduction to Medical Image Analysis54 DTU Compute Technical University of Denmark

                                              Template Matching Template

                                              ndash Skabelon paring dansk Locates objects in images

                                              Input

                                              Template

                                              Output Correlation image

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                                              Template Matching The correlation between the template and the input

                                              image is computed for each pixel

                                              Input

                                              Template

                                              Output Correlation image

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                                              Template Matching The pixel with the highest value is found in the

                                              output imagendash Here is the highest correlation

                                              Input

                                              Template

                                              Output Correlation image

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                                              Template Matching This corresponds to the found pattern in the input

                                              image

                                              Input

                                              Template

                                              Output Correlation image

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                                              2122018Introduction to Medical Image Analysis58 DTU Compute Technical University of Denmark

                                              Problematic Correlation Correlation matching has problem with light areas ndash

                                              why

                                              Input (f)

                                              Template (h)

                                              Output Correlation imageFake max

                                              Real max

                                              Very High119892119892 119909119909119910119910 = 119895119895=minus119877119877

                                              119877119877

                                              119894119894=minus119877119877

                                              119877119877

                                              ℎ(119894119894 119895119895) 119891119891(119909119909 + 119894119894119910119910 + 119895119895)

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                                              Normalised Cross Correlation

                                              Input (f)

                                              Template (h)

                                              Output Correlation image

                                              Real max

                                              NCC x y =Correlation

                                              Length of image patch sdot Length of template

                                              DTU Compute

                                              2122018Introduction to Medical Image Analysis60 DTU Compute Technical University of Denmark

                                              Length of template Vector length

                                              ndash Put all pixel values into a vectorndash Compute the length of this vector

                                              Describes the intensity of the templatendash Bright template has a large lengthndash Dark template has a small length

                                              Template (h)

                                              Length of template = 119895119895=minus119877119877

                                              119877119877

                                              119894119894=minus119877119877

                                              119877119877

                                              ℎ(119894119894 119895119895) ℎ(119894119894 119895119895)

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                                              2122018Introduction to Medical Image Analysis61 DTU Compute Technical University of Denmark

                                              Length of image patch Vector length based on pixel values in image patch Describes the intensity of the image patch

                                              Template (h)

                                              Input (f) with patch

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                                              2122018Introduction to Medical Image Analysis62 DTU Compute Technical University of Denmark

                                              Normalised Cross Correlation The length of the image patch and the length of

                                              template normalise the NCC If the image is very bright the NCC will be ldquopulled

                                              downrdquo

                                              NCC x y =Correlation

                                              Length of image patch sdot Length of template

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                                              Normalised Cross Correlation NCC will be between

                                              ndash 0 No similarity between template and image patchndash 1 Template and image patch are identical

                                              Input (f)

                                              Template (h)

                                              Output Correlation image

                                              Real max

                                              NCC x y =Correlation

                                              Length of image patch sdot Length of template

                                              DTU Compute

                                              2122018Introduction to Medical Image Analysis64 DTU Compute Technical University of Denmark

                                              Normalised Cross Correlation

                                              A) 010B) 033C) 083D) 062E) 098

                                              Der udfoslashres template matching med og normalized crosscorrelation (NCC) beregnes Hvad bliver NNC i den markerede pixel

                                              1

                                              2 2

                                              3

                                              2

                                              A B C D E

                                              Chart1

                                              1
                                              2
                                              2
                                              3
                                              2

                                              Sheet1

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                                              Edges An edge is where there is a

                                              high change in gray level values

                                              Objects are often separated from the background by edgesGray level profile

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                                              2122018Introduction to Medical Image Analysis67 DTU Compute Technical University of Denmark

                                              Edges The profile as a function f(d) What value is high when there

                                              is an edgendash The slope of fndash The slope of the tangent at d

                                              f(d)

                                              119891119891prime(119889119889)

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                                              Finite Difference Definition of slope

                                              Approximation

                                              Simpler approximationh = 1

                                              119891119891prime 119889119889 = limℎrarr0

                                              119891119891 119889119889 + ℎ minus 119891119891(119889119889)ℎ

                                              119891119891prime 119889119889 asymp119891119891 119889119889 + ℎ minus 119891119891(119889119889)

                                              ℎ

                                              119891119891prime 119889119889 asymp 119891119891 119889119889 + 1 minus 119891119891(119889119889)

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                                              Edges Discrete approximation of frsquo(d) Can be implemented as a filter

                                              -1 0 1

                                              f(d-2) f(d-1) f(d) f(d+1) f(d+2) f(d+3)

                                              f(d)

                                              119891119891prime 119889119889 asymp 119891119891 119889119889 + 1 minus 119891119891(119889119889)

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                                              Edges in 2D Changes in gray level values

                                              ndash Image gradientndash Gradient is the 2D derivative of a 2D function f(xy)ndash Equal to the slope of the imagendash A steep slope is equal to an edge

                                              120571120571119891119891 119909119909119910119910 = 119866(119892119892119909119909119892119892119910119910)

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                                              Edge filter kernel The Prewitt filter is a typical

                                              edge filter Output image has high

                                              values where there are edges

                                              -1 0 1

                                              -1 0 1

                                              -1 0 1Vertical Prewitt filter

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                                              Prewitt filter

                                              Original Prewitt Prewitt

                                              Hot colormapSmooth 15x15

                                              Smooth 15x15

                                              Prewitt

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                                              Edge detection Edge filter

                                              ndash Prewitt for example Thresholding

                                              ndash Separate edges from non-edges

                                              Output is binary imagendash Edges are white

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                                              Edge filtering

                                              A) MeanB) Horizontal SobelC) Vertical PrewittD) Horisontal PrewittE) Median

                                              Der udfoslashres en filtrering (correlation) med et filter paring billedet Der bruges ikke coefficient normalization Den filtrerede vaeligrdi i den markerede pixel bliver -119 Hvilket et 3x3 filter blev benyttet

                                              0

                                              8

                                              1 10

                                              A B C D E

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                                              8
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                                              02511 - Niveau af dagens emne forelaeligsingA) Meget letB) LetC) PassendeD) SvaeligrtE) Meget svaeligrt

                                              23

                                              6

                                              10

                                              A B C D E

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                                              3
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                                              02512 - Niveau af dagens emne forelaeligsingA) Meget letB) LetC) PassendeD) SvaeligrtE) Meget svaeligrt

                                              0 0

                                              1

                                              0 0

                                              A B C D E

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                                              0
                                              0
                                              1
                                              0
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                                              02511 - Mit eget udbytte af dagenA) Jeg har laeligrt meget lidtB) Lidt laeligringC) PassendeD) God laeligringE) Jeg har laeligrt meget

                                              0 0

                                              2

                                              6

                                              0

                                              A B C D E

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                                              0
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                                              2
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                                              02512 - Mit eget udbytte af dagenA) Jeg har laeligrt meget lidtB) Lidt laeligringC) PassendeD) God laeligringE) Jeg har laeligrt meget

                                              2

                                              1

                                              3

                                              2

                                              0

                                              A B C D E

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                                              2
                                              1
                                              3
                                              2
                                              0

                                              Sheet1

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                                              02511 - Sidste uges oslashvelser (pixelwiseoperations)A) Meget letteB) LetteC) PassendeD) SvaeligreE) Meget svaeligre

                                              0 0

                                              1

                                              4

                                              1

                                              A B C D E

                                              Chart1

                                              0
                                              0
                                              1
                                              4
                                              1

                                              Sheet1

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                                              02512 - Sidste uges oslashvelser (pixelwiseoperations)A) Meget letteB) LetteC) PassendeD) SvaeligreE) Meget svaeligre

                                              3

                                              0

                                              3

                                              0 0

                                              A B C D E

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                                              0
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                                              Denne uges brug af clickersA) click click click ndash jeg bliver

                                              sindssygB) For meget clickC) PassendeD) Jeg vil gerne have lidt mereE) Jeg kan ikrsquo faring nok

                                              0 0

                                              5

                                              0

                                              6

                                              A B C D E

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                                              5
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                                              What can you do after today Describe the difference between point processing and neighbourhood

                                              processing Compute a rank filtered image using the min max median and

                                              difference rank filters Compute a mean filtered image Decide if median or average filtering should be used for noise removal Choose the appropriate image border handling based on a given input

                                              image Implement and apply template matching Compute the normalised cross correlation and explain why it should be

                                              used Apply given image filter kernels to images Use edge filters on images Describe finite difference approximation of image gradients Describe the concept of edge detection

                                              DTU Compute

                                              2122018Introduction to Medical Image Analysis84 DTU Compute Technical University of Denmark

                                              Oslashvelsesrapport over oslashvelse 4 - 02511 Oslashvelser taeligller cirka 30 af karakteren Skal afleveres senest den 7 marts kl 2359 Kan afleveres af 1 eller 2 personer

                                              ndash I skal skrive jeres egen oslashvelsesrapportndash Brug mindst et af jeres egne billeder

                                              Afleveres som PDF Lad vaeligre med at kopiere opgaveteksten ind i jeres

                                              opgave Put Matlab kode i et Appendix og henvis fra teksten Eksempel rapport over oslashvelse findes paring

                                              hjemmesiden under eksamen

                                              DTU Compute

                                              2122018Introduction to Medical Image Analysis85 DTU Compute Technical University of Denmark

                                              Exercises

                                              • Introduction to Medical Image Analysis
                                              • Lecture 4 ndash Neighbourhood Processing
                                              • What can you do after today
                                              • Point processing
                                              • Point processing
                                              • Neighbourhood processing
                                              • Use of filtering
                                              • Salt and pepper noise
                                              • Salt and pepper noise
                                              • What is so special about noise
                                              • Noise ndash go away
                                              • What is the median Value
                                              • The median value
                                              • Noise away ndash the median filter
                                              • Noise removal ndash average filter
                                              • Noise removal ndash median filter
                                              • Image Filtering
                                              • Median filter
                                              • Rank filters
                                              • Median filter
                                              • Correlation
                                              • Why do we need similarity
                                              • Correlation (1D)
                                              • Correlation (1D)
                                              • Normalisation
                                              • Normalisation
                                              • Correlation on images
                                              • Correlation on images
                                              • Correlation on images
                                              • Draw your filter
                                              • Correlation on images ndash no normalisation
                                              • Correlation on images ndash no normalisation 2
                                              • Mathematics of 2D Correlation
                                              • Mathematics of 2D Correlation
                                              • Mathematics of 2D Correlation
                                              • Slide Number 40
                                              • 2D Kernel Normalisation
                                              • Correlation
                                              • Smoothing filters
                                              • Use of smoothing
                                              • Use of smoothing
                                              • Mean filter
                                              • Border handling
                                              • Border handling ndash extend the input
                                              • Correlation with zero padding
                                              • Border handling ndash extend the input
                                              • Template Matching
                                              • Template Matching
                                              • Template Matching
                                              • Template Matching
                                              • Problematic Correlation
                                              • Normalised Cross Correlation
                                              • Length of template
                                              • Length of image patch
                                              • Normalised Cross Correlation
                                              • Normalised Cross Correlation
                                              • Normalised Cross Correlation
                                              • Edges
                                              • Edges
                                              • Finite Difference
                                              • Edges
                                              • Edges in 2D
                                              • Edge filter kernel
                                              • Prewitt filter
                                              • Edge detection
                                              • Edge filtering
                                              • 02511 - Niveau af dagens emne forelaeligsing
                                              • 02512 - Niveau af dagens emne forelaeligsing
                                              • 02511 - Mit eget udbytte af dagen
                                              • 02512 - Mit eget udbytte af dagen
                                              • 02511 - Sidste uges oslashvelser (pixelwise operations)
                                              • 02512 - Sidste uges oslashvelser (pixelwise operations)
                                              • Denne uges brug af clickers
                                              • What can you do after today
                                              • Oslashvelsesrapport over oslashvelse 4 - 02511
                                              • Exercises
                                                A0
                                                B0
                                                C5
                                                D0
                                                E6
                                                A
                                                B
                                                C
                                                D
                                                E
                                                A3
                                                B0
                                                C3
                                                D0
                                                E0
                                                A
                                                B
                                                C
                                                D
                                                E
                                                A0
                                                B0
                                                C1
                                                D4
                                                E1
                                                A
                                                B
                                                C
                                                D
                                                E
                                                A2
                                                B1
                                                C3
                                                D2
                                                E0
                                                A
                                                B
                                                C
                                                D
                                                E
                                                A0
                                                B0
                                                C2
                                                D6
                                                E0
                                                A
                                                B
                                                C
                                                D
                                                E
                                                A0
                                                B0
                                                C1
                                                D0
                                                E0
                                                A
                                                B
                                                C
                                                D
                                                E
                                                A2
                                                B3
                                                C6
                                                D1
                                                E0
                                                A
                                                B
                                                C
                                                D
                                                E
                                                A0
                                                B8
                                                C1
                                                D1
                                                E0
                                                A
                                                B
                                                C
                                                D
                                                E
                                                A1
                                                B2
                                                C2
                                                D3
                                                E2
                                                A
                                                B
                                                C
                                                D
                                                E
                                                A0
                                                B13
                                                C0
                                                D0
                                                E0
                                                A
                                                B
                                                C
                                                D
                                                E
                                                A12
                                                B0
                                                C0
                                                D0
                                                E0
                                                A
                                                B
                                                C
                                                D
                                                E
                                                A0
                                                B0
                                                C0
                                                D0
                                                E13
                                                A
                                                B
                                                C
                                                D
                                                E
                                                A13
                                                B0
                                                C0
                                                D0
                                                E0
                                                A
                                                B
                                                C
                                                D
                                                E
                                                A1
                                                B0
                                                C14
                                                D0
                                                E0
                                                A
                                                B
                                                C
                                                D
                                                E
                                                A0
                                                B12
                                                C1
                                                D0
                                                E0
                                                A
                                                B
                                                C
                                                D
                                                E

                                                DTU Compute

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                                                Median filter

                                                A) 3B) 84C) 112D) 73E) 202

                                                0

                                                12

                                                10 0

                                                A B C D E

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                                                Correlation What is it Two measurements

                                                ndash Low correlationndash High correlation

                                                High correlation means that there is a relation between the values

                                                They look the same Correlation is a measure of

                                                similarity

                                                Low

                                                High

                                                Muscles

                                                Mat

                                                h Ski

                                                lls

                                                Muscles

                                                Ben

                                                ch P

                                                ress

                                                DTU Compute

                                                2122018Introduction to Medical Image Analysis24 DTU Compute Technical University of Denmark

                                                Why do we need similarity Image analysis is also about recognition of patterns Often an example pattern is used We need something to tell us if there is a high match

                                                between our pattern and a part of the image

                                                Example pattern

                                                Image

                                                Find matches

                                                DTU Compute

                                                2122018Introduction to Medical Image Analysis25 DTU Compute Technical University of Denmark

                                                Correlation (1D)

                                                1 1 2 2 1 1 2 2 1 1

                                                1 2 1

                                                45

                                                41

                                                1 1 + 2 1 + 1 2 = 5

                                                Normalise

                                                Kernel

                                                Signal (1D image)

                                                41

                                                DTU Compute

                                                2122018Introduction to Medical Image Analysis26 DTU Compute Technical University of Denmark

                                                Correlation (1D)

                                                1 1 2 2 1 1 2 2 1 1

                                                1 2 1

                                                45

                                                47

                                                47

                                                45

                                                45

                                                47

                                                47

                                                45

                                                41

                                                DTU Compute

                                                2122018Introduction to Medical Image Analysis27 DTU Compute Technical University of Denmark

                                                Normalisation

                                                1 1 2 2 1 1 2 2 1 1

                                                1 2 1

                                                45

                                                41

                                                1 1 + 2 1 + 1 2 = 5

                                                Normalise41

                                                bull The sum of the kernel elements is used

                                                bull Keep the values in the same range as the input image

                                                Sum is 4

                                                DTU Compute

                                                2122018Introduction to Medical Image Analysis28 DTU Compute Technical University of Denmark

                                                Normalisation Normalisation factor

                                                ndash Sum of kernel coefficients

                                                1 2 1h(x)

                                                119909119909

                                                ℎ 119909119909 = 1 + 2 + 1

                                                DTU Compute

                                                2122018Introduction to Medical Image Analysis29 DTU Compute Technical University of Denmark

                                                Correlation on images The filter is now 2D 1 1 1

                                                1 1 1

                                                1 1 1

                                                0 2 4

                                                1 2 2

                                                1 6 3

                                                1 2 12 5 3

                                                2 1 3

                                                1 3 1

                                                2 2 2

                                                0 1 3

                                                1 2 0

                                                2 1 4

                                                1 0 1

                                                912

                                                91

                                                Input OutputKernel

                                                Kernel coefficients

                                                DTU Compute

                                                2122018Introduction to Medical Image Analysis30 DTU Compute Technical University of Denmark

                                                Correlation on images

                                                1 1 11 1 11 1 1

                                                0 2 4

                                                1 2 2

                                                1 6 3

                                                1 2 0

                                                2 1 4

                                                1 0 1

                                                912

                                                911

                                                91

                                                Input Output

                                                1 3 1

                                                2 2 2

                                                0 1 3

                                                1 2 12 5 3

                                                2 1 3

                                                DTU Compute

                                                2122018Introduction to Medical Image Analysis31 DTU Compute Technical University of Denmark

                                                Correlation on images

                                                Input Output

                                                The mask is moved row by row

                                                No values at the border

                                                0 2 4

                                                1 2 2

                                                1 6 3

                                                1 2 0

                                                2 1 4

                                                1 0 1

                                                1 3 1

                                                2 2 2

                                                0 1 3

                                                1 2 12 5 3

                                                2 1 3

                                                DTU Compute

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                                                1 2 1

                                                1 3 1

                                                1 2 1

                                                -1 -2 -1

                                                0 0 0

                                                1 2 1

                                                Draw your filter

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                                                2122018Introduction to Medical Image Analysis33 DTU Compute Technical University of Denmark

                                                Correlation on images ndash no normalisationA) 4B) 7C) 16D) 23E) 25

                                                1 2 11 3 11 2 1

                                                0 2 41 2 2

                                                1 6 3

                                                1 2 12 5 3

                                                2 1 3

                                                1 3 1

                                                2 2 2

                                                0 1 3

                                                1 2 0

                                                2 1 4

                                                1 0 11 0

                                                14

                                                0 0

                                                A B C D E

                                                Chart1

                                                1
                                                0
                                                14
                                                0
                                                0

                                                Sheet1

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                                                Correlation on images ndash no normalisation 2A) 010B) 3 3C) 6 2D) 10 15E) 11 32

                                                13

                                                0 0 0 0

                                                A B C D E

                                                -1 -2 -10 0 01 2 1

                                                0 2 41 2 2

                                                1 6 3

                                                1 2 12 5 3

                                                2 1 3

                                                1 3 1

                                                2 2 2

                                                0 1 3

                                                1 2 0

                                                2 1 4

                                                1 0 1

                                                Chart1

                                                13
                                                0
                                                0
                                                0
                                                0

                                                Sheet1

                                                DTU Compute

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                                                Mathematics of 2D Correlation

                                                h

                                                f

                                                Correlation operator

                                                1 2 11 3 11 2 1

                                                0 2 4

                                                1 2 2

                                                1 6 3

                                                1 2 1

                                                2 5 3

                                                2 1 3

                                                1 3 1

                                                2 2 2

                                                0 1 3

                                                1 2 0

                                                2 1 4

                                                1 0 1

                                                119892119892 119909119909119910119910 = 119891119891 119909119909119910119910 ∘ ℎ(119909119909119910119910)

                                                DTU Compute

                                                2122018Introduction to Medical Image Analysis38 DTU Compute Technical University of Denmark

                                                Mathematics of 2D Correlation

                                                1 2 11 3 11 2 1

                                                0 2 4

                                                1 2 2

                                                1 6 3

                                                1 2 1

                                                2 5 3

                                                2 1 3

                                                1 3 1

                                                2 2 2

                                                0 1 3

                                                1 2 0

                                                2 1 4

                                                1 0 1

                                                h

                                                fh(00)

                                                f(21)

                                                Example g(21)

                                                i = -1 j = -1

                                                i = 1 j = 0

                                                119892119892 119909119909119910119910 = 119895119895=minus119877119877

                                                119877119877

                                                119894119894=minus119877119877

                                                119877119877

                                                ℎ(119894119894 119895119895) 119891119891(119909119909 + 119894119894119910119910 + 119895119895)

                                                DTU Compute

                                                2122018Introduction to Medical Image Analysis39 DTU Compute Technical University of Denmark

                                                Mathematics of 2D Correlation

                                                1 2 11 3 11 2 1

                                                0 2 4

                                                1 2 2

                                                1 6 3

                                                1 2 1

                                                2 5 3

                                                2 1 3

                                                1 3 1

                                                2 2 2

                                                0 1 3

                                                1 2 0

                                                2 1 4

                                                1 0 1

                                                h

                                                f

                                                119892119892 119909119909119910119910 = 119895119895=minus119877119877

                                                119877119877

                                                119894119894=minus119877119877

                                                119877119877

                                                ℎ(119894119894 119895119895) 119891119891(119909119909 + 119894119894119910119910 + 119895119895)

                                                119892119892(119909119909119910119910 = 1 2 + 2 0 + 1 1 + 1 1 + 3 4 + 1 2 + 1 0 + 2 1 + 1 0

                                                DTU Compute

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                                                119892119892 119909119909 119910119910 = 119895119895=minus119877119877

                                                119877119877

                                                119894119894=minus119877119877

                                                119877119877

                                                ℎ(119894119894 119895119895) 119891119891(119909119909 + 119894119894119910119910 + 119895119895)

                                                119892119892 22 =ℎ minus1minus1 sdot 119891119891 11 + ℎ 0minus1 sdot 119891119891 21 + ℎ 1minus1 sdot 119891119891 31 +ℎ minus10 sdot 119891119891 12 + ℎ 00 sdot 119891119891 22 + ℎ 10 sdot 119891119891 32 +ℎ minus11 sdot 119891119891 13 + ℎ 01 sdot 119891119891 23 + ℎ 11 sdot 119891119891 33

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                                                2D Kernel Normalisation

                                                1 2 11 3 11 2 1

                                                h

                                                Normalisation factor

                                                1 + 2 + 1 + 1 + 3 + 1 + 1 + 2 + 1 = 13

                                                119909119909

                                                119910119910

                                                ℎ(119909119909119910119910)

                                                DTU Compute

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                                                CorrelationA) 50122B) 123001C) 11233D) 2550E) 90454

                                                0 0 0 0

                                                13

                                                A B C D E

                                                Chart1

                                                0
                                                0
                                                0
                                                0
                                                13

                                                Sheet1

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                                                Smoothing filters

                                                Also know as ndash Smoothing kernel Mean filter Low pass filter blurring

                                                The simplest filter ndash Spatial low pass filterndash Removes high frequencies

                                                Another mask ndash Gaussian filter

                                                1 1 1

                                                1 1 1

                                                1 1 191

                                                1 2 1

                                                2 4 2

                                                1 2 1161

                                                Why Gaussian

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                                                Use of smoothing

                                                3x3 7x7 11x11 15x15

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                                                Use of smoothing Large kernels smooth more Removes high frequency information Good at enhancing big structures

                                                3x3 15x15

                                                DTU Compute

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                                                Mean filterA) 166B) 113C) 12D) 51E) 245

                                                0 0 0 0

                                                A B C D E

                                                Chart1

                                                12
                                                0
                                                0
                                                0
                                                0

                                                Sheet1

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                                                Border handling

                                                0 2 41 2 2

                                                1 6 3

                                                1 2 12 5 3

                                                2 1 3

                                                1 3 1

                                                2 2 2

                                                0 1 3

                                                1 2 0

                                                2 1 4

                                                1 0 1

                                                Input Output

                                                No values at the border

                                                DTU Compute

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                                                Border handling ndash extend the input

                                                0 2 41 2 2

                                                1 6 3

                                                1 2 12 5 3

                                                2 1 3

                                                1 3 1

                                                2 2 2

                                                0 1 3

                                                1 2 0

                                                2 1 4

                                                1 0 1

                                                Input

                                                0 0 0 0 000000

                                                bull Zero padding ndash what happens

                                                bull Zero is black ndash creates dark border around the image

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                                                Correlation with zero paddingA) 5 8B) 12 16C) 13 3D) 15 21E) 17 12

                                                1 2 11 3 11 2 1

                                                0 2 41 2 2

                                                1 6 3

                                                1 2 12 5 3

                                                2 1 3

                                                1 3 1

                                                2 2 2

                                                0 1 3

                                                1 2 0

                                                2 1 4

                                                1 0 1

                                                0

                                                13

                                                0 0 0

                                                A B C D E

                                                Chart1

                                                0
                                                13
                                                0
                                                0
                                                0

                                                Sheet1

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                                                Border handling ndash extend the input

                                                0 2 41 2 2

                                                1 6 3

                                                1 2 12 5 3

                                                2 1 3

                                                1 3 1

                                                2 2 2

                                                0 1 3

                                                1 2 0

                                                2 1 4

                                                1 0 1

                                                Input

                                                1 2 0 1 311211

                                                bull Reflection

                                                bull Normally better than zero padding

                                                DTU Compute

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                                                Template Matching Template

                                                ndash Skabelon paring dansk Locates objects in images

                                                Input

                                                Template

                                                Output Correlation image

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                                                Template Matching The correlation between the template and the input

                                                image is computed for each pixel

                                                Input

                                                Template

                                                Output Correlation image

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                                                2122018Introduction to Medical Image Analysis56 DTU Compute Technical University of Denmark

                                                Template Matching The pixel with the highest value is found in the

                                                output imagendash Here is the highest correlation

                                                Input

                                                Template

                                                Output Correlation image

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                                                Template Matching This corresponds to the found pattern in the input

                                                image

                                                Input

                                                Template

                                                Output Correlation image

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                                                2122018Introduction to Medical Image Analysis58 DTU Compute Technical University of Denmark

                                                Problematic Correlation Correlation matching has problem with light areas ndash

                                                why

                                                Input (f)

                                                Template (h)

                                                Output Correlation imageFake max

                                                Real max

                                                Very High119892119892 119909119909119910119910 = 119895119895=minus119877119877

                                                119877119877

                                                119894119894=minus119877119877

                                                119877119877

                                                ℎ(119894119894 119895119895) 119891119891(119909119909 + 119894119894119910119910 + 119895119895)

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                                                Normalised Cross Correlation

                                                Input (f)

                                                Template (h)

                                                Output Correlation image

                                                Real max

                                                NCC x y =Correlation

                                                Length of image patch sdot Length of template

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                                                2122018Introduction to Medical Image Analysis60 DTU Compute Technical University of Denmark

                                                Length of template Vector length

                                                ndash Put all pixel values into a vectorndash Compute the length of this vector

                                                Describes the intensity of the templatendash Bright template has a large lengthndash Dark template has a small length

                                                Template (h)

                                                Length of template = 119895119895=minus119877119877

                                                119877119877

                                                119894119894=minus119877119877

                                                119877119877

                                                ℎ(119894119894 119895119895) ℎ(119894119894 119895119895)

                                                DTU Compute

                                                2122018Introduction to Medical Image Analysis61 DTU Compute Technical University of Denmark

                                                Length of image patch Vector length based on pixel values in image patch Describes the intensity of the image patch

                                                Template (h)

                                                Input (f) with patch

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                                                2122018Introduction to Medical Image Analysis62 DTU Compute Technical University of Denmark

                                                Normalised Cross Correlation The length of the image patch and the length of

                                                template normalise the NCC If the image is very bright the NCC will be ldquopulled

                                                downrdquo

                                                NCC x y =Correlation

                                                Length of image patch sdot Length of template

                                                DTU Compute

                                                2122018Introduction to Medical Image Analysis63 DTU Compute Technical University of Denmark

                                                Normalised Cross Correlation NCC will be between

                                                ndash 0 No similarity between template and image patchndash 1 Template and image patch are identical

                                                Input (f)

                                                Template (h)

                                                Output Correlation image

                                                Real max

                                                NCC x y =Correlation

                                                Length of image patch sdot Length of template

                                                DTU Compute

                                                2122018Introduction to Medical Image Analysis64 DTU Compute Technical University of Denmark

                                                Normalised Cross Correlation

                                                A) 010B) 033C) 083D) 062E) 098

                                                Der udfoslashres template matching med og normalized crosscorrelation (NCC) beregnes Hvad bliver NNC i den markerede pixel

                                                1

                                                2 2

                                                3

                                                2

                                                A B C D E

                                                Chart1

                                                1
                                                2
                                                2
                                                3
                                                2

                                                Sheet1

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                                                Edges An edge is where there is a

                                                high change in gray level values

                                                Objects are often separated from the background by edgesGray level profile

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                                                2122018Introduction to Medical Image Analysis67 DTU Compute Technical University of Denmark

                                                Edges The profile as a function f(d) What value is high when there

                                                is an edgendash The slope of fndash The slope of the tangent at d

                                                f(d)

                                                119891119891prime(119889119889)

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                                                Finite Difference Definition of slope

                                                Approximation

                                                Simpler approximationh = 1

                                                119891119891prime 119889119889 = limℎrarr0

                                                119891119891 119889119889 + ℎ minus 119891119891(119889119889)ℎ

                                                119891119891prime 119889119889 asymp119891119891 119889119889 + ℎ minus 119891119891(119889119889)

                                                ℎ

                                                119891119891prime 119889119889 asymp 119891119891 119889119889 + 1 minus 119891119891(119889119889)

                                                DTU Compute

                                                2122018Introduction to Medical Image Analysis69 DTU Compute Technical University of Denmark

                                                Edges Discrete approximation of frsquo(d) Can be implemented as a filter

                                                -1 0 1

                                                f(d-2) f(d-1) f(d) f(d+1) f(d+2) f(d+3)

                                                f(d)

                                                119891119891prime 119889119889 asymp 119891119891 119889119889 + 1 minus 119891119891(119889119889)

                                                DTU Compute

                                                2122018Introduction to Medical Image Analysis70 DTU Compute Technical University of Denmark

                                                Edges in 2D Changes in gray level values

                                                ndash Image gradientndash Gradient is the 2D derivative of a 2D function f(xy)ndash Equal to the slope of the imagendash A steep slope is equal to an edge

                                                120571120571119891119891 119909119909119910119910 = 119866(119892119892119909119909119892119892119910119910)

                                                DTU Compute

                                                2122018Introduction to Medical Image Analysis71 DTU Compute Technical University of Denmark

                                                Edge filter kernel The Prewitt filter is a typical

                                                edge filter Output image has high

                                                values where there are edges

                                                -1 0 1

                                                -1 0 1

                                                -1 0 1Vertical Prewitt filter

                                                DTU Compute

                                                2122018Introduction to Medical Image Analysis72 DTU Compute Technical University of Denmark

                                                Prewitt filter

                                                Original Prewitt Prewitt

                                                Hot colormapSmooth 15x15

                                                Smooth 15x15

                                                Prewitt

                                                DTU Compute

                                                2122018Introduction to Medical Image Analysis73 DTU Compute Technical University of Denmark

                                                Edge detection Edge filter

                                                ndash Prewitt for example Thresholding

                                                ndash Separate edges from non-edges

                                                Output is binary imagendash Edges are white

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                                                2122018Introduction to Medical Image Analysis74 DTU Compute Technical University of Denmark

                                                Edge filtering

                                                A) MeanB) Horizontal SobelC) Vertical PrewittD) Horisontal PrewittE) Median

                                                Der udfoslashres en filtrering (correlation) med et filter paring billedet Der bruges ikke coefficient normalization Den filtrerede vaeligrdi i den markerede pixel bliver -119 Hvilket et 3x3 filter blev benyttet

                                                0

                                                8

                                                1 10

                                                A B C D E

                                                Chart1

                                                0
                                                8
                                                1
                                                1
                                                0

                                                Sheet1

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                                                02511 - Niveau af dagens emne forelaeligsingA) Meget letB) LetC) PassendeD) SvaeligrtE) Meget svaeligrt

                                                23

                                                6

                                                10

                                                A B C D E

                                                Chart1

                                                2
                                                3
                                                6
                                                1
                                                0

                                                Sheet1

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                                                02512 - Niveau af dagens emne forelaeligsingA) Meget letB) LetC) PassendeD) SvaeligrtE) Meget svaeligrt

                                                0 0

                                                1

                                                0 0

                                                A B C D E

                                                Chart1

                                                0
                                                0
                                                1
                                                0
                                                0

                                                Sheet1

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                                                02511 - Mit eget udbytte af dagenA) Jeg har laeligrt meget lidtB) Lidt laeligringC) PassendeD) God laeligringE) Jeg har laeligrt meget

                                                0 0

                                                2

                                                6

                                                0

                                                A B C D E

                                                Chart1

                                                0
                                                0
                                                2
                                                6
                                                0

                                                Sheet1

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                                                02512 - Mit eget udbytte af dagenA) Jeg har laeligrt meget lidtB) Lidt laeligringC) PassendeD) God laeligringE) Jeg har laeligrt meget

                                                2

                                                1

                                                3

                                                2

                                                0

                                                A B C D E

                                                Chart1

                                                2
                                                1
                                                3
                                                2
                                                0

                                                Sheet1

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                                                02511 - Sidste uges oslashvelser (pixelwiseoperations)A) Meget letteB) LetteC) PassendeD) SvaeligreE) Meget svaeligre

                                                0 0

                                                1

                                                4

                                                1

                                                A B C D E

                                                Chart1

                                                0
                                                0
                                                1
                                                4
                                                1

                                                Sheet1

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                                                2122018Introduction to Medical Image Analysis81 DTU Compute Technical University of Denmark

                                                02512 - Sidste uges oslashvelser (pixelwiseoperations)A) Meget letteB) LetteC) PassendeD) SvaeligreE) Meget svaeligre

                                                3

                                                0

                                                3

                                                0 0

                                                A B C D E

                                                Chart1

                                                3
                                                0
                                                3
                                                0
                                                0

                                                Sheet1

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                                                2122018Introduction to Medical Image Analysis82 DTU Compute Technical University of Denmark

                                                Denne uges brug af clickersA) click click click ndash jeg bliver

                                                sindssygB) For meget clickC) PassendeD) Jeg vil gerne have lidt mereE) Jeg kan ikrsquo faring nok

                                                0 0

                                                5

                                                0

                                                6

                                                A B C D E

                                                Chart1

                                                0
                                                0
                                                5
                                                0
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                                                Sheet1

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                                                What can you do after today Describe the difference between point processing and neighbourhood

                                                processing Compute a rank filtered image using the min max median and

                                                difference rank filters Compute a mean filtered image Decide if median or average filtering should be used for noise removal Choose the appropriate image border handling based on a given input

                                                image Implement and apply template matching Compute the normalised cross correlation and explain why it should be

                                                used Apply given image filter kernels to images Use edge filters on images Describe finite difference approximation of image gradients Describe the concept of edge detection

                                                DTU Compute

                                                2122018Introduction to Medical Image Analysis84 DTU Compute Technical University of Denmark

                                                Oslashvelsesrapport over oslashvelse 4 - 02511 Oslashvelser taeligller cirka 30 af karakteren Skal afleveres senest den 7 marts kl 2359 Kan afleveres af 1 eller 2 personer

                                                ndash I skal skrive jeres egen oslashvelsesrapportndash Brug mindst et af jeres egne billeder

                                                Afleveres som PDF Lad vaeligre med at kopiere opgaveteksten ind i jeres

                                                opgave Put Matlab kode i et Appendix og henvis fra teksten Eksempel rapport over oslashvelse findes paring

                                                hjemmesiden under eksamen

                                                DTU Compute

                                                2122018Introduction to Medical Image Analysis85 DTU Compute Technical University of Denmark

                                                Exercises

                                                • Introduction to Medical Image Analysis
                                                • Lecture 4 ndash Neighbourhood Processing
                                                • What can you do after today
                                                • Point processing
                                                • Point processing
                                                • Neighbourhood processing
                                                • Use of filtering
                                                • Salt and pepper noise
                                                • Salt and pepper noise
                                                • What is so special about noise
                                                • Noise ndash go away
                                                • What is the median Value
                                                • The median value
                                                • Noise away ndash the median filter
                                                • Noise removal ndash average filter
                                                • Noise removal ndash median filter
                                                • Image Filtering
                                                • Median filter
                                                • Rank filters
                                                • Median filter
                                                • Correlation
                                                • Why do we need similarity
                                                • Correlation (1D)
                                                • Correlation (1D)
                                                • Normalisation
                                                • Normalisation
                                                • Correlation on images
                                                • Correlation on images
                                                • Correlation on images
                                                • Draw your filter
                                                • Correlation on images ndash no normalisation
                                                • Correlation on images ndash no normalisation 2
                                                • Mathematics of 2D Correlation
                                                • Mathematics of 2D Correlation
                                                • Mathematics of 2D Correlation
                                                • Slide Number 40
                                                • 2D Kernel Normalisation
                                                • Correlation
                                                • Smoothing filters
                                                • Use of smoothing
                                                • Use of smoothing
                                                • Mean filter
                                                • Border handling
                                                • Border handling ndash extend the input
                                                • Correlation with zero padding
                                                • Border handling ndash extend the input
                                                • Template Matching
                                                • Template Matching
                                                • Template Matching
                                                • Template Matching
                                                • Problematic Correlation
                                                • Normalised Cross Correlation
                                                • Length of template
                                                • Length of image patch
                                                • Normalised Cross Correlation
                                                • Normalised Cross Correlation
                                                • Normalised Cross Correlation
                                                • Edges
                                                • Edges
                                                • Finite Difference
                                                • Edges
                                                • Edges in 2D
                                                • Edge filter kernel
                                                • Prewitt filter
                                                • Edge detection
                                                • Edge filtering
                                                • 02511 - Niveau af dagens emne forelaeligsing
                                                • 02512 - Niveau af dagens emne forelaeligsing
                                                • 02511 - Mit eget udbytte af dagen
                                                • 02512 - Mit eget udbytte af dagen
                                                • 02511 - Sidste uges oslashvelser (pixelwise operations)
                                                • 02512 - Sidste uges oslashvelser (pixelwise operations)
                                                • Denne uges brug af clickers
                                                • What can you do after today
                                                • Oslashvelsesrapport over oslashvelse 4 - 02511
                                                • Exercises
                                                  A0
                                                  B0
                                                  C5
                                                  D0
                                                  E6
                                                  A
                                                  B
                                                  C
                                                  D
                                                  E
                                                  A3
                                                  B0
                                                  C3
                                                  D0
                                                  E0
                                                  A
                                                  B
                                                  C
                                                  D
                                                  E
                                                  A0
                                                  B0
                                                  C1
                                                  D4
                                                  E1
                                                  A
                                                  B
                                                  C
                                                  D
                                                  E
                                                  A2
                                                  B1
                                                  C3
                                                  D2
                                                  E0
                                                  A
                                                  B
                                                  C
                                                  D
                                                  E
                                                  A0
                                                  B0
                                                  C2
                                                  D6
                                                  E0
                                                  A
                                                  B
                                                  C
                                                  D
                                                  E
                                                  A0
                                                  B0
                                                  C1
                                                  D0
                                                  E0
                                                  A
                                                  B
                                                  C
                                                  D
                                                  E
                                                  A2
                                                  B3
                                                  C6
                                                  D1
                                                  E0
                                                  A
                                                  B
                                                  C
                                                  D
                                                  E
                                                  A0
                                                  B8
                                                  C1
                                                  D1
                                                  E0
                                                  A
                                                  B
                                                  C
                                                  D
                                                  E
                                                  A1
                                                  B2
                                                  C2
                                                  D3
                                                  E2
                                                  A
                                                  B
                                                  C
                                                  D
                                                  E
                                                  A0
                                                  B13
                                                  C0
                                                  D0
                                                  E0
                                                  A
                                                  B
                                                  C
                                                  D
                                                  E
                                                  A12
                                                  B0
                                                  C0
                                                  D0
                                                  E0
                                                  A
                                                  B
                                                  C
                                                  D
                                                  E
                                                  A0
                                                  B0
                                                  C0
                                                  D0
                                                  E13
                                                  A
                                                  B
                                                  C
                                                  D
                                                  E
                                                  A13
                                                  B0
                                                  C0
                                                  D0
                                                  E0
                                                  A
                                                  B
                                                  C
                                                  D
                                                  E
                                                  A1
                                                  B0
                                                  C14
                                                  D0
                                                  E0
                                                  A
                                                  B
                                                  C
                                                  D
                                                  E
                                                  A0
                                                  B12
                                                  C1
                                                  D0
                                                  E0
                                                  A
                                                  B
                                                  C
                                                  D
                                                  E

                                                  Chart1

                                                  0
                                                  12
                                                  1
                                                  0
                                                  0

                                                  Sheet1

                                                  DTU Compute

                                                  2122018Introduction to Medical Image Analysis23 DTU Compute Technical University of Denmark

                                                  Correlation What is it Two measurements

                                                  ndash Low correlationndash High correlation

                                                  High correlation means that there is a relation between the values

                                                  They look the same Correlation is a measure of

                                                  similarity

                                                  Low

                                                  High

                                                  Muscles

                                                  Mat

                                                  h Ski

                                                  lls

                                                  Muscles

                                                  Ben

                                                  ch P

                                                  ress

                                                  DTU Compute

                                                  2122018Introduction to Medical Image Analysis24 DTU Compute Technical University of Denmark

                                                  Why do we need similarity Image analysis is also about recognition of patterns Often an example pattern is used We need something to tell us if there is a high match

                                                  between our pattern and a part of the image

                                                  Example pattern

                                                  Image

                                                  Find matches

                                                  DTU Compute

                                                  2122018Introduction to Medical Image Analysis25 DTU Compute Technical University of Denmark

                                                  Correlation (1D)

                                                  1 1 2 2 1 1 2 2 1 1

                                                  1 2 1

                                                  45

                                                  41

                                                  1 1 + 2 1 + 1 2 = 5

                                                  Normalise

                                                  Kernel

                                                  Signal (1D image)

                                                  41

                                                  DTU Compute

                                                  2122018Introduction to Medical Image Analysis26 DTU Compute Technical University of Denmark

                                                  Correlation (1D)

                                                  1 1 2 2 1 1 2 2 1 1

                                                  1 2 1

                                                  45

                                                  47

                                                  47

                                                  45

                                                  45

                                                  47

                                                  47

                                                  45

                                                  41

                                                  DTU Compute

                                                  2122018Introduction to Medical Image Analysis27 DTU Compute Technical University of Denmark

                                                  Normalisation

                                                  1 1 2 2 1 1 2 2 1 1

                                                  1 2 1

                                                  45

                                                  41

                                                  1 1 + 2 1 + 1 2 = 5

                                                  Normalise41

                                                  bull The sum of the kernel elements is used

                                                  bull Keep the values in the same range as the input image

                                                  Sum is 4

                                                  DTU Compute

                                                  2122018Introduction to Medical Image Analysis28 DTU Compute Technical University of Denmark

                                                  Normalisation Normalisation factor

                                                  ndash Sum of kernel coefficients

                                                  1 2 1h(x)

                                                  119909119909

                                                  ℎ 119909119909 = 1 + 2 + 1

                                                  DTU Compute

                                                  2122018Introduction to Medical Image Analysis29 DTU Compute Technical University of Denmark

                                                  Correlation on images The filter is now 2D 1 1 1

                                                  1 1 1

                                                  1 1 1

                                                  0 2 4

                                                  1 2 2

                                                  1 6 3

                                                  1 2 12 5 3

                                                  2 1 3

                                                  1 3 1

                                                  2 2 2

                                                  0 1 3

                                                  1 2 0

                                                  2 1 4

                                                  1 0 1

                                                  912

                                                  91

                                                  Input OutputKernel

                                                  Kernel coefficients

                                                  DTU Compute

                                                  2122018Introduction to Medical Image Analysis30 DTU Compute Technical University of Denmark

                                                  Correlation on images

                                                  1 1 11 1 11 1 1

                                                  0 2 4

                                                  1 2 2

                                                  1 6 3

                                                  1 2 0

                                                  2 1 4

                                                  1 0 1

                                                  912

                                                  911

                                                  91

                                                  Input Output

                                                  1 3 1

                                                  2 2 2

                                                  0 1 3

                                                  1 2 12 5 3

                                                  2 1 3

                                                  DTU Compute

                                                  2122018Introduction to Medical Image Analysis31 DTU Compute Technical University of Denmark

                                                  Correlation on images

                                                  Input Output

                                                  The mask is moved row by row

                                                  No values at the border

                                                  0 2 4

                                                  1 2 2

                                                  1 6 3

                                                  1 2 0

                                                  2 1 4

                                                  1 0 1

                                                  1 3 1

                                                  2 2 2

                                                  0 1 3

                                                  1 2 12 5 3

                                                  2 1 3

                                                  DTU Compute

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                                                  1 2 1

                                                  1 3 1

                                                  1 2 1

                                                  -1 -2 -1

                                                  0 0 0

                                                  1 2 1

                                                  Draw your filter

                                                  DTU Compute

                                                  2122018Introduction to Medical Image Analysis33 DTU Compute Technical University of Denmark

                                                  Correlation on images ndash no normalisationA) 4B) 7C) 16D) 23E) 25

                                                  1 2 11 3 11 2 1

                                                  0 2 41 2 2

                                                  1 6 3

                                                  1 2 12 5 3

                                                  2 1 3

                                                  1 3 1

                                                  2 2 2

                                                  0 1 3

                                                  1 2 0

                                                  2 1 4

                                                  1 0 11 0

                                                  14

                                                  0 0

                                                  A B C D E

                                                  Chart1

                                                  1
                                                  0
                                                  14
                                                  0
                                                  0

                                                  Sheet1

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                                                  Correlation on images ndash no normalisation 2A) 010B) 3 3C) 6 2D) 10 15E) 11 32

                                                  13

                                                  0 0 0 0

                                                  A B C D E

                                                  -1 -2 -10 0 01 2 1

                                                  0 2 41 2 2

                                                  1 6 3

                                                  1 2 12 5 3

                                                  2 1 3

                                                  1 3 1

                                                  2 2 2

                                                  0 1 3

                                                  1 2 0

                                                  2 1 4

                                                  1 0 1

                                                  Chart1

                                                  13
                                                  0
                                                  0
                                                  0
                                                  0

                                                  Sheet1

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                                                  Mathematics of 2D Correlation

                                                  h

                                                  f

                                                  Correlation operator

                                                  1 2 11 3 11 2 1

                                                  0 2 4

                                                  1 2 2

                                                  1 6 3

                                                  1 2 1

                                                  2 5 3

                                                  2 1 3

                                                  1 3 1

                                                  2 2 2

                                                  0 1 3

                                                  1 2 0

                                                  2 1 4

                                                  1 0 1

                                                  119892119892 119909119909119910119910 = 119891119891 119909119909119910119910 ∘ ℎ(119909119909119910119910)

                                                  DTU Compute

                                                  2122018Introduction to Medical Image Analysis38 DTU Compute Technical University of Denmark

                                                  Mathematics of 2D Correlation

                                                  1 2 11 3 11 2 1

                                                  0 2 4

                                                  1 2 2

                                                  1 6 3

                                                  1 2 1

                                                  2 5 3

                                                  2 1 3

                                                  1 3 1

                                                  2 2 2

                                                  0 1 3

                                                  1 2 0

                                                  2 1 4

                                                  1 0 1

                                                  h

                                                  fh(00)

                                                  f(21)

                                                  Example g(21)

                                                  i = -1 j = -1

                                                  i = 1 j = 0

                                                  119892119892 119909119909119910119910 = 119895119895=minus119877119877

                                                  119877119877

                                                  119894119894=minus119877119877

                                                  119877119877

                                                  ℎ(119894119894 119895119895) 119891119891(119909119909 + 119894119894119910119910 + 119895119895)

                                                  DTU Compute

                                                  2122018Introduction to Medical Image Analysis39 DTU Compute Technical University of Denmark

                                                  Mathematics of 2D Correlation

                                                  1 2 11 3 11 2 1

                                                  0 2 4

                                                  1 2 2

                                                  1 6 3

                                                  1 2 1

                                                  2 5 3

                                                  2 1 3

                                                  1 3 1

                                                  2 2 2

                                                  0 1 3

                                                  1 2 0

                                                  2 1 4

                                                  1 0 1

                                                  h

                                                  f

                                                  119892119892 119909119909119910119910 = 119895119895=minus119877119877

                                                  119877119877

                                                  119894119894=minus119877119877

                                                  119877119877

                                                  ℎ(119894119894 119895119895) 119891119891(119909119909 + 119894119894119910119910 + 119895119895)

                                                  119892119892(119909119909119910119910 = 1 2 + 2 0 + 1 1 + 1 1 + 3 4 + 1 2 + 1 0 + 2 1 + 1 0

                                                  DTU Compute

                                                  2122018Introduction to Medical Image Analysis40 DTU Compute Technical University of Denmark

                                                  119892119892 119909119909 119910119910 = 119895119895=minus119877119877

                                                  119877119877

                                                  119894119894=minus119877119877

                                                  119877119877

                                                  ℎ(119894119894 119895119895) 119891119891(119909119909 + 119894119894119910119910 + 119895119895)

                                                  119892119892 22 =ℎ minus1minus1 sdot 119891119891 11 + ℎ 0minus1 sdot 119891119891 21 + ℎ 1minus1 sdot 119891119891 31 +ℎ minus10 sdot 119891119891 12 + ℎ 00 sdot 119891119891 22 + ℎ 10 sdot 119891119891 32 +ℎ minus11 sdot 119891119891 13 + ℎ 01 sdot 119891119891 23 + ℎ 11 sdot 119891119891 33

                                                  DTU Compute

                                                  2122018Introduction to Medical Image Analysis41 DTU Compute Technical University of Denmark

                                                  2D Kernel Normalisation

                                                  1 2 11 3 11 2 1

                                                  h

                                                  Normalisation factor

                                                  1 + 2 + 1 + 1 + 3 + 1 + 1 + 2 + 1 = 13

                                                  119909119909

                                                  119910119910

                                                  ℎ(119909119909119910119910)

                                                  DTU Compute

                                                  2122018Introduction to Medical Image Analysis42 DTU Compute Technical University of Denmark

                                                  CorrelationA) 50122B) 123001C) 11233D) 2550E) 90454

                                                  0 0 0 0

                                                  13

                                                  A B C D E

                                                  Chart1

                                                  0
                                                  0
                                                  0
                                                  0
                                                  13

                                                  Sheet1

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                                                  2122018Introduction to Medical Image Analysis44 DTU Compute Technical University of Denmark

                                                  Smoothing filters

                                                  Also know as ndash Smoothing kernel Mean filter Low pass filter blurring

                                                  The simplest filter ndash Spatial low pass filterndash Removes high frequencies

                                                  Another mask ndash Gaussian filter

                                                  1 1 1

                                                  1 1 1

                                                  1 1 191

                                                  1 2 1

                                                  2 4 2

                                                  1 2 1161

                                                  Why Gaussian

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                                                  Use of smoothing

                                                  3x3 7x7 11x11 15x15

                                                  DTU Compute

                                                  2122018Introduction to Medical Image Analysis46 DTU Compute Technical University of Denmark

                                                  Use of smoothing Large kernels smooth more Removes high frequency information Good at enhancing big structures

                                                  3x3 15x15

                                                  DTU Compute

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                                                  Mean filterA) 166B) 113C) 12D) 51E) 245

                                                  0 0 0 0

                                                  A B C D E

                                                  Chart1

                                                  12
                                                  0
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                                                  0

                                                  Sheet1

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                                                  Border handling

                                                  0 2 41 2 2

                                                  1 6 3

                                                  1 2 12 5 3

                                                  2 1 3

                                                  1 3 1

                                                  2 2 2

                                                  0 1 3

                                                  1 2 0

                                                  2 1 4

                                                  1 0 1

                                                  Input Output

                                                  No values at the border

                                                  DTU Compute

                                                  2122018Introduction to Medical Image Analysis50 DTU Compute Technical University of Denmark

                                                  Border handling ndash extend the input

                                                  0 2 41 2 2

                                                  1 6 3

                                                  1 2 12 5 3

                                                  2 1 3

                                                  1 3 1

                                                  2 2 2

                                                  0 1 3

                                                  1 2 0

                                                  2 1 4

                                                  1 0 1

                                                  Input

                                                  0 0 0 0 000000

                                                  bull Zero padding ndash what happens

                                                  bull Zero is black ndash creates dark border around the image

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                                                  2122018Introduction to Medical Image Analysis51 DTU Compute Technical University of Denmark

                                                  Correlation with zero paddingA) 5 8B) 12 16C) 13 3D) 15 21E) 17 12

                                                  1 2 11 3 11 2 1

                                                  0 2 41 2 2

                                                  1 6 3

                                                  1 2 12 5 3

                                                  2 1 3

                                                  1 3 1

                                                  2 2 2

                                                  0 1 3

                                                  1 2 0

                                                  2 1 4

                                                  1 0 1

                                                  0

                                                  13

                                                  0 0 0

                                                  A B C D E

                                                  Chart1

                                                  0
                                                  13
                                                  0
                                                  0
                                                  0

                                                  Sheet1

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                                                  Border handling ndash extend the input

                                                  0 2 41 2 2

                                                  1 6 3

                                                  1 2 12 5 3

                                                  2 1 3

                                                  1 3 1

                                                  2 2 2

                                                  0 1 3

                                                  1 2 0

                                                  2 1 4

                                                  1 0 1

                                                  Input

                                                  1 2 0 1 311211

                                                  bull Reflection

                                                  bull Normally better than zero padding

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                                                  2122018Introduction to Medical Image Analysis54 DTU Compute Technical University of Denmark

                                                  Template Matching Template

                                                  ndash Skabelon paring dansk Locates objects in images

                                                  Input

                                                  Template

                                                  Output Correlation image

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                                                  2122018Introduction to Medical Image Analysis55 DTU Compute Technical University of Denmark

                                                  Template Matching The correlation between the template and the input

                                                  image is computed for each pixel

                                                  Input

                                                  Template

                                                  Output Correlation image

                                                  DTU Compute

                                                  2122018Introduction to Medical Image Analysis56 DTU Compute Technical University of Denmark

                                                  Template Matching The pixel with the highest value is found in the

                                                  output imagendash Here is the highest correlation

                                                  Input

                                                  Template

                                                  Output Correlation image

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                                                  2122018Introduction to Medical Image Analysis57 DTU Compute Technical University of Denmark

                                                  Template Matching This corresponds to the found pattern in the input

                                                  image

                                                  Input

                                                  Template

                                                  Output Correlation image

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                                                  2122018Introduction to Medical Image Analysis58 DTU Compute Technical University of Denmark

                                                  Problematic Correlation Correlation matching has problem with light areas ndash

                                                  why

                                                  Input (f)

                                                  Template (h)

                                                  Output Correlation imageFake max

                                                  Real max

                                                  Very High119892119892 119909119909119910119910 = 119895119895=minus119877119877

                                                  119877119877

                                                  119894119894=minus119877119877

                                                  119877119877

                                                  ℎ(119894119894 119895119895) 119891119891(119909119909 + 119894119894119910119910 + 119895119895)

                                                  DTU Compute

                                                  2122018Introduction to Medical Image Analysis59 DTU Compute Technical University of Denmark

                                                  Normalised Cross Correlation

                                                  Input (f)

                                                  Template (h)

                                                  Output Correlation image

                                                  Real max

                                                  NCC x y =Correlation

                                                  Length of image patch sdot Length of template

                                                  DTU Compute

                                                  2122018Introduction to Medical Image Analysis60 DTU Compute Technical University of Denmark

                                                  Length of template Vector length

                                                  ndash Put all pixel values into a vectorndash Compute the length of this vector

                                                  Describes the intensity of the templatendash Bright template has a large lengthndash Dark template has a small length

                                                  Template (h)

                                                  Length of template = 119895119895=minus119877119877

                                                  119877119877

                                                  119894119894=minus119877119877

                                                  119877119877

                                                  ℎ(119894119894 119895119895) ℎ(119894119894 119895119895)

                                                  DTU Compute

                                                  2122018Introduction to Medical Image Analysis61 DTU Compute Technical University of Denmark

                                                  Length of image patch Vector length based on pixel values in image patch Describes the intensity of the image patch

                                                  Template (h)

                                                  Input (f) with patch

                                                  DTU Compute

                                                  2122018Introduction to Medical Image Analysis62 DTU Compute Technical University of Denmark

                                                  Normalised Cross Correlation The length of the image patch and the length of

                                                  template normalise the NCC If the image is very bright the NCC will be ldquopulled

                                                  downrdquo

                                                  NCC x y =Correlation

                                                  Length of image patch sdot Length of template

                                                  DTU Compute

                                                  2122018Introduction to Medical Image Analysis63 DTU Compute Technical University of Denmark

                                                  Normalised Cross Correlation NCC will be between

                                                  ndash 0 No similarity between template and image patchndash 1 Template and image patch are identical

                                                  Input (f)

                                                  Template (h)

                                                  Output Correlation image

                                                  Real max

                                                  NCC x y =Correlation

                                                  Length of image patch sdot Length of template

                                                  DTU Compute

                                                  2122018Introduction to Medical Image Analysis64 DTU Compute Technical University of Denmark

                                                  Normalised Cross Correlation

                                                  A) 010B) 033C) 083D) 062E) 098

                                                  Der udfoslashres template matching med og normalized crosscorrelation (NCC) beregnes Hvad bliver NNC i den markerede pixel

                                                  1

                                                  2 2

                                                  3

                                                  2

                                                  A B C D E

                                                  Chart1

                                                  1
                                                  2
                                                  2
                                                  3
                                                  2

                                                  Sheet1

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                                                  Edges An edge is where there is a

                                                  high change in gray level values

                                                  Objects are often separated from the background by edgesGray level profile

                                                  DTU Compute

                                                  2122018Introduction to Medical Image Analysis67 DTU Compute Technical University of Denmark

                                                  Edges The profile as a function f(d) What value is high when there

                                                  is an edgendash The slope of fndash The slope of the tangent at d

                                                  f(d)

                                                  119891119891prime(119889119889)

                                                  DTU Compute

                                                  2122018Introduction to Medical Image Analysis68 DTU Compute Technical University of Denmark

                                                  Finite Difference Definition of slope

                                                  Approximation

                                                  Simpler approximationh = 1

                                                  119891119891prime 119889119889 = limℎrarr0

                                                  119891119891 119889119889 + ℎ minus 119891119891(119889119889)ℎ

                                                  119891119891prime 119889119889 asymp119891119891 119889119889 + ℎ minus 119891119891(119889119889)

                                                  ℎ

                                                  119891119891prime 119889119889 asymp 119891119891 119889119889 + 1 minus 119891119891(119889119889)

                                                  DTU Compute

                                                  2122018Introduction to Medical Image Analysis69 DTU Compute Technical University of Denmark

                                                  Edges Discrete approximation of frsquo(d) Can be implemented as a filter

                                                  -1 0 1

                                                  f(d-2) f(d-1) f(d) f(d+1) f(d+2) f(d+3)

                                                  f(d)

                                                  119891119891prime 119889119889 asymp 119891119891 119889119889 + 1 minus 119891119891(119889119889)

                                                  DTU Compute

                                                  2122018Introduction to Medical Image Analysis70 DTU Compute Technical University of Denmark

                                                  Edges in 2D Changes in gray level values

                                                  ndash Image gradientndash Gradient is the 2D derivative of a 2D function f(xy)ndash Equal to the slope of the imagendash A steep slope is equal to an edge

                                                  120571120571119891119891 119909119909119910119910 = 119866(119892119892119909119909119892119892119910119910)

                                                  DTU Compute

                                                  2122018Introduction to Medical Image Analysis71 DTU Compute Technical University of Denmark

                                                  Edge filter kernel The Prewitt filter is a typical

                                                  edge filter Output image has high

                                                  values where there are edges

                                                  -1 0 1

                                                  -1 0 1

                                                  -1 0 1Vertical Prewitt filter

                                                  DTU Compute

                                                  2122018Introduction to Medical Image Analysis72 DTU Compute Technical University of Denmark

                                                  Prewitt filter

                                                  Original Prewitt Prewitt

                                                  Hot colormapSmooth 15x15

                                                  Smooth 15x15

                                                  Prewitt

                                                  DTU Compute

                                                  2122018Introduction to Medical Image Analysis73 DTU Compute Technical University of Denmark

                                                  Edge detection Edge filter

                                                  ndash Prewitt for example Thresholding

                                                  ndash Separate edges from non-edges

                                                  Output is binary imagendash Edges are white

                                                  DTU Compute

                                                  2122018Introduction to Medical Image Analysis74 DTU Compute Technical University of Denmark

                                                  Edge filtering

                                                  A) MeanB) Horizontal SobelC) Vertical PrewittD) Horisontal PrewittE) Median

                                                  Der udfoslashres en filtrering (correlation) med et filter paring billedet Der bruges ikke coefficient normalization Den filtrerede vaeligrdi i den markerede pixel bliver -119 Hvilket et 3x3 filter blev benyttet

                                                  0

                                                  8

                                                  1 10

                                                  A B C D E

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                                                  8
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                                                  2122018Introduction to Medical Image Analysis76 DTU Compute Technical University of Denmark

                                                  02511 - Niveau af dagens emne forelaeligsingA) Meget letB) LetC) PassendeD) SvaeligrtE) Meget svaeligrt

                                                  23

                                                  6

                                                  10

                                                  A B C D E

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                                                  2
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                                                  02512 - Niveau af dagens emne forelaeligsingA) Meget letB) LetC) PassendeD) SvaeligrtE) Meget svaeligrt

                                                  0 0

                                                  1

                                                  0 0

                                                  A B C D E

                                                  Chart1

                                                  0
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                                                  1
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                                                  0

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                                                  2122018Introduction to Medical Image Analysis78 DTU Compute Technical University of Denmark

                                                  02511 - Mit eget udbytte af dagenA) Jeg har laeligrt meget lidtB) Lidt laeligringC) PassendeD) God laeligringE) Jeg har laeligrt meget

                                                  0 0

                                                  2

                                                  6

                                                  0

                                                  A B C D E

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                                                  2122018Introduction to Medical Image Analysis79 DTU Compute Technical University of Denmark

                                                  02512 - Mit eget udbytte af dagenA) Jeg har laeligrt meget lidtB) Lidt laeligringC) PassendeD) God laeligringE) Jeg har laeligrt meget

                                                  2

                                                  1

                                                  3

                                                  2

                                                  0

                                                  A B C D E

                                                  Chart1

                                                  2
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                                                  02511 - Sidste uges oslashvelser (pixelwiseoperations)A) Meget letteB) LetteC) PassendeD) SvaeligreE) Meget svaeligre

                                                  0 0

                                                  1

                                                  4

                                                  1

                                                  A B C D E

                                                  Chart1

                                                  0
                                                  0
                                                  1
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                                                  Sheet1

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                                                  2122018Introduction to Medical Image Analysis81 DTU Compute Technical University of Denmark

                                                  02512 - Sidste uges oslashvelser (pixelwiseoperations)A) Meget letteB) LetteC) PassendeD) SvaeligreE) Meget svaeligre

                                                  3

                                                  0

                                                  3

                                                  0 0

                                                  A B C D E

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                                                  Denne uges brug af clickersA) click click click ndash jeg bliver

                                                  sindssygB) For meget clickC) PassendeD) Jeg vil gerne have lidt mereE) Jeg kan ikrsquo faring nok

                                                  0 0

                                                  5

                                                  0

                                                  6

                                                  A B C D E

                                                  Chart1

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                                                  6

                                                  Sheet1

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                                                  What can you do after today Describe the difference between point processing and neighbourhood

                                                  processing Compute a rank filtered image using the min max median and

                                                  difference rank filters Compute a mean filtered image Decide if median or average filtering should be used for noise removal Choose the appropriate image border handling based on a given input

                                                  image Implement and apply template matching Compute the normalised cross correlation and explain why it should be

                                                  used Apply given image filter kernels to images Use edge filters on images Describe finite difference approximation of image gradients Describe the concept of edge detection

                                                  DTU Compute

                                                  2122018Introduction to Medical Image Analysis84 DTU Compute Technical University of Denmark

                                                  Oslashvelsesrapport over oslashvelse 4 - 02511 Oslashvelser taeligller cirka 30 af karakteren Skal afleveres senest den 7 marts kl 2359 Kan afleveres af 1 eller 2 personer

                                                  ndash I skal skrive jeres egen oslashvelsesrapportndash Brug mindst et af jeres egne billeder

                                                  Afleveres som PDF Lad vaeligre med at kopiere opgaveteksten ind i jeres

                                                  opgave Put Matlab kode i et Appendix og henvis fra teksten Eksempel rapport over oslashvelse findes paring

                                                  hjemmesiden under eksamen

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                                                  2122018Introduction to Medical Image Analysis85 DTU Compute Technical University of Denmark

                                                  Exercises

                                                  • Introduction to Medical Image Analysis
                                                  • Lecture 4 ndash Neighbourhood Processing
                                                  • What can you do after today
                                                  • Point processing
                                                  • Point processing
                                                  • Neighbourhood processing
                                                  • Use of filtering
                                                  • Salt and pepper noise
                                                  • Salt and pepper noise
                                                  • What is so special about noise
                                                  • Noise ndash go away
                                                  • What is the median Value
                                                  • The median value
                                                  • Noise away ndash the median filter
                                                  • Noise removal ndash average filter
                                                  • Noise removal ndash median filter
                                                  • Image Filtering
                                                  • Median filter
                                                  • Rank filters
                                                  • Median filter
                                                  • Correlation
                                                  • Why do we need similarity
                                                  • Correlation (1D)
                                                  • Correlation (1D)
                                                  • Normalisation
                                                  • Normalisation
                                                  • Correlation on images
                                                  • Correlation on images
                                                  • Correlation on images
                                                  • Draw your filter
                                                  • Correlation on images ndash no normalisation
                                                  • Correlation on images ndash no normalisation 2
                                                  • Mathematics of 2D Correlation
                                                  • Mathematics of 2D Correlation
                                                  • Mathematics of 2D Correlation
                                                  • Slide Number 40
                                                  • 2D Kernel Normalisation
                                                  • Correlation
                                                  • Smoothing filters
                                                  • Use of smoothing
                                                  • Use of smoothing
                                                  • Mean filter
                                                  • Border handling
                                                  • Border handling ndash extend the input
                                                  • Correlation with zero padding
                                                  • Border handling ndash extend the input
                                                  • Template Matching
                                                  • Template Matching
                                                  • Template Matching
                                                  • Template Matching
                                                  • Problematic Correlation
                                                  • Normalised Cross Correlation
                                                  • Length of template
                                                  • Length of image patch
                                                  • Normalised Cross Correlation
                                                  • Normalised Cross Correlation
                                                  • Normalised Cross Correlation
                                                  • Edges
                                                  • Edges
                                                  • Finite Difference
                                                  • Edges
                                                  • Edges in 2D
                                                  • Edge filter kernel
                                                  • Prewitt filter
                                                  • Edge detection
                                                  • Edge filtering
                                                  • 02511 - Niveau af dagens emne forelaeligsing
                                                  • 02512 - Niveau af dagens emne forelaeligsing
                                                  • 02511 - Mit eget udbytte af dagen
                                                  • 02512 - Mit eget udbytte af dagen
                                                  • 02511 - Sidste uges oslashvelser (pixelwise operations)
                                                  • 02512 - Sidste uges oslashvelser (pixelwise operations)
                                                  • Denne uges brug af clickers
                                                  • What can you do after today
                                                  • Oslashvelsesrapport over oslashvelse 4 - 02511
                                                  • Exercises
                                                    A0
                                                    B0
                                                    C5
                                                    D0
                                                    E6
                                                    A
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                                                    E
                                                    A3
                                                    B0
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                                                    D0
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                                                    A
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                                                    D
                                                    E
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                                                    D4
                                                    E1
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                                                    D
                                                    E
                                                    A2
                                                    B1
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                                                    D2
                                                    E0
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                                                    D6
                                                    E0
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                                                    D0
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                                                    E
                                                    A2
                                                    B3
                                                    C6
                                                    D1
                                                    E0
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                                                    B
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                                                    D
                                                    E
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                                                    B8
                                                    C1
                                                    D1
                                                    E0
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                                                    D
                                                    E
                                                    A1
                                                    B2
                                                    C2
                                                    D3
                                                    E2
                                                    A
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                                                    C
                                                    D
                                                    E
                                                    A0
                                                    B13
                                                    C0
                                                    D0
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                                                    E
                                                    A12
                                                    B0
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                                                    E
                                                    A0
                                                    B0
                                                    C0
                                                    D0
                                                    E13
                                                    A
                                                    B
                                                    C
                                                    D
                                                    E
                                                    A13
                                                    B0
                                                    C0
                                                    D0
                                                    E0
                                                    A
                                                    B
                                                    C
                                                    D
                                                    E
                                                    A1
                                                    B0
                                                    C14
                                                    D0
                                                    E0
                                                    A
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                                                    A0
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                                                    C1
                                                    D0
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                                                    E

                                                    Sheet1

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                                                    Correlation What is it Two measurements

                                                    ndash Low correlationndash High correlation

                                                    High correlation means that there is a relation between the values

                                                    They look the same Correlation is a measure of

                                                    similarity

                                                    Low

                                                    High

                                                    Muscles

                                                    Mat

                                                    h Ski

                                                    lls

                                                    Muscles

                                                    Ben

                                                    ch P

                                                    ress

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                                                    Why do we need similarity Image analysis is also about recognition of patterns Often an example pattern is used We need something to tell us if there is a high match

                                                    between our pattern and a part of the image

                                                    Example pattern

                                                    Image

                                                    Find matches

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                                                    Correlation (1D)

                                                    1 1 2 2 1 1 2 2 1 1

                                                    1 2 1

                                                    45

                                                    41

                                                    1 1 + 2 1 + 1 2 = 5

                                                    Normalise

                                                    Kernel

                                                    Signal (1D image)

                                                    41

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                                                    Correlation (1D)

                                                    1 1 2 2 1 1 2 2 1 1

                                                    1 2 1

                                                    45

                                                    47

                                                    47

                                                    45

                                                    45

                                                    47

                                                    47

                                                    45

                                                    41

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                                                    2122018Introduction to Medical Image Analysis27 DTU Compute Technical University of Denmark

                                                    Normalisation

                                                    1 1 2 2 1 1 2 2 1 1

                                                    1 2 1

                                                    45

                                                    41

                                                    1 1 + 2 1 + 1 2 = 5

                                                    Normalise41

                                                    bull The sum of the kernel elements is used

                                                    bull Keep the values in the same range as the input image

                                                    Sum is 4

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                                                    Normalisation Normalisation factor

                                                    ndash Sum of kernel coefficients

                                                    1 2 1h(x)

                                                    119909119909

                                                    ℎ 119909119909 = 1 + 2 + 1

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                                                    Correlation on images The filter is now 2D 1 1 1

                                                    1 1 1

                                                    1 1 1

                                                    0 2 4

                                                    1 2 2

                                                    1 6 3

                                                    1 2 12 5 3

                                                    2 1 3

                                                    1 3 1

                                                    2 2 2

                                                    0 1 3

                                                    1 2 0

                                                    2 1 4

                                                    1 0 1

                                                    912

                                                    91

                                                    Input OutputKernel

                                                    Kernel coefficients

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                                                    Correlation on images

                                                    1 1 11 1 11 1 1

                                                    0 2 4

                                                    1 2 2

                                                    1 6 3

                                                    1 2 0

                                                    2 1 4

                                                    1 0 1

                                                    912

                                                    911

                                                    91

                                                    Input Output

                                                    1 3 1

                                                    2 2 2

                                                    0 1 3

                                                    1 2 12 5 3

                                                    2 1 3

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                                                    Correlation on images

                                                    Input Output

                                                    The mask is moved row by row

                                                    No values at the border

                                                    0 2 4

                                                    1 2 2

                                                    1 6 3

                                                    1 2 0

                                                    2 1 4

                                                    1 0 1

                                                    1 3 1

                                                    2 2 2

                                                    0 1 3

                                                    1 2 12 5 3

                                                    2 1 3

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                                                    1 2 1

                                                    1 3 1

                                                    1 2 1

                                                    -1 -2 -1

                                                    0 0 0

                                                    1 2 1

                                                    Draw your filter

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                                                    Correlation on images ndash no normalisationA) 4B) 7C) 16D) 23E) 25

                                                    1 2 11 3 11 2 1

                                                    0 2 41 2 2

                                                    1 6 3

                                                    1 2 12 5 3

                                                    2 1 3

                                                    1 3 1

                                                    2 2 2

                                                    0 1 3

                                                    1 2 0

                                                    2 1 4

                                                    1 0 11 0

                                                    14

                                                    0 0

                                                    A B C D E

                                                    Chart1

                                                    1
                                                    0
                                                    14
                                                    0
                                                    0

                                                    Sheet1

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                                                    Correlation on images ndash no normalisation 2A) 010B) 3 3C) 6 2D) 10 15E) 11 32

                                                    13

                                                    0 0 0 0

                                                    A B C D E

                                                    -1 -2 -10 0 01 2 1

                                                    0 2 41 2 2

                                                    1 6 3

                                                    1 2 12 5 3

                                                    2 1 3

                                                    1 3 1

                                                    2 2 2

                                                    0 1 3

                                                    1 2 0

                                                    2 1 4

                                                    1 0 1

                                                    Chart1

                                                    13
                                                    0
                                                    0
                                                    0
                                                    0

                                                    Sheet1

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                                                    Mathematics of 2D Correlation

                                                    h

                                                    f

                                                    Correlation operator

                                                    1 2 11 3 11 2 1

                                                    0 2 4

                                                    1 2 2

                                                    1 6 3

                                                    1 2 1

                                                    2 5 3

                                                    2 1 3

                                                    1 3 1

                                                    2 2 2

                                                    0 1 3

                                                    1 2 0

                                                    2 1 4

                                                    1 0 1

                                                    119892119892 119909119909119910119910 = 119891119891 119909119909119910119910 ∘ ℎ(119909119909119910119910)

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                                                    Mathematics of 2D Correlation

                                                    1 2 11 3 11 2 1

                                                    0 2 4

                                                    1 2 2

                                                    1 6 3

                                                    1 2 1

                                                    2 5 3

                                                    2 1 3

                                                    1 3 1

                                                    2 2 2

                                                    0 1 3

                                                    1 2 0

                                                    2 1 4

                                                    1 0 1

                                                    h

                                                    fh(00)

                                                    f(21)

                                                    Example g(21)

                                                    i = -1 j = -1

                                                    i = 1 j = 0

                                                    119892119892 119909119909119910119910 = 119895119895=minus119877119877

                                                    119877119877

                                                    119894119894=minus119877119877

                                                    119877119877

                                                    ℎ(119894119894 119895119895) 119891119891(119909119909 + 119894119894119910119910 + 119895119895)

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                                                    Mathematics of 2D Correlation

                                                    1 2 11 3 11 2 1

                                                    0 2 4

                                                    1 2 2

                                                    1 6 3

                                                    1 2 1

                                                    2 5 3

                                                    2 1 3

                                                    1 3 1

                                                    2 2 2

                                                    0 1 3

                                                    1 2 0

                                                    2 1 4

                                                    1 0 1

                                                    h

                                                    f

                                                    119892119892 119909119909119910119910 = 119895119895=minus119877119877

                                                    119877119877

                                                    119894119894=minus119877119877

                                                    119877119877

                                                    ℎ(119894119894 119895119895) 119891119891(119909119909 + 119894119894119910119910 + 119895119895)

                                                    119892119892(119909119909119910119910 = 1 2 + 2 0 + 1 1 + 1 1 + 3 4 + 1 2 + 1 0 + 2 1 + 1 0

                                                    DTU Compute

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                                                    119892119892 119909119909 119910119910 = 119895119895=minus119877119877

                                                    119877119877

                                                    119894119894=minus119877119877

                                                    119877119877

                                                    ℎ(119894119894 119895119895) 119891119891(119909119909 + 119894119894119910119910 + 119895119895)

                                                    119892119892 22 =ℎ minus1minus1 sdot 119891119891 11 + ℎ 0minus1 sdot 119891119891 21 + ℎ 1minus1 sdot 119891119891 31 +ℎ minus10 sdot 119891119891 12 + ℎ 00 sdot 119891119891 22 + ℎ 10 sdot 119891119891 32 +ℎ minus11 sdot 119891119891 13 + ℎ 01 sdot 119891119891 23 + ℎ 11 sdot 119891119891 33

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                                                    2D Kernel Normalisation

                                                    1 2 11 3 11 2 1

                                                    h

                                                    Normalisation factor

                                                    1 + 2 + 1 + 1 + 3 + 1 + 1 + 2 + 1 = 13

                                                    119909119909

                                                    119910119910

                                                    ℎ(119909119909119910119910)

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                                                    CorrelationA) 50122B) 123001C) 11233D) 2550E) 90454

                                                    0 0 0 0

                                                    13

                                                    A B C D E

                                                    Chart1

                                                    0
                                                    0
                                                    0
                                                    0
                                                    13

                                                    Sheet1

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                                                    Smoothing filters

                                                    Also know as ndash Smoothing kernel Mean filter Low pass filter blurring

                                                    The simplest filter ndash Spatial low pass filterndash Removes high frequencies

                                                    Another mask ndash Gaussian filter

                                                    1 1 1

                                                    1 1 1

                                                    1 1 191

                                                    1 2 1

                                                    2 4 2

                                                    1 2 1161

                                                    Why Gaussian

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                                                    Use of smoothing

                                                    3x3 7x7 11x11 15x15

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                                                    Use of smoothing Large kernels smooth more Removes high frequency information Good at enhancing big structures

                                                    3x3 15x15

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                                                    Mean filterA) 166B) 113C) 12D) 51E) 245

                                                    0 0 0 0

                                                    A B C D E

                                                    Chart1

                                                    12
                                                    0
                                                    0
                                                    0
                                                    0

                                                    Sheet1

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                                                    Border handling

                                                    0 2 41 2 2

                                                    1 6 3

                                                    1 2 12 5 3

                                                    2 1 3

                                                    1 3 1

                                                    2 2 2

                                                    0 1 3

                                                    1 2 0

                                                    2 1 4

                                                    1 0 1

                                                    Input Output

                                                    No values at the border

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                                                    Border handling ndash extend the input

                                                    0 2 41 2 2

                                                    1 6 3

                                                    1 2 12 5 3

                                                    2 1 3

                                                    1 3 1

                                                    2 2 2

                                                    0 1 3

                                                    1 2 0

                                                    2 1 4

                                                    1 0 1

                                                    Input

                                                    0 0 0 0 000000

                                                    bull Zero padding ndash what happens

                                                    bull Zero is black ndash creates dark border around the image

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                                                    Correlation with zero paddingA) 5 8B) 12 16C) 13 3D) 15 21E) 17 12

                                                    1 2 11 3 11 2 1

                                                    0 2 41 2 2

                                                    1 6 3

                                                    1 2 12 5 3

                                                    2 1 3

                                                    1 3 1

                                                    2 2 2

                                                    0 1 3

                                                    1 2 0

                                                    2 1 4

                                                    1 0 1

                                                    0

                                                    13

                                                    0 0 0

                                                    A B C D E

                                                    Chart1

                                                    0
                                                    13
                                                    0
                                                    0
                                                    0

                                                    Sheet1

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                                                    Border handling ndash extend the input

                                                    0 2 41 2 2

                                                    1 6 3

                                                    1 2 12 5 3

                                                    2 1 3

                                                    1 3 1

                                                    2 2 2

                                                    0 1 3

                                                    1 2 0

                                                    2 1 4

                                                    1 0 1

                                                    Input

                                                    1 2 0 1 311211

                                                    bull Reflection

                                                    bull Normally better than zero padding

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                                                    Template Matching Template

                                                    ndash Skabelon paring dansk Locates objects in images

                                                    Input

                                                    Template

                                                    Output Correlation image

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                                                    Template Matching The correlation between the template and the input

                                                    image is computed for each pixel

                                                    Input

                                                    Template

                                                    Output Correlation image

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                                                    Template Matching The pixel with the highest value is found in the

                                                    output imagendash Here is the highest correlation

                                                    Input

                                                    Template

                                                    Output Correlation image

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                                                    Template Matching This corresponds to the found pattern in the input

                                                    image

                                                    Input

                                                    Template

                                                    Output Correlation image

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                                                    Problematic Correlation Correlation matching has problem with light areas ndash

                                                    why

                                                    Input (f)

                                                    Template (h)

                                                    Output Correlation imageFake max

                                                    Real max

                                                    Very High119892119892 119909119909119910119910 = 119895119895=minus119877119877

                                                    119877119877

                                                    119894119894=minus119877119877

                                                    119877119877

                                                    ℎ(119894119894 119895119895) 119891119891(119909119909 + 119894119894119910119910 + 119895119895)

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                                                    Normalised Cross Correlation

                                                    Input (f)

                                                    Template (h)

                                                    Output Correlation image

                                                    Real max

                                                    NCC x y =Correlation

                                                    Length of image patch sdot Length of template

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                                                    Length of template Vector length

                                                    ndash Put all pixel values into a vectorndash Compute the length of this vector

                                                    Describes the intensity of the templatendash Bright template has a large lengthndash Dark template has a small length

                                                    Template (h)

                                                    Length of template = 119895119895=minus119877119877

                                                    119877119877

                                                    119894119894=minus119877119877

                                                    119877119877

                                                    ℎ(119894119894 119895119895) ℎ(119894119894 119895119895)

                                                    DTU Compute

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                                                    Length of image patch Vector length based on pixel values in image patch Describes the intensity of the image patch

                                                    Template (h)

                                                    Input (f) with patch

                                                    DTU Compute

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                                                    Normalised Cross Correlation The length of the image patch and the length of

                                                    template normalise the NCC If the image is very bright the NCC will be ldquopulled

                                                    downrdquo

                                                    NCC x y =Correlation

                                                    Length of image patch sdot Length of template

                                                    DTU Compute

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                                                    Normalised Cross Correlation NCC will be between

                                                    ndash 0 No similarity between template and image patchndash 1 Template and image patch are identical

                                                    Input (f)

                                                    Template (h)

                                                    Output Correlation image

                                                    Real max

                                                    NCC x y =Correlation

                                                    Length of image patch sdot Length of template

                                                    DTU Compute

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                                                    Normalised Cross Correlation

                                                    A) 010B) 033C) 083D) 062E) 098

                                                    Der udfoslashres template matching med og normalized crosscorrelation (NCC) beregnes Hvad bliver NNC i den markerede pixel

                                                    1

                                                    2 2

                                                    3

                                                    2

                                                    A B C D E

                                                    Chart1

                                                    1
                                                    2
                                                    2
                                                    3
                                                    2

                                                    Sheet1

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                                                    Edges An edge is where there is a

                                                    high change in gray level values

                                                    Objects are often separated from the background by edgesGray level profile

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                                                    Edges The profile as a function f(d) What value is high when there

                                                    is an edgendash The slope of fndash The slope of the tangent at d

                                                    f(d)

                                                    119891119891prime(119889119889)

                                                    DTU Compute

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                                                    Finite Difference Definition of slope

                                                    Approximation

                                                    Simpler approximationh = 1

                                                    119891119891prime 119889119889 = limℎrarr0

                                                    119891119891 119889119889 + ℎ minus 119891119891(119889119889)ℎ

                                                    119891119891prime 119889119889 asymp119891119891 119889119889 + ℎ minus 119891119891(119889119889)

                                                    ℎ

                                                    119891119891prime 119889119889 asymp 119891119891 119889119889 + 1 minus 119891119891(119889119889)

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                                                    Edges Discrete approximation of frsquo(d) Can be implemented as a filter

                                                    -1 0 1

                                                    f(d-2) f(d-1) f(d) f(d+1) f(d+2) f(d+3)

                                                    f(d)

                                                    119891119891prime 119889119889 asymp 119891119891 119889119889 + 1 minus 119891119891(119889119889)

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                                                    Edges in 2D Changes in gray level values

                                                    ndash Image gradientndash Gradient is the 2D derivative of a 2D function f(xy)ndash Equal to the slope of the imagendash A steep slope is equal to an edge

                                                    120571120571119891119891 119909119909119910119910 = 119866(119892119892119909119909119892119892119910119910)

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                                                    Edge filter kernel The Prewitt filter is a typical

                                                    edge filter Output image has high

                                                    values where there are edges

                                                    -1 0 1

                                                    -1 0 1

                                                    -1 0 1Vertical Prewitt filter

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                                                    Prewitt filter

                                                    Original Prewitt Prewitt

                                                    Hot colormapSmooth 15x15

                                                    Smooth 15x15

                                                    Prewitt

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                                                    Edge detection Edge filter

                                                    ndash Prewitt for example Thresholding

                                                    ndash Separate edges from non-edges

                                                    Output is binary imagendash Edges are white

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                                                    Edge filtering

                                                    A) MeanB) Horizontal SobelC) Vertical PrewittD) Horisontal PrewittE) Median

                                                    Der udfoslashres en filtrering (correlation) med et filter paring billedet Der bruges ikke coefficient normalization Den filtrerede vaeligrdi i den markerede pixel bliver -119 Hvilket et 3x3 filter blev benyttet

                                                    0

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                                                    02511 - Niveau af dagens emne forelaeligsingA) Meget letB) LetC) PassendeD) SvaeligrtE) Meget svaeligrt

                                                    23

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                                                    02512 - Niveau af dagens emne forelaeligsingA) Meget letB) LetC) PassendeD) SvaeligrtE) Meget svaeligrt

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                                                    02511 - Mit eget udbytte af dagenA) Jeg har laeligrt meget lidtB) Lidt laeligringC) PassendeD) God laeligringE) Jeg har laeligrt meget

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                                                    02512 - Mit eget udbytte af dagenA) Jeg har laeligrt meget lidtB) Lidt laeligringC) PassendeD) God laeligringE) Jeg har laeligrt meget

                                                    2

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                                                    02511 - Sidste uges oslashvelser (pixelwiseoperations)A) Meget letteB) LetteC) PassendeD) SvaeligreE) Meget svaeligre

                                                    0 0

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                                                    02512 - Sidste uges oslashvelser (pixelwiseoperations)A) Meget letteB) LetteC) PassendeD) SvaeligreE) Meget svaeligre

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                                                    Denne uges brug af clickersA) click click click ndash jeg bliver

                                                    sindssygB) For meget clickC) PassendeD) Jeg vil gerne have lidt mereE) Jeg kan ikrsquo faring nok

                                                    0 0

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                                                    What can you do after today Describe the difference between point processing and neighbourhood

                                                    processing Compute a rank filtered image using the min max median and

                                                    difference rank filters Compute a mean filtered image Decide if median or average filtering should be used for noise removal Choose the appropriate image border handling based on a given input

                                                    image Implement and apply template matching Compute the normalised cross correlation and explain why it should be

                                                    used Apply given image filter kernels to images Use edge filters on images Describe finite difference approximation of image gradients Describe the concept of edge detection

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                                                    Oslashvelsesrapport over oslashvelse 4 - 02511 Oslashvelser taeligller cirka 30 af karakteren Skal afleveres senest den 7 marts kl 2359 Kan afleveres af 1 eller 2 personer

                                                    ndash I skal skrive jeres egen oslashvelsesrapportndash Brug mindst et af jeres egne billeder

                                                    Afleveres som PDF Lad vaeligre med at kopiere opgaveteksten ind i jeres

                                                    opgave Put Matlab kode i et Appendix og henvis fra teksten Eksempel rapport over oslashvelse findes paring

                                                    hjemmesiden under eksamen

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                                                    2122018Introduction to Medical Image Analysis85 DTU Compute Technical University of Denmark

                                                    Exercises

                                                    • Introduction to Medical Image Analysis
                                                    • Lecture 4 ndash Neighbourhood Processing
                                                    • What can you do after today
                                                    • Point processing
                                                    • Point processing
                                                    • Neighbourhood processing
                                                    • Use of filtering
                                                    • Salt and pepper noise
                                                    • Salt and pepper noise
                                                    • What is so special about noise
                                                    • Noise ndash go away
                                                    • What is the median Value
                                                    • The median value
                                                    • Noise away ndash the median filter
                                                    • Noise removal ndash average filter
                                                    • Noise removal ndash median filter
                                                    • Image Filtering
                                                    • Median filter
                                                    • Rank filters
                                                    • Median filter
                                                    • Correlation
                                                    • Why do we need similarity
                                                    • Correlation (1D)
                                                    • Correlation (1D)
                                                    • Normalisation
                                                    • Normalisation
                                                    • Correlation on images
                                                    • Correlation on images
                                                    • Correlation on images
                                                    • Draw your filter
                                                    • Correlation on images ndash no normalisation
                                                    • Correlation on images ndash no normalisation 2
                                                    • Mathematics of 2D Correlation
                                                    • Mathematics of 2D Correlation
                                                    • Mathematics of 2D Correlation
                                                    • Slide Number 40
                                                    • 2D Kernel Normalisation
                                                    • Correlation
                                                    • Smoothing filters
                                                    • Use of smoothing
                                                    • Use of smoothing
                                                    • Mean filter
                                                    • Border handling
                                                    • Border handling ndash extend the input
                                                    • Correlation with zero padding
                                                    • Border handling ndash extend the input
                                                    • Template Matching
                                                    • Template Matching
                                                    • Template Matching
                                                    • Template Matching
                                                    • Problematic Correlation
                                                    • Normalised Cross Correlation
                                                    • Length of template
                                                    • Length of image patch
                                                    • Normalised Cross Correlation
                                                    • Normalised Cross Correlation
                                                    • Normalised Cross Correlation
                                                    • Edges
                                                    • Edges
                                                    • Finite Difference
                                                    • Edges
                                                    • Edges in 2D
                                                    • Edge filter kernel
                                                    • Prewitt filter
                                                    • Edge detection
                                                    • Edge filtering
                                                    • 02511 - Niveau af dagens emne forelaeligsing
                                                    • 02512 - Niveau af dagens emne forelaeligsing
                                                    • 02511 - Mit eget udbytte af dagen
                                                    • 02512 - Mit eget udbytte af dagen
                                                    • 02511 - Sidste uges oslashvelser (pixelwise operations)
                                                    • 02512 - Sidste uges oslashvelser (pixelwise operations)
                                                    • Denne uges brug af clickers
                                                    • What can you do after today
                                                    • Oslashvelsesrapport over oslashvelse 4 - 02511
                                                    • Exercises
                                                      A0
                                                      B0
                                                      C5
                                                      D0
                                                      E6
                                                      A
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                                                      D
                                                      E
                                                      A3
                                                      B0
                                                      C3
                                                      D0
                                                      E0
                                                      A
                                                      B
                                                      C
                                                      D
                                                      E
                                                      A0
                                                      B0
                                                      C1
                                                      D4
                                                      E1
                                                      A
                                                      B
                                                      C
                                                      D
                                                      E
                                                      A2
                                                      B1
                                                      C3
                                                      D2
                                                      E0
                                                      A
                                                      B
                                                      C
                                                      D
                                                      E
                                                      A0
                                                      B0
                                                      C2
                                                      D6
                                                      E0
                                                      A
                                                      B
                                                      C
                                                      D
                                                      E
                                                      A0
                                                      B0
                                                      C1
                                                      D0
                                                      E0
                                                      A
                                                      B
                                                      C
                                                      D
                                                      E
                                                      A2
                                                      B3
                                                      C6
                                                      D1
                                                      E0
                                                      A
                                                      B
                                                      C
                                                      D
                                                      E
                                                      A0
                                                      B8
                                                      C1
                                                      D1
                                                      E0
                                                      A
                                                      B
                                                      C
                                                      D
                                                      E
                                                      A1
                                                      B2
                                                      C2
                                                      D3
                                                      E2
                                                      A
                                                      B
                                                      C
                                                      D
                                                      E
                                                      A0
                                                      B13
                                                      C0
                                                      D0
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                                                      A
                                                      B
                                                      C
                                                      D
                                                      E
                                                      A12
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                                                      B
                                                      C
                                                      D
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                                                      E13
                                                      A
                                                      B
                                                      C
                                                      D
                                                      E
                                                      A13
                                                      B0
                                                      C0
                                                      D0
                                                      E0
                                                      A
                                                      B
                                                      C
                                                      D
                                                      E
                                                      A1
                                                      B0
                                                      C14
                                                      D0
                                                      E0
                                                      A
                                                      B
                                                      C
                                                      D
                                                      E
                                                      A0
                                                      B12
                                                      C1
                                                      D0
                                                      E0

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                                                      Correlation What is it Two measurements

                                                      ndash Low correlationndash High correlation

                                                      High correlation means that there is a relation between the values

                                                      They look the same Correlation is a measure of

                                                      similarity

                                                      Low

                                                      High

                                                      Muscles

                                                      Mat

                                                      h Ski

                                                      lls

                                                      Muscles

                                                      Ben

                                                      ch P

                                                      ress

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                                                      Why do we need similarity Image analysis is also about recognition of patterns Often an example pattern is used We need something to tell us if there is a high match

                                                      between our pattern and a part of the image

                                                      Example pattern

                                                      Image

                                                      Find matches

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                                                      Correlation (1D)

                                                      1 1 2 2 1 1 2 2 1 1

                                                      1 2 1

                                                      45

                                                      41

                                                      1 1 + 2 1 + 1 2 = 5

                                                      Normalise

                                                      Kernel

                                                      Signal (1D image)

                                                      41

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                                                      Correlation (1D)

                                                      1 1 2 2 1 1 2 2 1 1

                                                      1 2 1

                                                      45

                                                      47

                                                      47

                                                      45

                                                      45

                                                      47

                                                      47

                                                      45

                                                      41

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                                                      Normalisation

                                                      1 1 2 2 1 1 2 2 1 1

                                                      1 2 1

                                                      45

                                                      41

                                                      1 1 + 2 1 + 1 2 = 5

                                                      Normalise41

                                                      bull The sum of the kernel elements is used

                                                      bull Keep the values in the same range as the input image

                                                      Sum is 4

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                                                      Normalisation Normalisation factor

                                                      ndash Sum of kernel coefficients

                                                      1 2 1h(x)

                                                      119909119909

                                                      ℎ 119909119909 = 1 + 2 + 1

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                                                      Correlation on images The filter is now 2D 1 1 1

                                                      1 1 1

                                                      1 1 1

                                                      0 2 4

                                                      1 2 2

                                                      1 6 3

                                                      1 2 12 5 3

                                                      2 1 3

                                                      1 3 1

                                                      2 2 2

                                                      0 1 3

                                                      1 2 0

                                                      2 1 4

                                                      1 0 1

                                                      912

                                                      91

                                                      Input OutputKernel

                                                      Kernel coefficients

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                                                      Correlation on images

                                                      1 1 11 1 11 1 1

                                                      0 2 4

                                                      1 2 2

                                                      1 6 3

                                                      1 2 0

                                                      2 1 4

                                                      1 0 1

                                                      912

                                                      911

                                                      91

                                                      Input Output

                                                      1 3 1

                                                      2 2 2

                                                      0 1 3

                                                      1 2 12 5 3

                                                      2 1 3

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                                                      Correlation on images

                                                      Input Output

                                                      The mask is moved row by row

                                                      No values at the border

                                                      0 2 4

                                                      1 2 2

                                                      1 6 3

                                                      1 2 0

                                                      2 1 4

                                                      1 0 1

                                                      1 3 1

                                                      2 2 2

                                                      0 1 3

                                                      1 2 12 5 3

                                                      2 1 3

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                                                      1 2 1

                                                      1 3 1

                                                      1 2 1

                                                      -1 -2 -1

                                                      0 0 0

                                                      1 2 1

                                                      Draw your filter

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                                                      Correlation on images ndash no normalisationA) 4B) 7C) 16D) 23E) 25

                                                      1 2 11 3 11 2 1

                                                      0 2 41 2 2

                                                      1 6 3

                                                      1 2 12 5 3

                                                      2 1 3

                                                      1 3 1

                                                      2 2 2

                                                      0 1 3

                                                      1 2 0

                                                      2 1 4

                                                      1 0 11 0

                                                      14

                                                      0 0

                                                      A B C D E

                                                      Chart1

                                                      1
                                                      0
                                                      14
                                                      0
                                                      0

                                                      Sheet1

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                                                      Correlation on images ndash no normalisation 2A) 010B) 3 3C) 6 2D) 10 15E) 11 32

                                                      13

                                                      0 0 0 0

                                                      A B C D E

                                                      -1 -2 -10 0 01 2 1

                                                      0 2 41 2 2

                                                      1 6 3

                                                      1 2 12 5 3

                                                      2 1 3

                                                      1 3 1

                                                      2 2 2

                                                      0 1 3

                                                      1 2 0

                                                      2 1 4

                                                      1 0 1

                                                      Chart1

                                                      13
                                                      0
                                                      0
                                                      0
                                                      0

                                                      Sheet1

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                                                      Mathematics of 2D Correlation

                                                      h

                                                      f

                                                      Correlation operator

                                                      1 2 11 3 11 2 1

                                                      0 2 4

                                                      1 2 2

                                                      1 6 3

                                                      1 2 1

                                                      2 5 3

                                                      2 1 3

                                                      1 3 1

                                                      2 2 2

                                                      0 1 3

                                                      1 2 0

                                                      2 1 4

                                                      1 0 1

                                                      119892119892 119909119909119910119910 = 119891119891 119909119909119910119910 ∘ ℎ(119909119909119910119910)

                                                      DTU Compute

                                                      2122018Introduction to Medical Image Analysis38 DTU Compute Technical University of Denmark

                                                      Mathematics of 2D Correlation

                                                      1 2 11 3 11 2 1

                                                      0 2 4

                                                      1 2 2

                                                      1 6 3

                                                      1 2 1

                                                      2 5 3

                                                      2 1 3

                                                      1 3 1

                                                      2 2 2

                                                      0 1 3

                                                      1 2 0

                                                      2 1 4

                                                      1 0 1

                                                      h

                                                      fh(00)

                                                      f(21)

                                                      Example g(21)

                                                      i = -1 j = -1

                                                      i = 1 j = 0

                                                      119892119892 119909119909119910119910 = 119895119895=minus119877119877

                                                      119877119877

                                                      119894119894=minus119877119877

                                                      119877119877

                                                      ℎ(119894119894 119895119895) 119891119891(119909119909 + 119894119894119910119910 + 119895119895)

                                                      DTU Compute

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                                                      Mathematics of 2D Correlation

                                                      1 2 11 3 11 2 1

                                                      0 2 4

                                                      1 2 2

                                                      1 6 3

                                                      1 2 1

                                                      2 5 3

                                                      2 1 3

                                                      1 3 1

                                                      2 2 2

                                                      0 1 3

                                                      1 2 0

                                                      2 1 4

                                                      1 0 1

                                                      h

                                                      f

                                                      119892119892 119909119909119910119910 = 119895119895=minus119877119877

                                                      119877119877

                                                      119894119894=minus119877119877

                                                      119877119877

                                                      ℎ(119894119894 119895119895) 119891119891(119909119909 + 119894119894119910119910 + 119895119895)

                                                      119892119892(119909119909119910119910 = 1 2 + 2 0 + 1 1 + 1 1 + 3 4 + 1 2 + 1 0 + 2 1 + 1 0

                                                      DTU Compute

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                                                      119892119892 119909119909 119910119910 = 119895119895=minus119877119877

                                                      119877119877

                                                      119894119894=minus119877119877

                                                      119877119877

                                                      ℎ(119894119894 119895119895) 119891119891(119909119909 + 119894119894119910119910 + 119895119895)

                                                      119892119892 22 =ℎ minus1minus1 sdot 119891119891 11 + ℎ 0minus1 sdot 119891119891 21 + ℎ 1minus1 sdot 119891119891 31 +ℎ minus10 sdot 119891119891 12 + ℎ 00 sdot 119891119891 22 + ℎ 10 sdot 119891119891 32 +ℎ minus11 sdot 119891119891 13 + ℎ 01 sdot 119891119891 23 + ℎ 11 sdot 119891119891 33

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                                                      2D Kernel Normalisation

                                                      1 2 11 3 11 2 1

                                                      h

                                                      Normalisation factor

                                                      1 + 2 + 1 + 1 + 3 + 1 + 1 + 2 + 1 = 13

                                                      119909119909

                                                      119910119910

                                                      ℎ(119909119909119910119910)

                                                      DTU Compute

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                                                      CorrelationA) 50122B) 123001C) 11233D) 2550E) 90454

                                                      0 0 0 0

                                                      13

                                                      A B C D E

                                                      Chart1

                                                      0
                                                      0
                                                      0
                                                      0
                                                      13

                                                      Sheet1

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                                                      Smoothing filters

                                                      Also know as ndash Smoothing kernel Mean filter Low pass filter blurring

                                                      The simplest filter ndash Spatial low pass filterndash Removes high frequencies

                                                      Another mask ndash Gaussian filter

                                                      1 1 1

                                                      1 1 1

                                                      1 1 191

                                                      1 2 1

                                                      2 4 2

                                                      1 2 1161

                                                      Why Gaussian

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                                                      Use of smoothing

                                                      3x3 7x7 11x11 15x15

                                                      DTU Compute

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                                                      Use of smoothing Large kernels smooth more Removes high frequency information Good at enhancing big structures

                                                      3x3 15x15

                                                      DTU Compute

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                                                      Mean filterA) 166B) 113C) 12D) 51E) 245

                                                      0 0 0 0

                                                      A B C D E

                                                      Chart1

                                                      12
                                                      0
                                                      0
                                                      0
                                                      0

                                                      Sheet1

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                                                      Border handling

                                                      0 2 41 2 2

                                                      1 6 3

                                                      1 2 12 5 3

                                                      2 1 3

                                                      1 3 1

                                                      2 2 2

                                                      0 1 3

                                                      1 2 0

                                                      2 1 4

                                                      1 0 1

                                                      Input Output

                                                      No values at the border

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                                                      Border handling ndash extend the input

                                                      0 2 41 2 2

                                                      1 6 3

                                                      1 2 12 5 3

                                                      2 1 3

                                                      1 3 1

                                                      2 2 2

                                                      0 1 3

                                                      1 2 0

                                                      2 1 4

                                                      1 0 1

                                                      Input

                                                      0 0 0 0 000000

                                                      bull Zero padding ndash what happens

                                                      bull Zero is black ndash creates dark border around the image

                                                      DTU Compute

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                                                      Correlation with zero paddingA) 5 8B) 12 16C) 13 3D) 15 21E) 17 12

                                                      1 2 11 3 11 2 1

                                                      0 2 41 2 2

                                                      1 6 3

                                                      1 2 12 5 3

                                                      2 1 3

                                                      1 3 1

                                                      2 2 2

                                                      0 1 3

                                                      1 2 0

                                                      2 1 4

                                                      1 0 1

                                                      0

                                                      13

                                                      0 0 0

                                                      A B C D E

                                                      Chart1

                                                      0
                                                      13
                                                      0
                                                      0
                                                      0

                                                      Sheet1

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                                                      Border handling ndash extend the input

                                                      0 2 41 2 2

                                                      1 6 3

                                                      1 2 12 5 3

                                                      2 1 3

                                                      1 3 1

                                                      2 2 2

                                                      0 1 3

                                                      1 2 0

                                                      2 1 4

                                                      1 0 1

                                                      Input

                                                      1 2 0 1 311211

                                                      bull Reflection

                                                      bull Normally better than zero padding

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                                                      Template Matching Template

                                                      ndash Skabelon paring dansk Locates objects in images

                                                      Input

                                                      Template

                                                      Output Correlation image

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                                                      Template Matching The correlation between the template and the input

                                                      image is computed for each pixel

                                                      Input

                                                      Template

                                                      Output Correlation image

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                                                      Template Matching The pixel with the highest value is found in the

                                                      output imagendash Here is the highest correlation

                                                      Input

                                                      Template

                                                      Output Correlation image

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                                                      Template Matching This corresponds to the found pattern in the input

                                                      image

                                                      Input

                                                      Template

                                                      Output Correlation image

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                                                      Problematic Correlation Correlation matching has problem with light areas ndash

                                                      why

                                                      Input (f)

                                                      Template (h)

                                                      Output Correlation imageFake max

                                                      Real max

                                                      Very High119892119892 119909119909119910119910 = 119895119895=minus119877119877

                                                      119877119877

                                                      119894119894=minus119877119877

                                                      119877119877

                                                      ℎ(119894119894 119895119895) 119891119891(119909119909 + 119894119894119910119910 + 119895119895)

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                                                      Normalised Cross Correlation

                                                      Input (f)

                                                      Template (h)

                                                      Output Correlation image

                                                      Real max

                                                      NCC x y =Correlation

                                                      Length of image patch sdot Length of template

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                                                      Length of template Vector length

                                                      ndash Put all pixel values into a vectorndash Compute the length of this vector

                                                      Describes the intensity of the templatendash Bright template has a large lengthndash Dark template has a small length

                                                      Template (h)

                                                      Length of template = 119895119895=minus119877119877

                                                      119877119877

                                                      119894119894=minus119877119877

                                                      119877119877

                                                      ℎ(119894119894 119895119895) ℎ(119894119894 119895119895)

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                                                      Length of image patch Vector length based on pixel values in image patch Describes the intensity of the image patch

                                                      Template (h)

                                                      Input (f) with patch

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                                                      Normalised Cross Correlation The length of the image patch and the length of

                                                      template normalise the NCC If the image is very bright the NCC will be ldquopulled

                                                      downrdquo

                                                      NCC x y =Correlation

                                                      Length of image patch sdot Length of template

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                                                      Normalised Cross Correlation NCC will be between

                                                      ndash 0 No similarity between template and image patchndash 1 Template and image patch are identical

                                                      Input (f)

                                                      Template (h)

                                                      Output Correlation image

                                                      Real max

                                                      NCC x y =Correlation

                                                      Length of image patch sdot Length of template

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                                                      Normalised Cross Correlation

                                                      A) 010B) 033C) 083D) 062E) 098

                                                      Der udfoslashres template matching med og normalized crosscorrelation (NCC) beregnes Hvad bliver NNC i den markerede pixel

                                                      1

                                                      2 2

                                                      3

                                                      2

                                                      A B C D E

                                                      Chart1

                                                      1
                                                      2
                                                      2
                                                      3
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                                                      Sheet1

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                                                      Edges An edge is where there is a

                                                      high change in gray level values

                                                      Objects are often separated from the background by edgesGray level profile

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                                                      Edges The profile as a function f(d) What value is high when there

                                                      is an edgendash The slope of fndash The slope of the tangent at d

                                                      f(d)

                                                      119891119891prime(119889119889)

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                                                      Finite Difference Definition of slope

                                                      Approximation

                                                      Simpler approximationh = 1

                                                      119891119891prime 119889119889 = limℎrarr0

                                                      119891119891 119889119889 + ℎ minus 119891119891(119889119889)ℎ

                                                      119891119891prime 119889119889 asymp119891119891 119889119889 + ℎ minus 119891119891(119889119889)

                                                      ℎ

                                                      119891119891prime 119889119889 asymp 119891119891 119889119889 + 1 minus 119891119891(119889119889)

                                                      DTU Compute

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                                                      Edges Discrete approximation of frsquo(d) Can be implemented as a filter

                                                      -1 0 1

                                                      f(d-2) f(d-1) f(d) f(d+1) f(d+2) f(d+3)

                                                      f(d)

                                                      119891119891prime 119889119889 asymp 119891119891 119889119889 + 1 minus 119891119891(119889119889)

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                                                      Edges in 2D Changes in gray level values

                                                      ndash Image gradientndash Gradient is the 2D derivative of a 2D function f(xy)ndash Equal to the slope of the imagendash A steep slope is equal to an edge

                                                      120571120571119891119891 119909119909119910119910 = 119866(119892119892119909119909119892119892119910119910)

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                                                      Edge filter kernel The Prewitt filter is a typical

                                                      edge filter Output image has high

                                                      values where there are edges

                                                      -1 0 1

                                                      -1 0 1

                                                      -1 0 1Vertical Prewitt filter

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                                                      Prewitt filter

                                                      Original Prewitt Prewitt

                                                      Hot colormapSmooth 15x15

                                                      Smooth 15x15

                                                      Prewitt

                                                      DTU Compute

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                                                      Edge detection Edge filter

                                                      ndash Prewitt for example Thresholding

                                                      ndash Separate edges from non-edges

                                                      Output is binary imagendash Edges are white

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                                                      Edge filtering

                                                      A) MeanB) Horizontal SobelC) Vertical PrewittD) Horisontal PrewittE) Median

                                                      Der udfoslashres en filtrering (correlation) med et filter paring billedet Der bruges ikke coefficient normalization Den filtrerede vaeligrdi i den markerede pixel bliver -119 Hvilket et 3x3 filter blev benyttet

                                                      0

                                                      8

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                                                      02511 - Niveau af dagens emne forelaeligsingA) Meget letB) LetC) PassendeD) SvaeligrtE) Meget svaeligrt

                                                      23

                                                      6

                                                      10

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                                                      02512 - Niveau af dagens emne forelaeligsingA) Meget letB) LetC) PassendeD) SvaeligrtE) Meget svaeligrt

                                                      0 0

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                                                      02511 - Mit eget udbytte af dagenA) Jeg har laeligrt meget lidtB) Lidt laeligringC) PassendeD) God laeligringE) Jeg har laeligrt meget

                                                      0 0

                                                      2

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                                                      02512 - Mit eget udbytte af dagenA) Jeg har laeligrt meget lidtB) Lidt laeligringC) PassendeD) God laeligringE) Jeg har laeligrt meget

                                                      2

                                                      1

                                                      3

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                                                      02511 - Sidste uges oslashvelser (pixelwiseoperations)A) Meget letteB) LetteC) PassendeD) SvaeligreE) Meget svaeligre

                                                      0 0

                                                      1

                                                      4

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                                                      02512 - Sidste uges oslashvelser (pixelwiseoperations)A) Meget letteB) LetteC) PassendeD) SvaeligreE) Meget svaeligre

                                                      3

                                                      0

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                                                      Denne uges brug af clickersA) click click click ndash jeg bliver

                                                      sindssygB) For meget clickC) PassendeD) Jeg vil gerne have lidt mereE) Jeg kan ikrsquo faring nok

                                                      0 0

                                                      5

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                                                      6

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                                                      What can you do after today Describe the difference between point processing and neighbourhood

                                                      processing Compute a rank filtered image using the min max median and

                                                      difference rank filters Compute a mean filtered image Decide if median or average filtering should be used for noise removal Choose the appropriate image border handling based on a given input

                                                      image Implement and apply template matching Compute the normalised cross correlation and explain why it should be

                                                      used Apply given image filter kernels to images Use edge filters on images Describe finite difference approximation of image gradients Describe the concept of edge detection

                                                      DTU Compute

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                                                      Oslashvelsesrapport over oslashvelse 4 - 02511 Oslashvelser taeligller cirka 30 af karakteren Skal afleveres senest den 7 marts kl 2359 Kan afleveres af 1 eller 2 personer

                                                      ndash I skal skrive jeres egen oslashvelsesrapportndash Brug mindst et af jeres egne billeder

                                                      Afleveres som PDF Lad vaeligre med at kopiere opgaveteksten ind i jeres

                                                      opgave Put Matlab kode i et Appendix og henvis fra teksten Eksempel rapport over oslashvelse findes paring

                                                      hjemmesiden under eksamen

                                                      DTU Compute

                                                      2122018Introduction to Medical Image Analysis85 DTU Compute Technical University of Denmark

                                                      Exercises

                                                      • Introduction to Medical Image Analysis
                                                      • Lecture 4 ndash Neighbourhood Processing
                                                      • What can you do after today
                                                      • Point processing
                                                      • Point processing
                                                      • Neighbourhood processing
                                                      • Use of filtering
                                                      • Salt and pepper noise
                                                      • Salt and pepper noise
                                                      • What is so special about noise
                                                      • Noise ndash go away
                                                      • What is the median Value
                                                      • The median value
                                                      • Noise away ndash the median filter
                                                      • Noise removal ndash average filter
                                                      • Noise removal ndash median filter
                                                      • Image Filtering
                                                      • Median filter
                                                      • Rank filters
                                                      • Median filter
                                                      • Correlation
                                                      • Why do we need similarity
                                                      • Correlation (1D)
                                                      • Correlation (1D)
                                                      • Normalisation
                                                      • Normalisation
                                                      • Correlation on images
                                                      • Correlation on images
                                                      • Correlation on images
                                                      • Draw your filter
                                                      • Correlation on images ndash no normalisation
                                                      • Correlation on images ndash no normalisation 2
                                                      • Mathematics of 2D Correlation
                                                      • Mathematics of 2D Correlation
                                                      • Mathematics of 2D Correlation
                                                      • Slide Number 40
                                                      • 2D Kernel Normalisation
                                                      • Correlation
                                                      • Smoothing filters
                                                      • Use of smoothing
                                                      • Use of smoothing
                                                      • Mean filter
                                                      • Border handling
                                                      • Border handling ndash extend the input
                                                      • Correlation with zero padding
                                                      • Border handling ndash extend the input
                                                      • Template Matching
                                                      • Template Matching
                                                      • Template Matching
                                                      • Template Matching
                                                      • Problematic Correlation
                                                      • Normalised Cross Correlation
                                                      • Length of template
                                                      • Length of image patch
                                                      • Normalised Cross Correlation
                                                      • Normalised Cross Correlation
                                                      • Normalised Cross Correlation
                                                      • Edges
                                                      • Edges
                                                      • Finite Difference
                                                      • Edges
                                                      • Edges in 2D
                                                      • Edge filter kernel
                                                      • Prewitt filter
                                                      • Edge detection
                                                      • Edge filtering
                                                      • 02511 - Niveau af dagens emne forelaeligsing
                                                      • 02512 - Niveau af dagens emne forelaeligsing
                                                      • 02511 - Mit eget udbytte af dagen
                                                      • 02512 - Mit eget udbytte af dagen
                                                      • 02511 - Sidste uges oslashvelser (pixelwise operations)
                                                      • 02512 - Sidste uges oslashvelser (pixelwise operations)
                                                      • Denne uges brug af clickers
                                                      • What can you do after today
                                                      • Oslashvelsesrapport over oslashvelse 4 - 02511
                                                      • Exercises
                                                        A0
                                                        B0
                                                        C5
                                                        D0
                                                        E6
                                                        A
                                                        B
                                                        C
                                                        D
                                                        E
                                                        A3
                                                        B0
                                                        C3
                                                        D0
                                                        E0
                                                        A
                                                        B
                                                        C
                                                        D
                                                        E
                                                        A0
                                                        B0
                                                        C1
                                                        D4
                                                        E1
                                                        A
                                                        B
                                                        C
                                                        D
                                                        E
                                                        A2
                                                        B1
                                                        C3
                                                        D2
                                                        E0
                                                        A
                                                        B
                                                        C
                                                        D
                                                        E
                                                        A0
                                                        B0
                                                        C2
                                                        D6
                                                        E0
                                                        A
                                                        B
                                                        C
                                                        D
                                                        E
                                                        A0
                                                        B0
                                                        C1
                                                        D0
                                                        E0
                                                        A
                                                        B
                                                        C
                                                        D
                                                        E
                                                        A2
                                                        B3
                                                        C6
                                                        D1
                                                        E0
                                                        A
                                                        B
                                                        C
                                                        D
                                                        E
                                                        A0
                                                        B8
                                                        C1
                                                        D1
                                                        E0
                                                        A
                                                        B
                                                        C
                                                        D
                                                        E
                                                        A1
                                                        B2
                                                        C2
                                                        D3
                                                        E2
                                                        A
                                                        B
                                                        C
                                                        D
                                                        E
                                                        A0
                                                        B13
                                                        C0
                                                        D0
                                                        E0
                                                        A
                                                        B
                                                        C
                                                        D
                                                        E
                                                        A12
                                                        B0
                                                        C0
                                                        D0
                                                        E0
                                                        A
                                                        B
                                                        C
                                                        D
                                                        E
                                                        A0
                                                        B0
                                                        C0
                                                        D0
                                                        E13
                                                        A
                                                        B
                                                        C
                                                        D
                                                        E
                                                        A13
                                                        B0
                                                        C0
                                                        D0
                                                        E0
                                                        A
                                                        B
                                                        C
                                                        D
                                                        E
                                                        A1
                                                        B0
                                                        C14
                                                        D0
                                                        E0
                                                        A
                                                        B
                                                        C
                                                        D
                                                        E

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                                                        Why do we need similarity Image analysis is also about recognition of patterns Often an example pattern is used We need something to tell us if there is a high match

                                                        between our pattern and a part of the image

                                                        Example pattern

                                                        Image

                                                        Find matches

                                                        DTU Compute

                                                        2122018Introduction to Medical Image Analysis25 DTU Compute Technical University of Denmark

                                                        Correlation (1D)

                                                        1 1 2 2 1 1 2 2 1 1

                                                        1 2 1

                                                        45

                                                        41

                                                        1 1 + 2 1 + 1 2 = 5

                                                        Normalise

                                                        Kernel

                                                        Signal (1D image)

                                                        41

                                                        DTU Compute

                                                        2122018Introduction to Medical Image Analysis26 DTU Compute Technical University of Denmark

                                                        Correlation (1D)

                                                        1 1 2 2 1 1 2 2 1 1

                                                        1 2 1

                                                        45

                                                        47

                                                        47

                                                        45

                                                        45

                                                        47

                                                        47

                                                        45

                                                        41

                                                        DTU Compute

                                                        2122018Introduction to Medical Image Analysis27 DTU Compute Technical University of Denmark

                                                        Normalisation

                                                        1 1 2 2 1 1 2 2 1 1

                                                        1 2 1

                                                        45

                                                        41

                                                        1 1 + 2 1 + 1 2 = 5

                                                        Normalise41

                                                        bull The sum of the kernel elements is used

                                                        bull Keep the values in the same range as the input image

                                                        Sum is 4

                                                        DTU Compute

                                                        2122018Introduction to Medical Image Analysis28 DTU Compute Technical University of Denmark

                                                        Normalisation Normalisation factor

                                                        ndash Sum of kernel coefficients

                                                        1 2 1h(x)

                                                        119909119909

                                                        ℎ 119909119909 = 1 + 2 + 1

                                                        DTU Compute

                                                        2122018Introduction to Medical Image Analysis29 DTU Compute Technical University of Denmark

                                                        Correlation on images The filter is now 2D 1 1 1

                                                        1 1 1

                                                        1 1 1

                                                        0 2 4

                                                        1 2 2

                                                        1 6 3

                                                        1 2 12 5 3

                                                        2 1 3

                                                        1 3 1

                                                        2 2 2

                                                        0 1 3

                                                        1 2 0

                                                        2 1 4

                                                        1 0 1

                                                        912

                                                        91

                                                        Input OutputKernel

                                                        Kernel coefficients

                                                        DTU Compute

                                                        2122018Introduction to Medical Image Analysis30 DTU Compute Technical University of Denmark

                                                        Correlation on images

                                                        1 1 11 1 11 1 1

                                                        0 2 4

                                                        1 2 2

                                                        1 6 3

                                                        1 2 0

                                                        2 1 4

                                                        1 0 1

                                                        912

                                                        911

                                                        91

                                                        Input Output

                                                        1 3 1

                                                        2 2 2

                                                        0 1 3

                                                        1 2 12 5 3

                                                        2 1 3

                                                        DTU Compute

                                                        2122018Introduction to Medical Image Analysis31 DTU Compute Technical University of Denmark

                                                        Correlation on images

                                                        Input Output

                                                        The mask is moved row by row

                                                        No values at the border

                                                        0 2 4

                                                        1 2 2

                                                        1 6 3

                                                        1 2 0

                                                        2 1 4

                                                        1 0 1

                                                        1 3 1

                                                        2 2 2

                                                        0 1 3

                                                        1 2 12 5 3

                                                        2 1 3

                                                        DTU Compute

                                                        2122018Introduction to Medical Image Analysis32 DTU Compute Technical University of Denmark

                                                        1 2 1

                                                        1 3 1

                                                        1 2 1

                                                        -1 -2 -1

                                                        0 0 0

                                                        1 2 1

                                                        Draw your filter

                                                        DTU Compute

                                                        2122018Introduction to Medical Image Analysis33 DTU Compute Technical University of Denmark

                                                        Correlation on images ndash no normalisationA) 4B) 7C) 16D) 23E) 25

                                                        1 2 11 3 11 2 1

                                                        0 2 41 2 2

                                                        1 6 3

                                                        1 2 12 5 3

                                                        2 1 3

                                                        1 3 1

                                                        2 2 2

                                                        0 1 3

                                                        1 2 0

                                                        2 1 4

                                                        1 0 11 0

                                                        14

                                                        0 0

                                                        A B C D E

                                                        Chart1

                                                        1
                                                        0
                                                        14
                                                        0
                                                        0

                                                        Sheet1

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                                                        Correlation on images ndash no normalisation 2A) 010B) 3 3C) 6 2D) 10 15E) 11 32

                                                        13

                                                        0 0 0 0

                                                        A B C D E

                                                        -1 -2 -10 0 01 2 1

                                                        0 2 41 2 2

                                                        1 6 3

                                                        1 2 12 5 3

                                                        2 1 3

                                                        1 3 1

                                                        2 2 2

                                                        0 1 3

                                                        1 2 0

                                                        2 1 4

                                                        1 0 1

                                                        Chart1

                                                        13
                                                        0
                                                        0
                                                        0
                                                        0

                                                        Sheet1

                                                        DTU Compute

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                                                        Mathematics of 2D Correlation

                                                        h

                                                        f

                                                        Correlation operator

                                                        1 2 11 3 11 2 1

                                                        0 2 4

                                                        1 2 2

                                                        1 6 3

                                                        1 2 1

                                                        2 5 3

                                                        2 1 3

                                                        1 3 1

                                                        2 2 2

                                                        0 1 3

                                                        1 2 0

                                                        2 1 4

                                                        1 0 1

                                                        119892119892 119909119909119910119910 = 119891119891 119909119909119910119910 ∘ ℎ(119909119909119910119910)

                                                        DTU Compute

                                                        2122018Introduction to Medical Image Analysis38 DTU Compute Technical University of Denmark

                                                        Mathematics of 2D Correlation

                                                        1 2 11 3 11 2 1

                                                        0 2 4

                                                        1 2 2

                                                        1 6 3

                                                        1 2 1

                                                        2 5 3

                                                        2 1 3

                                                        1 3 1

                                                        2 2 2

                                                        0 1 3

                                                        1 2 0

                                                        2 1 4

                                                        1 0 1

                                                        h

                                                        fh(00)

                                                        f(21)

                                                        Example g(21)

                                                        i = -1 j = -1

                                                        i = 1 j = 0

                                                        119892119892 119909119909119910119910 = 119895119895=minus119877119877

                                                        119877119877

                                                        119894119894=minus119877119877

                                                        119877119877

                                                        ℎ(119894119894 119895119895) 119891119891(119909119909 + 119894119894119910119910 + 119895119895)

                                                        DTU Compute

                                                        2122018Introduction to Medical Image Analysis39 DTU Compute Technical University of Denmark

                                                        Mathematics of 2D Correlation

                                                        1 2 11 3 11 2 1

                                                        0 2 4

                                                        1 2 2

                                                        1 6 3

                                                        1 2 1

                                                        2 5 3

                                                        2 1 3

                                                        1 3 1

                                                        2 2 2

                                                        0 1 3

                                                        1 2 0

                                                        2 1 4

                                                        1 0 1

                                                        h

                                                        f

                                                        119892119892 119909119909119910119910 = 119895119895=minus119877119877

                                                        119877119877

                                                        119894119894=minus119877119877

                                                        119877119877

                                                        ℎ(119894119894 119895119895) 119891119891(119909119909 + 119894119894119910119910 + 119895119895)

                                                        119892119892(119909119909119910119910 = 1 2 + 2 0 + 1 1 + 1 1 + 3 4 + 1 2 + 1 0 + 2 1 + 1 0

                                                        DTU Compute

                                                        2122018Introduction to Medical Image Analysis40 DTU Compute Technical University of Denmark

                                                        119892119892 119909119909 119910119910 = 119895119895=minus119877119877

                                                        119877119877

                                                        119894119894=minus119877119877

                                                        119877119877

                                                        ℎ(119894119894 119895119895) 119891119891(119909119909 + 119894119894119910119910 + 119895119895)

                                                        119892119892 22 =ℎ minus1minus1 sdot 119891119891 11 + ℎ 0minus1 sdot 119891119891 21 + ℎ 1minus1 sdot 119891119891 31 +ℎ minus10 sdot 119891119891 12 + ℎ 00 sdot 119891119891 22 + ℎ 10 sdot 119891119891 32 +ℎ minus11 sdot 119891119891 13 + ℎ 01 sdot 119891119891 23 + ℎ 11 sdot 119891119891 33

                                                        DTU Compute

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                                                        2D Kernel Normalisation

                                                        1 2 11 3 11 2 1

                                                        h

                                                        Normalisation factor

                                                        1 + 2 + 1 + 1 + 3 + 1 + 1 + 2 + 1 = 13

                                                        119909119909

                                                        119910119910

                                                        ℎ(119909119909119910119910)

                                                        DTU Compute

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                                                        CorrelationA) 50122B) 123001C) 11233D) 2550E) 90454

                                                        0 0 0 0

                                                        13

                                                        A B C D E

                                                        Chart1

                                                        0
                                                        0
                                                        0
                                                        0
                                                        13

                                                        Sheet1

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                                                        Smoothing filters

                                                        Also know as ndash Smoothing kernel Mean filter Low pass filter blurring

                                                        The simplest filter ndash Spatial low pass filterndash Removes high frequencies

                                                        Another mask ndash Gaussian filter

                                                        1 1 1

                                                        1 1 1

                                                        1 1 191

                                                        1 2 1

                                                        2 4 2

                                                        1 2 1161

                                                        Why Gaussian

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                                                        Use of smoothing

                                                        3x3 7x7 11x11 15x15

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                                                        Use of smoothing Large kernels smooth more Removes high frequency information Good at enhancing big structures

                                                        3x3 15x15

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                                                        Mean filterA) 166B) 113C) 12D) 51E) 245

                                                        0 0 0 0

                                                        A B C D E

                                                        Chart1

                                                        12
                                                        0
                                                        0
                                                        0
                                                        0

                                                        Sheet1

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                                                        Border handling

                                                        0 2 41 2 2

                                                        1 6 3

                                                        1 2 12 5 3

                                                        2 1 3

                                                        1 3 1

                                                        2 2 2

                                                        0 1 3

                                                        1 2 0

                                                        2 1 4

                                                        1 0 1

                                                        Input Output

                                                        No values at the border

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                                                        Border handling ndash extend the input

                                                        0 2 41 2 2

                                                        1 6 3

                                                        1 2 12 5 3

                                                        2 1 3

                                                        1 3 1

                                                        2 2 2

                                                        0 1 3

                                                        1 2 0

                                                        2 1 4

                                                        1 0 1

                                                        Input

                                                        0 0 0 0 000000

                                                        bull Zero padding ndash what happens

                                                        bull Zero is black ndash creates dark border around the image

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                                                        Correlation with zero paddingA) 5 8B) 12 16C) 13 3D) 15 21E) 17 12

                                                        1 2 11 3 11 2 1

                                                        0 2 41 2 2

                                                        1 6 3

                                                        1 2 12 5 3

                                                        2 1 3

                                                        1 3 1

                                                        2 2 2

                                                        0 1 3

                                                        1 2 0

                                                        2 1 4

                                                        1 0 1

                                                        0

                                                        13

                                                        0 0 0

                                                        A B C D E

                                                        Chart1

                                                        0
                                                        13
                                                        0
                                                        0
                                                        0

                                                        Sheet1

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                                                        Border handling ndash extend the input

                                                        0 2 41 2 2

                                                        1 6 3

                                                        1 2 12 5 3

                                                        2 1 3

                                                        1 3 1

                                                        2 2 2

                                                        0 1 3

                                                        1 2 0

                                                        2 1 4

                                                        1 0 1

                                                        Input

                                                        1 2 0 1 311211

                                                        bull Reflection

                                                        bull Normally better than zero padding

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                                                        Template Matching Template

                                                        ndash Skabelon paring dansk Locates objects in images

                                                        Input

                                                        Template

                                                        Output Correlation image

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                                                        Template Matching The correlation between the template and the input

                                                        image is computed for each pixel

                                                        Input

                                                        Template

                                                        Output Correlation image

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                                                        Template Matching The pixel with the highest value is found in the

                                                        output imagendash Here is the highest correlation

                                                        Input

                                                        Template

                                                        Output Correlation image

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                                                        Template Matching This corresponds to the found pattern in the input

                                                        image

                                                        Input

                                                        Template

                                                        Output Correlation image

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                                                        Problematic Correlation Correlation matching has problem with light areas ndash

                                                        why

                                                        Input (f)

                                                        Template (h)

                                                        Output Correlation imageFake max

                                                        Real max

                                                        Very High119892119892 119909119909119910119910 = 119895119895=minus119877119877

                                                        119877119877

                                                        119894119894=minus119877119877

                                                        119877119877

                                                        ℎ(119894119894 119895119895) 119891119891(119909119909 + 119894119894119910119910 + 119895119895)

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                                                        Normalised Cross Correlation

                                                        Input (f)

                                                        Template (h)

                                                        Output Correlation image

                                                        Real max

                                                        NCC x y =Correlation

                                                        Length of image patch sdot Length of template

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                                                        Length of template Vector length

                                                        ndash Put all pixel values into a vectorndash Compute the length of this vector

                                                        Describes the intensity of the templatendash Bright template has a large lengthndash Dark template has a small length

                                                        Template (h)

                                                        Length of template = 119895119895=minus119877119877

                                                        119877119877

                                                        119894119894=minus119877119877

                                                        119877119877

                                                        ℎ(119894119894 119895119895) ℎ(119894119894 119895119895)

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                                                        Length of image patch Vector length based on pixel values in image patch Describes the intensity of the image patch

                                                        Template (h)

                                                        Input (f) with patch

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                                                        Normalised Cross Correlation The length of the image patch and the length of

                                                        template normalise the NCC If the image is very bright the NCC will be ldquopulled

                                                        downrdquo

                                                        NCC x y =Correlation

                                                        Length of image patch sdot Length of template

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                                                        Normalised Cross Correlation NCC will be between

                                                        ndash 0 No similarity between template and image patchndash 1 Template and image patch are identical

                                                        Input (f)

                                                        Template (h)

                                                        Output Correlation image

                                                        Real max

                                                        NCC x y =Correlation

                                                        Length of image patch sdot Length of template

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                                                        Normalised Cross Correlation

                                                        A) 010B) 033C) 083D) 062E) 098

                                                        Der udfoslashres template matching med og normalized crosscorrelation (NCC) beregnes Hvad bliver NNC i den markerede pixel

                                                        1

                                                        2 2

                                                        3

                                                        2

                                                        A B C D E

                                                        Chart1

                                                        1
                                                        2
                                                        2
                                                        3
                                                        2

                                                        Sheet1

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                                                        Edges An edge is where there is a

                                                        high change in gray level values

                                                        Objects are often separated from the background by edgesGray level profile

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                                                        Edges The profile as a function f(d) What value is high when there

                                                        is an edgendash The slope of fndash The slope of the tangent at d

                                                        f(d)

                                                        119891119891prime(119889119889)

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                                                        Finite Difference Definition of slope

                                                        Approximation

                                                        Simpler approximationh = 1

                                                        119891119891prime 119889119889 = limℎrarr0

                                                        119891119891 119889119889 + ℎ minus 119891119891(119889119889)ℎ

                                                        119891119891prime 119889119889 asymp119891119891 119889119889 + ℎ minus 119891119891(119889119889)

                                                        ℎ

                                                        119891119891prime 119889119889 asymp 119891119891 119889119889 + 1 minus 119891119891(119889119889)

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                                                        Edges Discrete approximation of frsquo(d) Can be implemented as a filter

                                                        -1 0 1

                                                        f(d-2) f(d-1) f(d) f(d+1) f(d+2) f(d+3)

                                                        f(d)

                                                        119891119891prime 119889119889 asymp 119891119891 119889119889 + 1 minus 119891119891(119889119889)

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                                                        Edges in 2D Changes in gray level values

                                                        ndash Image gradientndash Gradient is the 2D derivative of a 2D function f(xy)ndash Equal to the slope of the imagendash A steep slope is equal to an edge

                                                        120571120571119891119891 119909119909119910119910 = 119866(119892119892119909119909119892119892119910119910)

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                                                        Edge filter kernel The Prewitt filter is a typical

                                                        edge filter Output image has high

                                                        values where there are edges

                                                        -1 0 1

                                                        -1 0 1

                                                        -1 0 1Vertical Prewitt filter

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                                                        Prewitt filter

                                                        Original Prewitt Prewitt

                                                        Hot colormapSmooth 15x15

                                                        Smooth 15x15

                                                        Prewitt

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                                                        Edge detection Edge filter

                                                        ndash Prewitt for example Thresholding

                                                        ndash Separate edges from non-edges

                                                        Output is binary imagendash Edges are white

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                                                        Edge filtering

                                                        A) MeanB) Horizontal SobelC) Vertical PrewittD) Horisontal PrewittE) Median

                                                        Der udfoslashres en filtrering (correlation) med et filter paring billedet Der bruges ikke coefficient normalization Den filtrerede vaeligrdi i den markerede pixel bliver -119 Hvilket et 3x3 filter blev benyttet

                                                        0

                                                        8

                                                        1 10

                                                        A B C D E

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                                                        0
                                                        8
                                                        1
                                                        1
                                                        0

                                                        Sheet1

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                                                        02511 - Niveau af dagens emne forelaeligsingA) Meget letB) LetC) PassendeD) SvaeligrtE) Meget svaeligrt

                                                        23

                                                        6

                                                        10

                                                        A B C D E

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                                                        2
                                                        3
                                                        6
                                                        1
                                                        0

                                                        Sheet1

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                                                        02512 - Niveau af dagens emne forelaeligsingA) Meget letB) LetC) PassendeD) SvaeligrtE) Meget svaeligrt

                                                        0 0

                                                        1

                                                        0 0

                                                        A B C D E

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                                                        0
                                                        0
                                                        1
                                                        0
                                                        0

                                                        Sheet1

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                                                        02511 - Mit eget udbytte af dagenA) Jeg har laeligrt meget lidtB) Lidt laeligringC) PassendeD) God laeligringE) Jeg har laeligrt meget

                                                        0 0

                                                        2

                                                        6

                                                        0

                                                        A B C D E

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                                                        0
                                                        0
                                                        2
                                                        6
                                                        0

                                                        Sheet1

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                                                        02512 - Mit eget udbytte af dagenA) Jeg har laeligrt meget lidtB) Lidt laeligringC) PassendeD) God laeligringE) Jeg har laeligrt meget

                                                        2

                                                        1

                                                        3

                                                        2

                                                        0

                                                        A B C D E

                                                        Chart1

                                                        2
                                                        1
                                                        3
                                                        2
                                                        0

                                                        Sheet1

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                                                        02511 - Sidste uges oslashvelser (pixelwiseoperations)A) Meget letteB) LetteC) PassendeD) SvaeligreE) Meget svaeligre

                                                        0 0

                                                        1

                                                        4

                                                        1

                                                        A B C D E

                                                        Chart1

                                                        0
                                                        0
                                                        1
                                                        4
                                                        1

                                                        Sheet1

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                                                        02512 - Sidste uges oslashvelser (pixelwiseoperations)A) Meget letteB) LetteC) PassendeD) SvaeligreE) Meget svaeligre

                                                        3

                                                        0

                                                        3

                                                        0 0

                                                        A B C D E

                                                        Chart1

                                                        3
                                                        0
                                                        3
                                                        0
                                                        0

                                                        Sheet1

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                                                        Denne uges brug af clickersA) click click click ndash jeg bliver

                                                        sindssygB) For meget clickC) PassendeD) Jeg vil gerne have lidt mereE) Jeg kan ikrsquo faring nok

                                                        0 0

                                                        5

                                                        0

                                                        6

                                                        A B C D E

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                                                        0
                                                        0
                                                        5
                                                        0
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                                                        Sheet1

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                                                        What can you do after today Describe the difference between point processing and neighbourhood

                                                        processing Compute a rank filtered image using the min max median and

                                                        difference rank filters Compute a mean filtered image Decide if median or average filtering should be used for noise removal Choose the appropriate image border handling based on a given input

                                                        image Implement and apply template matching Compute the normalised cross correlation and explain why it should be

                                                        used Apply given image filter kernels to images Use edge filters on images Describe finite difference approximation of image gradients Describe the concept of edge detection

                                                        DTU Compute

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                                                        Oslashvelsesrapport over oslashvelse 4 - 02511 Oslashvelser taeligller cirka 30 af karakteren Skal afleveres senest den 7 marts kl 2359 Kan afleveres af 1 eller 2 personer

                                                        ndash I skal skrive jeres egen oslashvelsesrapportndash Brug mindst et af jeres egne billeder

                                                        Afleveres som PDF Lad vaeligre med at kopiere opgaveteksten ind i jeres

                                                        opgave Put Matlab kode i et Appendix og henvis fra teksten Eksempel rapport over oslashvelse findes paring

                                                        hjemmesiden under eksamen

                                                        DTU Compute

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                                                        Exercises

                                                        • Introduction to Medical Image Analysis
                                                        • Lecture 4 ndash Neighbourhood Processing
                                                        • What can you do after today
                                                        • Point processing
                                                        • Point processing
                                                        • Neighbourhood processing
                                                        • Use of filtering
                                                        • Salt and pepper noise
                                                        • Salt and pepper noise
                                                        • What is so special about noise
                                                        • Noise ndash go away
                                                        • What is the median Value
                                                        • The median value
                                                        • Noise away ndash the median filter
                                                        • Noise removal ndash average filter
                                                        • Noise removal ndash median filter
                                                        • Image Filtering
                                                        • Median filter
                                                        • Rank filters
                                                        • Median filter
                                                        • Correlation
                                                        • Why do we need similarity
                                                        • Correlation (1D)
                                                        • Correlation (1D)
                                                        • Normalisation
                                                        • Normalisation
                                                        • Correlation on images
                                                        • Correlation on images
                                                        • Correlation on images
                                                        • Draw your filter
                                                        • Correlation on images ndash no normalisation
                                                        • Correlation on images ndash no normalisation 2
                                                        • Mathematics of 2D Correlation
                                                        • Mathematics of 2D Correlation
                                                        • Mathematics of 2D Correlation
                                                        • Slide Number 40
                                                        • 2D Kernel Normalisation
                                                        • Correlation
                                                        • Smoothing filters
                                                        • Use of smoothing
                                                        • Use of smoothing
                                                        • Mean filter
                                                        • Border handling
                                                        • Border handling ndash extend the input
                                                        • Correlation with zero padding
                                                        • Border handling ndash extend the input
                                                        • Template Matching
                                                        • Template Matching
                                                        • Template Matching
                                                        • Template Matching
                                                        • Problematic Correlation
                                                        • Normalised Cross Correlation
                                                        • Length of template
                                                        • Length of image patch
                                                        • Normalised Cross Correlation
                                                        • Normalised Cross Correlation
                                                        • Normalised Cross Correlation
                                                        • Edges
                                                        • Edges
                                                        • Finite Difference
                                                        • Edges
                                                        • Edges in 2D
                                                        • Edge filter kernel
                                                        • Prewitt filter
                                                        • Edge detection
                                                        • Edge filtering
                                                        • 02511 - Niveau af dagens emne forelaeligsing
                                                        • 02512 - Niveau af dagens emne forelaeligsing
                                                        • 02511 - Mit eget udbytte af dagen
                                                        • 02512 - Mit eget udbytte af dagen
                                                        • 02511 - Sidste uges oslashvelser (pixelwise operations)
                                                        • 02512 - Sidste uges oslashvelser (pixelwise operations)
                                                        • Denne uges brug af clickers
                                                        • What can you do after today
                                                        • Oslashvelsesrapport over oslashvelse 4 - 02511
                                                        • Exercises
                                                          A0
                                                          B0
                                                          C5
                                                          D0
                                                          E6
                                                          A
                                                          B
                                                          C
                                                          D
                                                          E
                                                          A3
                                                          B0
                                                          C3
                                                          D0
                                                          E0
                                                          A
                                                          B
                                                          C
                                                          D
                                                          E
                                                          A0
                                                          B0
                                                          C1
                                                          D4
                                                          E1
                                                          A
                                                          B
                                                          C
                                                          D
                                                          E
                                                          A2
                                                          B1
                                                          C3
                                                          D2
                                                          E0
                                                          A
                                                          B
                                                          C
                                                          D
                                                          E
                                                          A0
                                                          B0
                                                          C2
                                                          D6
                                                          E0
                                                          A
                                                          B
                                                          C
                                                          D
                                                          E
                                                          A0
                                                          B0
                                                          C1
                                                          D0
                                                          E0
                                                          A
                                                          B
                                                          C
                                                          D
                                                          E
                                                          A2
                                                          B3
                                                          C6
                                                          D1
                                                          E0
                                                          A
                                                          B
                                                          C
                                                          D
                                                          E
                                                          A0
                                                          B8
                                                          C1
                                                          D1
                                                          E0
                                                          A
                                                          B
                                                          C
                                                          D
                                                          E
                                                          A1
                                                          B2
                                                          C2
                                                          D3
                                                          E2
                                                          A
                                                          B
                                                          C
                                                          D
                                                          E
                                                          A0
                                                          B13
                                                          C0
                                                          D0
                                                          E0
                                                          A
                                                          B
                                                          C
                                                          D
                                                          E
                                                          A12
                                                          B0
                                                          C0
                                                          D0
                                                          E0
                                                          A
                                                          B
                                                          C
                                                          D
                                                          E
                                                          A0
                                                          B0
                                                          C0
                                                          D0
                                                          E13
                                                          A
                                                          B
                                                          C
                                                          D
                                                          E
                                                          A13
                                                          B0
                                                          C0
                                                          D0
                                                          E0
                                                          A
                                                          B
                                                          C
                                                          D
                                                          E
                                                          A1
                                                          B0
                                                          C14
                                                          D0
                                                          E0
                                                          A
                                                          B
                                                          C
                                                          D
                                                          E

                                                          DTU Compute

                                                          2122018Introduction to Medical Image Analysis25 DTU Compute Technical University of Denmark

                                                          Correlation (1D)

                                                          1 1 2 2 1 1 2 2 1 1

                                                          1 2 1

                                                          45

                                                          41

                                                          1 1 + 2 1 + 1 2 = 5

                                                          Normalise

                                                          Kernel

                                                          Signal (1D image)

                                                          41

                                                          DTU Compute

                                                          2122018Introduction to Medical Image Analysis26 DTU Compute Technical University of Denmark

                                                          Correlation (1D)

                                                          1 1 2 2 1 1 2 2 1 1

                                                          1 2 1

                                                          45

                                                          47

                                                          47

                                                          45

                                                          45

                                                          47

                                                          47

                                                          45

                                                          41

                                                          DTU Compute

                                                          2122018Introduction to Medical Image Analysis27 DTU Compute Technical University of Denmark

                                                          Normalisation

                                                          1 1 2 2 1 1 2 2 1 1

                                                          1 2 1

                                                          45

                                                          41

                                                          1 1 + 2 1 + 1 2 = 5

                                                          Normalise41

                                                          bull The sum of the kernel elements is used

                                                          bull Keep the values in the same range as the input image

                                                          Sum is 4

                                                          DTU Compute

                                                          2122018Introduction to Medical Image Analysis28 DTU Compute Technical University of Denmark

                                                          Normalisation Normalisation factor

                                                          ndash Sum of kernel coefficients

                                                          1 2 1h(x)

                                                          119909119909

                                                          ℎ 119909119909 = 1 + 2 + 1

                                                          DTU Compute

                                                          2122018Introduction to Medical Image Analysis29 DTU Compute Technical University of Denmark

                                                          Correlation on images The filter is now 2D 1 1 1

                                                          1 1 1

                                                          1 1 1

                                                          0 2 4

                                                          1 2 2

                                                          1 6 3

                                                          1 2 12 5 3

                                                          2 1 3

                                                          1 3 1

                                                          2 2 2

                                                          0 1 3

                                                          1 2 0

                                                          2 1 4

                                                          1 0 1

                                                          912

                                                          91

                                                          Input OutputKernel

                                                          Kernel coefficients

                                                          DTU Compute

                                                          2122018Introduction to Medical Image Analysis30 DTU Compute Technical University of Denmark

                                                          Correlation on images

                                                          1 1 11 1 11 1 1

                                                          0 2 4

                                                          1 2 2

                                                          1 6 3

                                                          1 2 0

                                                          2 1 4

                                                          1 0 1

                                                          912

                                                          911

                                                          91

                                                          Input Output

                                                          1 3 1

                                                          2 2 2

                                                          0 1 3

                                                          1 2 12 5 3

                                                          2 1 3

                                                          DTU Compute

                                                          2122018Introduction to Medical Image Analysis31 DTU Compute Technical University of Denmark

                                                          Correlation on images

                                                          Input Output

                                                          The mask is moved row by row

                                                          No values at the border

                                                          0 2 4

                                                          1 2 2

                                                          1 6 3

                                                          1 2 0

                                                          2 1 4

                                                          1 0 1

                                                          1 3 1

                                                          2 2 2

                                                          0 1 3

                                                          1 2 12 5 3

                                                          2 1 3

                                                          DTU Compute

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                                                          1 2 1

                                                          1 3 1

                                                          1 2 1

                                                          -1 -2 -1

                                                          0 0 0

                                                          1 2 1

                                                          Draw your filter

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                                                          2122018Introduction to Medical Image Analysis33 DTU Compute Technical University of Denmark

                                                          Correlation on images ndash no normalisationA) 4B) 7C) 16D) 23E) 25

                                                          1 2 11 3 11 2 1

                                                          0 2 41 2 2

                                                          1 6 3

                                                          1 2 12 5 3

                                                          2 1 3

                                                          1 3 1

                                                          2 2 2

                                                          0 1 3

                                                          1 2 0

                                                          2 1 4

                                                          1 0 11 0

                                                          14

                                                          0 0

                                                          A B C D E

                                                          Chart1

                                                          1
                                                          0
                                                          14
                                                          0
                                                          0

                                                          Sheet1

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                                                          Correlation on images ndash no normalisation 2A) 010B) 3 3C) 6 2D) 10 15E) 11 32

                                                          13

                                                          0 0 0 0

                                                          A B C D E

                                                          -1 -2 -10 0 01 2 1

                                                          0 2 41 2 2

                                                          1 6 3

                                                          1 2 12 5 3

                                                          2 1 3

                                                          1 3 1

                                                          2 2 2

                                                          0 1 3

                                                          1 2 0

                                                          2 1 4

                                                          1 0 1

                                                          Chart1

                                                          13
                                                          0
                                                          0
                                                          0
                                                          0

                                                          Sheet1

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                                                          Mathematics of 2D Correlation

                                                          h

                                                          f

                                                          Correlation operator

                                                          1 2 11 3 11 2 1

                                                          0 2 4

                                                          1 2 2

                                                          1 6 3

                                                          1 2 1

                                                          2 5 3

                                                          2 1 3

                                                          1 3 1

                                                          2 2 2

                                                          0 1 3

                                                          1 2 0

                                                          2 1 4

                                                          1 0 1

                                                          119892119892 119909119909119910119910 = 119891119891 119909119909119910119910 ∘ ℎ(119909119909119910119910)

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                                                          Mathematics of 2D Correlation

                                                          1 2 11 3 11 2 1

                                                          0 2 4

                                                          1 2 2

                                                          1 6 3

                                                          1 2 1

                                                          2 5 3

                                                          2 1 3

                                                          1 3 1

                                                          2 2 2

                                                          0 1 3

                                                          1 2 0

                                                          2 1 4

                                                          1 0 1

                                                          h

                                                          fh(00)

                                                          f(21)

                                                          Example g(21)

                                                          i = -1 j = -1

                                                          i = 1 j = 0

                                                          119892119892 119909119909119910119910 = 119895119895=minus119877119877

                                                          119877119877

                                                          119894119894=minus119877119877

                                                          119877119877

                                                          ℎ(119894119894 119895119895) 119891119891(119909119909 + 119894119894119910119910 + 119895119895)

                                                          DTU Compute

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                                                          Mathematics of 2D Correlation

                                                          1 2 11 3 11 2 1

                                                          0 2 4

                                                          1 2 2

                                                          1 6 3

                                                          1 2 1

                                                          2 5 3

                                                          2 1 3

                                                          1 3 1

                                                          2 2 2

                                                          0 1 3

                                                          1 2 0

                                                          2 1 4

                                                          1 0 1

                                                          h

                                                          f

                                                          119892119892 119909119909119910119910 = 119895119895=minus119877119877

                                                          119877119877

                                                          119894119894=minus119877119877

                                                          119877119877

                                                          ℎ(119894119894 119895119895) 119891119891(119909119909 + 119894119894119910119910 + 119895119895)

                                                          119892119892(119909119909119910119910 = 1 2 + 2 0 + 1 1 + 1 1 + 3 4 + 1 2 + 1 0 + 2 1 + 1 0

                                                          DTU Compute

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                                                          119892119892 119909119909 119910119910 = 119895119895=minus119877119877

                                                          119877119877

                                                          119894119894=minus119877119877

                                                          119877119877

                                                          ℎ(119894119894 119895119895) 119891119891(119909119909 + 119894119894119910119910 + 119895119895)

                                                          119892119892 22 =ℎ minus1minus1 sdot 119891119891 11 + ℎ 0minus1 sdot 119891119891 21 + ℎ 1minus1 sdot 119891119891 31 +ℎ minus10 sdot 119891119891 12 + ℎ 00 sdot 119891119891 22 + ℎ 10 sdot 119891119891 32 +ℎ minus11 sdot 119891119891 13 + ℎ 01 sdot 119891119891 23 + ℎ 11 sdot 119891119891 33

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                                                          2D Kernel Normalisation

                                                          1 2 11 3 11 2 1

                                                          h

                                                          Normalisation factor

                                                          1 + 2 + 1 + 1 + 3 + 1 + 1 + 2 + 1 = 13

                                                          119909119909

                                                          119910119910

                                                          ℎ(119909119909119910119910)

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                                                          CorrelationA) 50122B) 123001C) 11233D) 2550E) 90454

                                                          0 0 0 0

                                                          13

                                                          A B C D E

                                                          Chart1

                                                          0
                                                          0
                                                          0
                                                          0
                                                          13

                                                          Sheet1

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                                                          Smoothing filters

                                                          Also know as ndash Smoothing kernel Mean filter Low pass filter blurring

                                                          The simplest filter ndash Spatial low pass filterndash Removes high frequencies

                                                          Another mask ndash Gaussian filter

                                                          1 1 1

                                                          1 1 1

                                                          1 1 191

                                                          1 2 1

                                                          2 4 2

                                                          1 2 1161

                                                          Why Gaussian

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                                                          Use of smoothing

                                                          3x3 7x7 11x11 15x15

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                                                          Use of smoothing Large kernels smooth more Removes high frequency information Good at enhancing big structures

                                                          3x3 15x15

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                                                          Mean filterA) 166B) 113C) 12D) 51E) 245

                                                          0 0 0 0

                                                          A B C D E

                                                          Chart1

                                                          12
                                                          0
                                                          0
                                                          0
                                                          0

                                                          Sheet1

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                                                          Border handling

                                                          0 2 41 2 2

                                                          1 6 3

                                                          1 2 12 5 3

                                                          2 1 3

                                                          1 3 1

                                                          2 2 2

                                                          0 1 3

                                                          1 2 0

                                                          2 1 4

                                                          1 0 1

                                                          Input Output

                                                          No values at the border

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                                                          Border handling ndash extend the input

                                                          0 2 41 2 2

                                                          1 6 3

                                                          1 2 12 5 3

                                                          2 1 3

                                                          1 3 1

                                                          2 2 2

                                                          0 1 3

                                                          1 2 0

                                                          2 1 4

                                                          1 0 1

                                                          Input

                                                          0 0 0 0 000000

                                                          bull Zero padding ndash what happens

                                                          bull Zero is black ndash creates dark border around the image

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                                                          Correlation with zero paddingA) 5 8B) 12 16C) 13 3D) 15 21E) 17 12

                                                          1 2 11 3 11 2 1

                                                          0 2 41 2 2

                                                          1 6 3

                                                          1 2 12 5 3

                                                          2 1 3

                                                          1 3 1

                                                          2 2 2

                                                          0 1 3

                                                          1 2 0

                                                          2 1 4

                                                          1 0 1

                                                          0

                                                          13

                                                          0 0 0

                                                          A B C D E

                                                          Chart1

                                                          0
                                                          13
                                                          0
                                                          0
                                                          0

                                                          Sheet1

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                                                          Border handling ndash extend the input

                                                          0 2 41 2 2

                                                          1 6 3

                                                          1 2 12 5 3

                                                          2 1 3

                                                          1 3 1

                                                          2 2 2

                                                          0 1 3

                                                          1 2 0

                                                          2 1 4

                                                          1 0 1

                                                          Input

                                                          1 2 0 1 311211

                                                          bull Reflection

                                                          bull Normally better than zero padding

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                                                          Template Matching Template

                                                          ndash Skabelon paring dansk Locates objects in images

                                                          Input

                                                          Template

                                                          Output Correlation image

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                                                          Template Matching The correlation between the template and the input

                                                          image is computed for each pixel

                                                          Input

                                                          Template

                                                          Output Correlation image

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                                                          Template Matching The pixel with the highest value is found in the

                                                          output imagendash Here is the highest correlation

                                                          Input

                                                          Template

                                                          Output Correlation image

                                                          DTU Compute

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                                                          Template Matching This corresponds to the found pattern in the input

                                                          image

                                                          Input

                                                          Template

                                                          Output Correlation image

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                                                          Problematic Correlation Correlation matching has problem with light areas ndash

                                                          why

                                                          Input (f)

                                                          Template (h)

                                                          Output Correlation imageFake max

                                                          Real max

                                                          Very High119892119892 119909119909119910119910 = 119895119895=minus119877119877

                                                          119877119877

                                                          119894119894=minus119877119877

                                                          119877119877

                                                          ℎ(119894119894 119895119895) 119891119891(119909119909 + 119894119894119910119910 + 119895119895)

                                                          DTU Compute

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                                                          Normalised Cross Correlation

                                                          Input (f)

                                                          Template (h)

                                                          Output Correlation image

                                                          Real max

                                                          NCC x y =Correlation

                                                          Length of image patch sdot Length of template

                                                          DTU Compute

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                                                          Length of template Vector length

                                                          ndash Put all pixel values into a vectorndash Compute the length of this vector

                                                          Describes the intensity of the templatendash Bright template has a large lengthndash Dark template has a small length

                                                          Template (h)

                                                          Length of template = 119895119895=minus119877119877

                                                          119877119877

                                                          119894119894=minus119877119877

                                                          119877119877

                                                          ℎ(119894119894 119895119895) ℎ(119894119894 119895119895)

                                                          DTU Compute

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                                                          Length of image patch Vector length based on pixel values in image patch Describes the intensity of the image patch

                                                          Template (h)

                                                          Input (f) with patch

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                                                          Normalised Cross Correlation The length of the image patch and the length of

                                                          template normalise the NCC If the image is very bright the NCC will be ldquopulled

                                                          downrdquo

                                                          NCC x y =Correlation

                                                          Length of image patch sdot Length of template

                                                          DTU Compute

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                                                          Normalised Cross Correlation NCC will be between

                                                          ndash 0 No similarity between template and image patchndash 1 Template and image patch are identical

                                                          Input (f)

                                                          Template (h)

                                                          Output Correlation image

                                                          Real max

                                                          NCC x y =Correlation

                                                          Length of image patch sdot Length of template

                                                          DTU Compute

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                                                          Normalised Cross Correlation

                                                          A) 010B) 033C) 083D) 062E) 098

                                                          Der udfoslashres template matching med og normalized crosscorrelation (NCC) beregnes Hvad bliver NNC i den markerede pixel

                                                          1

                                                          2 2

                                                          3

                                                          2

                                                          A B C D E

                                                          Chart1

                                                          1
                                                          2
                                                          2
                                                          3
                                                          2

                                                          Sheet1

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                                                          Edges An edge is where there is a

                                                          high change in gray level values

                                                          Objects are often separated from the background by edgesGray level profile

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                                                          Edges The profile as a function f(d) What value is high when there

                                                          is an edgendash The slope of fndash The slope of the tangent at d

                                                          f(d)

                                                          119891119891prime(119889119889)

                                                          DTU Compute

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                                                          Finite Difference Definition of slope

                                                          Approximation

                                                          Simpler approximationh = 1

                                                          119891119891prime 119889119889 = limℎrarr0

                                                          119891119891 119889119889 + ℎ minus 119891119891(119889119889)ℎ

                                                          119891119891prime 119889119889 asymp119891119891 119889119889 + ℎ minus 119891119891(119889119889)

                                                          ℎ

                                                          119891119891prime 119889119889 asymp 119891119891 119889119889 + 1 minus 119891119891(119889119889)

                                                          DTU Compute

                                                          2122018Introduction to Medical Image Analysis69 DTU Compute Technical University of Denmark

                                                          Edges Discrete approximation of frsquo(d) Can be implemented as a filter

                                                          -1 0 1

                                                          f(d-2) f(d-1) f(d) f(d+1) f(d+2) f(d+3)

                                                          f(d)

                                                          119891119891prime 119889119889 asymp 119891119891 119889119889 + 1 minus 119891119891(119889119889)

                                                          DTU Compute

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                                                          Edges in 2D Changes in gray level values

                                                          ndash Image gradientndash Gradient is the 2D derivative of a 2D function f(xy)ndash Equal to the slope of the imagendash A steep slope is equal to an edge

                                                          120571120571119891119891 119909119909119910119910 = 119866(119892119892119909119909119892119892119910119910)

                                                          DTU Compute

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                                                          Edge filter kernel The Prewitt filter is a typical

                                                          edge filter Output image has high

                                                          values where there are edges

                                                          -1 0 1

                                                          -1 0 1

                                                          -1 0 1Vertical Prewitt filter

                                                          DTU Compute

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                                                          Prewitt filter

                                                          Original Prewitt Prewitt

                                                          Hot colormapSmooth 15x15

                                                          Smooth 15x15

                                                          Prewitt

                                                          DTU Compute

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                                                          Edge detection Edge filter

                                                          ndash Prewitt for example Thresholding

                                                          ndash Separate edges from non-edges

                                                          Output is binary imagendash Edges are white

                                                          DTU Compute

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                                                          Edge filtering

                                                          A) MeanB) Horizontal SobelC) Vertical PrewittD) Horisontal PrewittE) Median

                                                          Der udfoslashres en filtrering (correlation) med et filter paring billedet Der bruges ikke coefficient normalization Den filtrerede vaeligrdi i den markerede pixel bliver -119 Hvilket et 3x3 filter blev benyttet

                                                          0

                                                          8

                                                          1 10

                                                          A B C D E

                                                          Chart1

                                                          0
                                                          8
                                                          1
                                                          1
                                                          0

                                                          Sheet1

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                                                          02511 - Niveau af dagens emne forelaeligsingA) Meget letB) LetC) PassendeD) SvaeligrtE) Meget svaeligrt

                                                          23

                                                          6

                                                          10

                                                          A B C D E

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                                                          2
                                                          3
                                                          6
                                                          1
                                                          0

                                                          Sheet1

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                                                          02512 - Niveau af dagens emne forelaeligsingA) Meget letB) LetC) PassendeD) SvaeligrtE) Meget svaeligrt

                                                          0 0

                                                          1

                                                          0 0

                                                          A B C D E

                                                          Chart1

                                                          0
                                                          0
                                                          1
                                                          0
                                                          0

                                                          Sheet1

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                                                          02511 - Mit eget udbytte af dagenA) Jeg har laeligrt meget lidtB) Lidt laeligringC) PassendeD) God laeligringE) Jeg har laeligrt meget

                                                          0 0

                                                          2

                                                          6

                                                          0

                                                          A B C D E

                                                          Chart1

                                                          0
                                                          0
                                                          2
                                                          6
                                                          0

                                                          Sheet1

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                                                          02512 - Mit eget udbytte af dagenA) Jeg har laeligrt meget lidtB) Lidt laeligringC) PassendeD) God laeligringE) Jeg har laeligrt meget

                                                          2

                                                          1

                                                          3

                                                          2

                                                          0

                                                          A B C D E

                                                          Chart1

                                                          2
                                                          1
                                                          3
                                                          2
                                                          0

                                                          Sheet1

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                                                          02511 - Sidste uges oslashvelser (pixelwiseoperations)A) Meget letteB) LetteC) PassendeD) SvaeligreE) Meget svaeligre

                                                          0 0

                                                          1

                                                          4

                                                          1

                                                          A B C D E

                                                          Chart1

                                                          0
                                                          0
                                                          1
                                                          4
                                                          1

                                                          Sheet1

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                                                          02512 - Sidste uges oslashvelser (pixelwiseoperations)A) Meget letteB) LetteC) PassendeD) SvaeligreE) Meget svaeligre

                                                          3

                                                          0

                                                          3

                                                          0 0

                                                          A B C D E

                                                          Chart1

                                                          3
                                                          0
                                                          3
                                                          0
                                                          0

                                                          Sheet1

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                                                          Denne uges brug af clickersA) click click click ndash jeg bliver

                                                          sindssygB) For meget clickC) PassendeD) Jeg vil gerne have lidt mereE) Jeg kan ikrsquo faring nok

                                                          0 0

                                                          5

                                                          0

                                                          6

                                                          A B C D E

                                                          Chart1

                                                          0
                                                          0
                                                          5
                                                          0
                                                          6

                                                          Sheet1

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                                                          What can you do after today Describe the difference between point processing and neighbourhood

                                                          processing Compute a rank filtered image using the min max median and

                                                          difference rank filters Compute a mean filtered image Decide if median or average filtering should be used for noise removal Choose the appropriate image border handling based on a given input

                                                          image Implement and apply template matching Compute the normalised cross correlation and explain why it should be

                                                          used Apply given image filter kernels to images Use edge filters on images Describe finite difference approximation of image gradients Describe the concept of edge detection

                                                          DTU Compute

                                                          2122018Introduction to Medical Image Analysis84 DTU Compute Technical University of Denmark

                                                          Oslashvelsesrapport over oslashvelse 4 - 02511 Oslashvelser taeligller cirka 30 af karakteren Skal afleveres senest den 7 marts kl 2359 Kan afleveres af 1 eller 2 personer

                                                          ndash I skal skrive jeres egen oslashvelsesrapportndash Brug mindst et af jeres egne billeder

                                                          Afleveres som PDF Lad vaeligre med at kopiere opgaveteksten ind i jeres

                                                          opgave Put Matlab kode i et Appendix og henvis fra teksten Eksempel rapport over oslashvelse findes paring

                                                          hjemmesiden under eksamen

                                                          DTU Compute

                                                          2122018Introduction to Medical Image Analysis85 DTU Compute Technical University of Denmark

                                                          Exercises

                                                          • Introduction to Medical Image Analysis
                                                          • Lecture 4 ndash Neighbourhood Processing
                                                          • What can you do after today
                                                          • Point processing
                                                          • Point processing
                                                          • Neighbourhood processing
                                                          • Use of filtering
                                                          • Salt and pepper noise
                                                          • Salt and pepper noise
                                                          • What is so special about noise
                                                          • Noise ndash go away
                                                          • What is the median Value
                                                          • The median value
                                                          • Noise away ndash the median filter
                                                          • Noise removal ndash average filter
                                                          • Noise removal ndash median filter
                                                          • Image Filtering
                                                          • Median filter
                                                          • Rank filters
                                                          • Median filter
                                                          • Correlation
                                                          • Why do we need similarity
                                                          • Correlation (1D)
                                                          • Correlation (1D)
                                                          • Normalisation
                                                          • Normalisation
                                                          • Correlation on images
                                                          • Correlation on images
                                                          • Correlation on images
                                                          • Draw your filter
                                                          • Correlation on images ndash no normalisation
                                                          • Correlation on images ndash no normalisation 2
                                                          • Mathematics of 2D Correlation
                                                          • Mathematics of 2D Correlation
                                                          • Mathematics of 2D Correlation
                                                          • Slide Number 40
                                                          • 2D Kernel Normalisation
                                                          • Correlation
                                                          • Smoothing filters
                                                          • Use of smoothing
                                                          • Use of smoothing
                                                          • Mean filter
                                                          • Border handling
                                                          • Border handling ndash extend the input
                                                          • Correlation with zero padding
                                                          • Border handling ndash extend the input
                                                          • Template Matching
                                                          • Template Matching
                                                          • Template Matching
                                                          • Template Matching
                                                          • Problematic Correlation
                                                          • Normalised Cross Correlation
                                                          • Length of template
                                                          • Length of image patch
                                                          • Normalised Cross Correlation
                                                          • Normalised Cross Correlation
                                                          • Normalised Cross Correlation
                                                          • Edges
                                                          • Edges
                                                          • Finite Difference
                                                          • Edges
                                                          • Edges in 2D
                                                          • Edge filter kernel
                                                          • Prewitt filter
                                                          • Edge detection
                                                          • Edge filtering
                                                          • 02511 - Niveau af dagens emne forelaeligsing
                                                          • 02512 - Niveau af dagens emne forelaeligsing
                                                          • 02511 - Mit eget udbytte af dagen
                                                          • 02512 - Mit eget udbytte af dagen
                                                          • 02511 - Sidste uges oslashvelser (pixelwise operations)
                                                          • 02512 - Sidste uges oslashvelser (pixelwise operations)
                                                          • Denne uges brug af clickers
                                                          • What can you do after today
                                                          • Oslashvelsesrapport over oslashvelse 4 - 02511
                                                          • Exercises
                                                            A0
                                                            B0
                                                            C5
                                                            D0
                                                            E6
                                                            A
                                                            B
                                                            C
                                                            D
                                                            E
                                                            A3
                                                            B0
                                                            C3
                                                            D0
                                                            E0
                                                            A
                                                            B
                                                            C
                                                            D
                                                            E
                                                            A0
                                                            B0
                                                            C1
                                                            D4
                                                            E1
                                                            A
                                                            B
                                                            C
                                                            D
                                                            E
                                                            A2
                                                            B1
                                                            C3
                                                            D2
                                                            E0
                                                            A
                                                            B
                                                            C
                                                            D
                                                            E
                                                            A0
                                                            B0
                                                            C2
                                                            D6
                                                            E0
                                                            A
                                                            B
                                                            C
                                                            D
                                                            E
                                                            A0
                                                            B0
                                                            C1
                                                            D0
                                                            E0
                                                            A
                                                            B
                                                            C
                                                            D
                                                            E
                                                            A2
                                                            B3
                                                            C6
                                                            D1
                                                            E0
                                                            A
                                                            B
                                                            C
                                                            D
                                                            E
                                                            A0
                                                            B8
                                                            C1
                                                            D1
                                                            E0
                                                            A
                                                            B
                                                            C
                                                            D
                                                            E
                                                            A1
                                                            B2
                                                            C2
                                                            D3
                                                            E2
                                                            A
                                                            B
                                                            C
                                                            D
                                                            E
                                                            A0
                                                            B13
                                                            C0
                                                            D0
                                                            E0
                                                            A
                                                            B
                                                            C
                                                            D
                                                            E
                                                            A12
                                                            B0
                                                            C0
                                                            D0
                                                            E0
                                                            A
                                                            B
                                                            C
                                                            D
                                                            E
                                                            A0
                                                            B0
                                                            C0
                                                            D0
                                                            E13
                                                            A
                                                            B
                                                            C
                                                            D
                                                            E
                                                            A13
                                                            B0
                                                            C0
                                                            D0
                                                            E0
                                                            A
                                                            B
                                                            C
                                                            D
                                                            E
                                                            A1
                                                            B0
                                                            C14
                                                            D0
                                                            E0
                                                            A
                                                            B
                                                            C
                                                            D
                                                            E

                                                            DTU Compute

                                                            2122018Introduction to Medical Image Analysis26 DTU Compute Technical University of Denmark

                                                            Correlation (1D)

                                                            1 1 2 2 1 1 2 2 1 1

                                                            1 2 1

                                                            45

                                                            47

                                                            47

                                                            45

                                                            45

                                                            47

                                                            47

                                                            45

                                                            41

                                                            DTU Compute

                                                            2122018Introduction to Medical Image Analysis27 DTU Compute Technical University of Denmark

                                                            Normalisation

                                                            1 1 2 2 1 1 2 2 1 1

                                                            1 2 1

                                                            45

                                                            41

                                                            1 1 + 2 1 + 1 2 = 5

                                                            Normalise41

                                                            bull The sum of the kernel elements is used

                                                            bull Keep the values in the same range as the input image

                                                            Sum is 4

                                                            DTU Compute

                                                            2122018Introduction to Medical Image Analysis28 DTU Compute Technical University of Denmark

                                                            Normalisation Normalisation factor

                                                            ndash Sum of kernel coefficients

                                                            1 2 1h(x)

                                                            119909119909

                                                            ℎ 119909119909 = 1 + 2 + 1

                                                            DTU Compute

                                                            2122018Introduction to Medical Image Analysis29 DTU Compute Technical University of Denmark

                                                            Correlation on images The filter is now 2D 1 1 1

                                                            1 1 1

                                                            1 1 1

                                                            0 2 4

                                                            1 2 2

                                                            1 6 3

                                                            1 2 12 5 3

                                                            2 1 3

                                                            1 3 1

                                                            2 2 2

                                                            0 1 3

                                                            1 2 0

                                                            2 1 4

                                                            1 0 1

                                                            912

                                                            91

                                                            Input OutputKernel

                                                            Kernel coefficients

                                                            DTU Compute

                                                            2122018Introduction to Medical Image Analysis30 DTU Compute Technical University of Denmark

                                                            Correlation on images

                                                            1 1 11 1 11 1 1

                                                            0 2 4

                                                            1 2 2

                                                            1 6 3

                                                            1 2 0

                                                            2 1 4

                                                            1 0 1

                                                            912

                                                            911

                                                            91

                                                            Input Output

                                                            1 3 1

                                                            2 2 2

                                                            0 1 3

                                                            1 2 12 5 3

                                                            2 1 3

                                                            DTU Compute

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                                                            Correlation on images

                                                            Input Output

                                                            The mask is moved row by row

                                                            No values at the border

                                                            0 2 4

                                                            1 2 2

                                                            1 6 3

                                                            1 2 0

                                                            2 1 4

                                                            1 0 1

                                                            1 3 1

                                                            2 2 2

                                                            0 1 3

                                                            1 2 12 5 3

                                                            2 1 3

                                                            DTU Compute

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                                                            1 2 1

                                                            1 3 1

                                                            1 2 1

                                                            -1 -2 -1

                                                            0 0 0

                                                            1 2 1

                                                            Draw your filter

                                                            DTU Compute

                                                            2122018Introduction to Medical Image Analysis33 DTU Compute Technical University of Denmark

                                                            Correlation on images ndash no normalisationA) 4B) 7C) 16D) 23E) 25

                                                            1 2 11 3 11 2 1

                                                            0 2 41 2 2

                                                            1 6 3

                                                            1 2 12 5 3

                                                            2 1 3

                                                            1 3 1

                                                            2 2 2

                                                            0 1 3

                                                            1 2 0

                                                            2 1 4

                                                            1 0 11 0

                                                            14

                                                            0 0

                                                            A B C D E

                                                            Chart1

                                                            1
                                                            0
                                                            14
                                                            0
                                                            0

                                                            Sheet1

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                                                            Correlation on images ndash no normalisation 2A) 010B) 3 3C) 6 2D) 10 15E) 11 32

                                                            13

                                                            0 0 0 0

                                                            A B C D E

                                                            -1 -2 -10 0 01 2 1

                                                            0 2 41 2 2

                                                            1 6 3

                                                            1 2 12 5 3

                                                            2 1 3

                                                            1 3 1

                                                            2 2 2

                                                            0 1 3

                                                            1 2 0

                                                            2 1 4

                                                            1 0 1

                                                            Chart1

                                                            13
                                                            0
                                                            0
                                                            0
                                                            0

                                                            Sheet1

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                                                            Mathematics of 2D Correlation

                                                            h

                                                            f

                                                            Correlation operator

                                                            1 2 11 3 11 2 1

                                                            0 2 4

                                                            1 2 2

                                                            1 6 3

                                                            1 2 1

                                                            2 5 3

                                                            2 1 3

                                                            1 3 1

                                                            2 2 2

                                                            0 1 3

                                                            1 2 0

                                                            2 1 4

                                                            1 0 1

                                                            119892119892 119909119909119910119910 = 119891119891 119909119909119910119910 ∘ ℎ(119909119909119910119910)

                                                            DTU Compute

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                                                            Mathematics of 2D Correlation

                                                            1 2 11 3 11 2 1

                                                            0 2 4

                                                            1 2 2

                                                            1 6 3

                                                            1 2 1

                                                            2 5 3

                                                            2 1 3

                                                            1 3 1

                                                            2 2 2

                                                            0 1 3

                                                            1 2 0

                                                            2 1 4

                                                            1 0 1

                                                            h

                                                            fh(00)

                                                            f(21)

                                                            Example g(21)

                                                            i = -1 j = -1

                                                            i = 1 j = 0

                                                            119892119892 119909119909119910119910 = 119895119895=minus119877119877

                                                            119877119877

                                                            119894119894=minus119877119877

                                                            119877119877

                                                            ℎ(119894119894 119895119895) 119891119891(119909119909 + 119894119894119910119910 + 119895119895)

                                                            DTU Compute

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                                                            Mathematics of 2D Correlation

                                                            1 2 11 3 11 2 1

                                                            0 2 4

                                                            1 2 2

                                                            1 6 3

                                                            1 2 1

                                                            2 5 3

                                                            2 1 3

                                                            1 3 1

                                                            2 2 2

                                                            0 1 3

                                                            1 2 0

                                                            2 1 4

                                                            1 0 1

                                                            h

                                                            f

                                                            119892119892 119909119909119910119910 = 119895119895=minus119877119877

                                                            119877119877

                                                            119894119894=minus119877119877

                                                            119877119877

                                                            ℎ(119894119894 119895119895) 119891119891(119909119909 + 119894119894119910119910 + 119895119895)

                                                            119892119892(119909119909119910119910 = 1 2 + 2 0 + 1 1 + 1 1 + 3 4 + 1 2 + 1 0 + 2 1 + 1 0

                                                            DTU Compute

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                                                            119892119892 119909119909 119910119910 = 119895119895=minus119877119877

                                                            119877119877

                                                            119894119894=minus119877119877

                                                            119877119877

                                                            ℎ(119894119894 119895119895) 119891119891(119909119909 + 119894119894119910119910 + 119895119895)

                                                            119892119892 22 =ℎ minus1minus1 sdot 119891119891 11 + ℎ 0minus1 sdot 119891119891 21 + ℎ 1minus1 sdot 119891119891 31 +ℎ minus10 sdot 119891119891 12 + ℎ 00 sdot 119891119891 22 + ℎ 10 sdot 119891119891 32 +ℎ minus11 sdot 119891119891 13 + ℎ 01 sdot 119891119891 23 + ℎ 11 sdot 119891119891 33

                                                            DTU Compute

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                                                            2D Kernel Normalisation

                                                            1 2 11 3 11 2 1

                                                            h

                                                            Normalisation factor

                                                            1 + 2 + 1 + 1 + 3 + 1 + 1 + 2 + 1 = 13

                                                            119909119909

                                                            119910119910

                                                            ℎ(119909119909119910119910)

                                                            DTU Compute

                                                            2122018Introduction to Medical Image Analysis42 DTU Compute Technical University of Denmark

                                                            CorrelationA) 50122B) 123001C) 11233D) 2550E) 90454

                                                            0 0 0 0

                                                            13

                                                            A B C D E

                                                            Chart1

                                                            0
                                                            0
                                                            0
                                                            0
                                                            13

                                                            Sheet1

                                                            DTU Compute

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                                                            Smoothing filters

                                                            Also know as ndash Smoothing kernel Mean filter Low pass filter blurring

                                                            The simplest filter ndash Spatial low pass filterndash Removes high frequencies

                                                            Another mask ndash Gaussian filter

                                                            1 1 1

                                                            1 1 1

                                                            1 1 191

                                                            1 2 1

                                                            2 4 2

                                                            1 2 1161

                                                            Why Gaussian

                                                            DTU Compute

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                                                            Use of smoothing

                                                            3x3 7x7 11x11 15x15

                                                            DTU Compute

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                                                            Use of smoothing Large kernels smooth more Removes high frequency information Good at enhancing big structures

                                                            3x3 15x15

                                                            DTU Compute

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                                                            Mean filterA) 166B) 113C) 12D) 51E) 245

                                                            0 0 0 0

                                                            A B C D E

                                                            Chart1

                                                            12
                                                            0
                                                            0
                                                            0
                                                            0

                                                            Sheet1

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                                                            Border handling

                                                            0 2 41 2 2

                                                            1 6 3

                                                            1 2 12 5 3

                                                            2 1 3

                                                            1 3 1

                                                            2 2 2

                                                            0 1 3

                                                            1 2 0

                                                            2 1 4

                                                            1 0 1

                                                            Input Output

                                                            No values at the border

                                                            DTU Compute

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                                                            Border handling ndash extend the input

                                                            0 2 41 2 2

                                                            1 6 3

                                                            1 2 12 5 3

                                                            2 1 3

                                                            1 3 1

                                                            2 2 2

                                                            0 1 3

                                                            1 2 0

                                                            2 1 4

                                                            1 0 1

                                                            Input

                                                            0 0 0 0 000000

                                                            bull Zero padding ndash what happens

                                                            bull Zero is black ndash creates dark border around the image

                                                            DTU Compute

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                                                            Correlation with zero paddingA) 5 8B) 12 16C) 13 3D) 15 21E) 17 12

                                                            1 2 11 3 11 2 1

                                                            0 2 41 2 2

                                                            1 6 3

                                                            1 2 12 5 3

                                                            2 1 3

                                                            1 3 1

                                                            2 2 2

                                                            0 1 3

                                                            1 2 0

                                                            2 1 4

                                                            1 0 1

                                                            0

                                                            13

                                                            0 0 0

                                                            A B C D E

                                                            Chart1

                                                            0
                                                            13
                                                            0
                                                            0
                                                            0

                                                            Sheet1

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                                                            Border handling ndash extend the input

                                                            0 2 41 2 2

                                                            1 6 3

                                                            1 2 12 5 3

                                                            2 1 3

                                                            1 3 1

                                                            2 2 2

                                                            0 1 3

                                                            1 2 0

                                                            2 1 4

                                                            1 0 1

                                                            Input

                                                            1 2 0 1 311211

                                                            bull Reflection

                                                            bull Normally better than zero padding

                                                            DTU Compute

                                                            2122018Introduction to Medical Image Analysis54 DTU Compute Technical University of Denmark

                                                            Template Matching Template

                                                            ndash Skabelon paring dansk Locates objects in images

                                                            Input

                                                            Template

                                                            Output Correlation image

                                                            DTU Compute

                                                            2122018Introduction to Medical Image Analysis55 DTU Compute Technical University of Denmark

                                                            Template Matching The correlation between the template and the input

                                                            image is computed for each pixel

                                                            Input

                                                            Template

                                                            Output Correlation image

                                                            DTU Compute

                                                            2122018Introduction to Medical Image Analysis56 DTU Compute Technical University of Denmark

                                                            Template Matching The pixel with the highest value is found in the

                                                            output imagendash Here is the highest correlation

                                                            Input

                                                            Template

                                                            Output Correlation image

                                                            DTU Compute

                                                            2122018Introduction to Medical Image Analysis57 DTU Compute Technical University of Denmark

                                                            Template Matching This corresponds to the found pattern in the input

                                                            image

                                                            Input

                                                            Template

                                                            Output Correlation image

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                                                            2122018Introduction to Medical Image Analysis58 DTU Compute Technical University of Denmark

                                                            Problematic Correlation Correlation matching has problem with light areas ndash

                                                            why

                                                            Input (f)

                                                            Template (h)

                                                            Output Correlation imageFake max

                                                            Real max

                                                            Very High119892119892 119909119909119910119910 = 119895119895=minus119877119877

                                                            119877119877

                                                            119894119894=minus119877119877

                                                            119877119877

                                                            ℎ(119894119894 119895119895) 119891119891(119909119909 + 119894119894119910119910 + 119895119895)

                                                            DTU Compute

                                                            2122018Introduction to Medical Image Analysis59 DTU Compute Technical University of Denmark

                                                            Normalised Cross Correlation

                                                            Input (f)

                                                            Template (h)

                                                            Output Correlation image

                                                            Real max

                                                            NCC x y =Correlation

                                                            Length of image patch sdot Length of template

                                                            DTU Compute

                                                            2122018Introduction to Medical Image Analysis60 DTU Compute Technical University of Denmark

                                                            Length of template Vector length

                                                            ndash Put all pixel values into a vectorndash Compute the length of this vector

                                                            Describes the intensity of the templatendash Bright template has a large lengthndash Dark template has a small length

                                                            Template (h)

                                                            Length of template = 119895119895=minus119877119877

                                                            119877119877

                                                            119894119894=minus119877119877

                                                            119877119877

                                                            ℎ(119894119894 119895119895) ℎ(119894119894 119895119895)

                                                            DTU Compute

                                                            2122018Introduction to Medical Image Analysis61 DTU Compute Technical University of Denmark

                                                            Length of image patch Vector length based on pixel values in image patch Describes the intensity of the image patch

                                                            Template (h)

                                                            Input (f) with patch

                                                            DTU Compute

                                                            2122018Introduction to Medical Image Analysis62 DTU Compute Technical University of Denmark

                                                            Normalised Cross Correlation The length of the image patch and the length of

                                                            template normalise the NCC If the image is very bright the NCC will be ldquopulled

                                                            downrdquo

                                                            NCC x y =Correlation

                                                            Length of image patch sdot Length of template

                                                            DTU Compute

                                                            2122018Introduction to Medical Image Analysis63 DTU Compute Technical University of Denmark

                                                            Normalised Cross Correlation NCC will be between

                                                            ndash 0 No similarity between template and image patchndash 1 Template and image patch are identical

                                                            Input (f)

                                                            Template (h)

                                                            Output Correlation image

                                                            Real max

                                                            NCC x y =Correlation

                                                            Length of image patch sdot Length of template

                                                            DTU Compute

                                                            2122018Introduction to Medical Image Analysis64 DTU Compute Technical University of Denmark

                                                            Normalised Cross Correlation

                                                            A) 010B) 033C) 083D) 062E) 098

                                                            Der udfoslashres template matching med og normalized crosscorrelation (NCC) beregnes Hvad bliver NNC i den markerede pixel

                                                            1

                                                            2 2

                                                            3

                                                            2

                                                            A B C D E

                                                            Chart1

                                                            1
                                                            2
                                                            2
                                                            3
                                                            2

                                                            Sheet1

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                                                            Edges An edge is where there is a

                                                            high change in gray level values

                                                            Objects are often separated from the background by edgesGray level profile

                                                            DTU Compute

                                                            2122018Introduction to Medical Image Analysis67 DTU Compute Technical University of Denmark

                                                            Edges The profile as a function f(d) What value is high when there

                                                            is an edgendash The slope of fndash The slope of the tangent at d

                                                            f(d)

                                                            119891119891prime(119889119889)

                                                            DTU Compute

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                                                            Finite Difference Definition of slope

                                                            Approximation

                                                            Simpler approximationh = 1

                                                            119891119891prime 119889119889 = limℎrarr0

                                                            119891119891 119889119889 + ℎ minus 119891119891(119889119889)ℎ

                                                            119891119891prime 119889119889 asymp119891119891 119889119889 + ℎ minus 119891119891(119889119889)

                                                            ℎ

                                                            119891119891prime 119889119889 asymp 119891119891 119889119889 + 1 minus 119891119891(119889119889)

                                                            DTU Compute

                                                            2122018Introduction to Medical Image Analysis69 DTU Compute Technical University of Denmark

                                                            Edges Discrete approximation of frsquo(d) Can be implemented as a filter

                                                            -1 0 1

                                                            f(d-2) f(d-1) f(d) f(d+1) f(d+2) f(d+3)

                                                            f(d)

                                                            119891119891prime 119889119889 asymp 119891119891 119889119889 + 1 minus 119891119891(119889119889)

                                                            DTU Compute

                                                            2122018Introduction to Medical Image Analysis70 DTU Compute Technical University of Denmark

                                                            Edges in 2D Changes in gray level values

                                                            ndash Image gradientndash Gradient is the 2D derivative of a 2D function f(xy)ndash Equal to the slope of the imagendash A steep slope is equal to an edge

                                                            120571120571119891119891 119909119909119910119910 = 119866(119892119892119909119909119892119892119910119910)

                                                            DTU Compute

                                                            2122018Introduction to Medical Image Analysis71 DTU Compute Technical University of Denmark

                                                            Edge filter kernel The Prewitt filter is a typical

                                                            edge filter Output image has high

                                                            values where there are edges

                                                            -1 0 1

                                                            -1 0 1

                                                            -1 0 1Vertical Prewitt filter

                                                            DTU Compute

                                                            2122018Introduction to Medical Image Analysis72 DTU Compute Technical University of Denmark

                                                            Prewitt filter

                                                            Original Prewitt Prewitt

                                                            Hot colormapSmooth 15x15

                                                            Smooth 15x15

                                                            Prewitt

                                                            DTU Compute

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                                                            Edge detection Edge filter

                                                            ndash Prewitt for example Thresholding

                                                            ndash Separate edges from non-edges

                                                            Output is binary imagendash Edges are white

                                                            DTU Compute

                                                            2122018Introduction to Medical Image Analysis74 DTU Compute Technical University of Denmark

                                                            Edge filtering

                                                            A) MeanB) Horizontal SobelC) Vertical PrewittD) Horisontal PrewittE) Median

                                                            Der udfoslashres en filtrering (correlation) med et filter paring billedet Der bruges ikke coefficient normalization Den filtrerede vaeligrdi i den markerede pixel bliver -119 Hvilket et 3x3 filter blev benyttet

                                                            0

                                                            8

                                                            1 10

                                                            A B C D E

                                                            Chart1

                                                            0
                                                            8
                                                            1
                                                            1
                                                            0

                                                            Sheet1

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                                                            02511 - Niveau af dagens emne forelaeligsingA) Meget letB) LetC) PassendeD) SvaeligrtE) Meget svaeligrt

                                                            23

                                                            6

                                                            10

                                                            A B C D E

                                                            Chart1

                                                            2
                                                            3
                                                            6
                                                            1
                                                            0

                                                            Sheet1

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                                                            02512 - Niveau af dagens emne forelaeligsingA) Meget letB) LetC) PassendeD) SvaeligrtE) Meget svaeligrt

                                                            0 0

                                                            1

                                                            0 0

                                                            A B C D E

                                                            Chart1

                                                            0
                                                            0
                                                            1
                                                            0
                                                            0

                                                            Sheet1

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                                                            02511 - Mit eget udbytte af dagenA) Jeg har laeligrt meget lidtB) Lidt laeligringC) PassendeD) God laeligringE) Jeg har laeligrt meget

                                                            0 0

                                                            2

                                                            6

                                                            0

                                                            A B C D E

                                                            Chart1

                                                            0
                                                            0
                                                            2
                                                            6
                                                            0

                                                            Sheet1

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                                                            02512 - Mit eget udbytte af dagenA) Jeg har laeligrt meget lidtB) Lidt laeligringC) PassendeD) God laeligringE) Jeg har laeligrt meget

                                                            2

                                                            1

                                                            3

                                                            2

                                                            0

                                                            A B C D E

                                                            Chart1

                                                            2
                                                            1
                                                            3
                                                            2
                                                            0

                                                            Sheet1

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                                                            02511 - Sidste uges oslashvelser (pixelwiseoperations)A) Meget letteB) LetteC) PassendeD) SvaeligreE) Meget svaeligre

                                                            0 0

                                                            1

                                                            4

                                                            1

                                                            A B C D E

                                                            Chart1

                                                            0
                                                            0
                                                            1
                                                            4
                                                            1

                                                            Sheet1

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                                                            02512 - Sidste uges oslashvelser (pixelwiseoperations)A) Meget letteB) LetteC) PassendeD) SvaeligreE) Meget svaeligre

                                                            3

                                                            0

                                                            3

                                                            0 0

                                                            A B C D E

                                                            Chart1

                                                            3
                                                            0
                                                            3
                                                            0
                                                            0

                                                            Sheet1

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                                                            Denne uges brug af clickersA) click click click ndash jeg bliver

                                                            sindssygB) For meget clickC) PassendeD) Jeg vil gerne have lidt mereE) Jeg kan ikrsquo faring nok

                                                            0 0

                                                            5

                                                            0

                                                            6

                                                            A B C D E

                                                            Chart1

                                                            0
                                                            0
                                                            5
                                                            0
                                                            6

                                                            Sheet1

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                                                            What can you do after today Describe the difference between point processing and neighbourhood

                                                            processing Compute a rank filtered image using the min max median and

                                                            difference rank filters Compute a mean filtered image Decide if median or average filtering should be used for noise removal Choose the appropriate image border handling based on a given input

                                                            image Implement and apply template matching Compute the normalised cross correlation and explain why it should be

                                                            used Apply given image filter kernels to images Use edge filters on images Describe finite difference approximation of image gradients Describe the concept of edge detection

                                                            DTU Compute

                                                            2122018Introduction to Medical Image Analysis84 DTU Compute Technical University of Denmark

                                                            Oslashvelsesrapport over oslashvelse 4 - 02511 Oslashvelser taeligller cirka 30 af karakteren Skal afleveres senest den 7 marts kl 2359 Kan afleveres af 1 eller 2 personer

                                                            ndash I skal skrive jeres egen oslashvelsesrapportndash Brug mindst et af jeres egne billeder

                                                            Afleveres som PDF Lad vaeligre med at kopiere opgaveteksten ind i jeres

                                                            opgave Put Matlab kode i et Appendix og henvis fra teksten Eksempel rapport over oslashvelse findes paring

                                                            hjemmesiden under eksamen

                                                            DTU Compute

                                                            2122018Introduction to Medical Image Analysis85 DTU Compute Technical University of Denmark

                                                            Exercises

                                                            • Introduction to Medical Image Analysis
                                                            • Lecture 4 ndash Neighbourhood Processing
                                                            • What can you do after today
                                                            • Point processing
                                                            • Point processing
                                                            • Neighbourhood processing
                                                            • Use of filtering
                                                            • Salt and pepper noise
                                                            • Salt and pepper noise
                                                            • What is so special about noise
                                                            • Noise ndash go away
                                                            • What is the median Value
                                                            • The median value
                                                            • Noise away ndash the median filter
                                                            • Noise removal ndash average filter
                                                            • Noise removal ndash median filter
                                                            • Image Filtering
                                                            • Median filter
                                                            • Rank filters
                                                            • Median filter
                                                            • Correlation
                                                            • Why do we need similarity
                                                            • Correlation (1D)
                                                            • Correlation (1D)
                                                            • Normalisation
                                                            • Normalisation
                                                            • Correlation on images
                                                            • Correlation on images
                                                            • Correlation on images
                                                            • Draw your filter
                                                            • Correlation on images ndash no normalisation
                                                            • Correlation on images ndash no normalisation 2
                                                            • Mathematics of 2D Correlation
                                                            • Mathematics of 2D Correlation
                                                            • Mathematics of 2D Correlation
                                                            • Slide Number 40
                                                            • 2D Kernel Normalisation
                                                            • Correlation
                                                            • Smoothing filters
                                                            • Use of smoothing
                                                            • Use of smoothing
                                                            • Mean filter
                                                            • Border handling
                                                            • Border handling ndash extend the input
                                                            • Correlation with zero padding
                                                            • Border handling ndash extend the input
                                                            • Template Matching
                                                            • Template Matching
                                                            • Template Matching
                                                            • Template Matching
                                                            • Problematic Correlation
                                                            • Normalised Cross Correlation
                                                            • Length of template
                                                            • Length of image patch
                                                            • Normalised Cross Correlation
                                                            • Normalised Cross Correlation
                                                            • Normalised Cross Correlation
                                                            • Edges
                                                            • Edges
                                                            • Finite Difference
                                                            • Edges
                                                            • Edges in 2D
                                                            • Edge filter kernel
                                                            • Prewitt filter
                                                            • Edge detection
                                                            • Edge filtering
                                                            • 02511 - Niveau af dagens emne forelaeligsing
                                                            • 02512 - Niveau af dagens emne forelaeligsing
                                                            • 02511 - Mit eget udbytte af dagen
                                                            • 02512 - Mit eget udbytte af dagen
                                                            • 02511 - Sidste uges oslashvelser (pixelwise operations)
                                                            • 02512 - Sidste uges oslashvelser (pixelwise operations)
                                                            • Denne uges brug af clickers
                                                            • What can you do after today
                                                            • Oslashvelsesrapport over oslashvelse 4 - 02511
                                                            • Exercises
                                                              A0
                                                              B0
                                                              C5
                                                              D0
                                                              E6
                                                              A
                                                              B
                                                              C
                                                              D
                                                              E
                                                              A3
                                                              B0
                                                              C3
                                                              D0
                                                              E0
                                                              A
                                                              B
                                                              C
                                                              D
                                                              E
                                                              A0
                                                              B0
                                                              C1
                                                              D4
                                                              E1
                                                              A
                                                              B
                                                              C
                                                              D
                                                              E
                                                              A2
                                                              B1
                                                              C3
                                                              D2
                                                              E0
                                                              A
                                                              B
                                                              C
                                                              D
                                                              E
                                                              A0
                                                              B0
                                                              C2
                                                              D6
                                                              E0
                                                              A
                                                              B
                                                              C
                                                              D
                                                              E
                                                              A0
                                                              B0
                                                              C1
                                                              D0
                                                              E0
                                                              A
                                                              B
                                                              C
                                                              D
                                                              E
                                                              A2
                                                              B3
                                                              C6
                                                              D1
                                                              E0
                                                              A
                                                              B
                                                              C
                                                              D
                                                              E
                                                              A0
                                                              B8
                                                              C1
                                                              D1
                                                              E0
                                                              A
                                                              B
                                                              C
                                                              D
                                                              E
                                                              A1
                                                              B2
                                                              C2
                                                              D3
                                                              E2
                                                              A
                                                              B
                                                              C
                                                              D
                                                              E
                                                              A0
                                                              B13
                                                              C0
                                                              D0
                                                              E0
                                                              A
                                                              B
                                                              C
                                                              D
                                                              E
                                                              A12
                                                              B0
                                                              C0
                                                              D0
                                                              E0
                                                              A
                                                              B
                                                              C
                                                              D
                                                              E
                                                              A0
                                                              B0
                                                              C0
                                                              D0
                                                              E13
                                                              A
                                                              B
                                                              C
                                                              D
                                                              E
                                                              A13
                                                              B0
                                                              C0
                                                              D0
                                                              E0
                                                              A
                                                              B
                                                              C
                                                              D
                                                              E
                                                              A1
                                                              B0
                                                              C14
                                                              D0
                                                              E0
                                                              A
                                                              B
                                                              C
                                                              D
                                                              E

                                                              DTU Compute

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                                                              Normalisation

                                                              1 1 2 2 1 1 2 2 1 1

                                                              1 2 1

                                                              45

                                                              41

                                                              1 1 + 2 1 + 1 2 = 5

                                                              Normalise41

                                                              bull The sum of the kernel elements is used

                                                              bull Keep the values in the same range as the input image

                                                              Sum is 4

                                                              DTU Compute

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                                                              Normalisation Normalisation factor

                                                              ndash Sum of kernel coefficients

                                                              1 2 1h(x)

                                                              119909119909

                                                              ℎ 119909119909 = 1 + 2 + 1

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                                                              Correlation on images The filter is now 2D 1 1 1

                                                              1 1 1

                                                              1 1 1

                                                              0 2 4

                                                              1 2 2

                                                              1 6 3

                                                              1 2 12 5 3

                                                              2 1 3

                                                              1 3 1

                                                              2 2 2

                                                              0 1 3

                                                              1 2 0

                                                              2 1 4

                                                              1 0 1

                                                              912

                                                              91

                                                              Input OutputKernel

                                                              Kernel coefficients

                                                              DTU Compute

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                                                              Correlation on images

                                                              1 1 11 1 11 1 1

                                                              0 2 4

                                                              1 2 2

                                                              1 6 3

                                                              1 2 0

                                                              2 1 4

                                                              1 0 1

                                                              912

                                                              911

                                                              91

                                                              Input Output

                                                              1 3 1

                                                              2 2 2

                                                              0 1 3

                                                              1 2 12 5 3

                                                              2 1 3

                                                              DTU Compute

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                                                              Correlation on images

                                                              Input Output

                                                              The mask is moved row by row

                                                              No values at the border

                                                              0 2 4

                                                              1 2 2

                                                              1 6 3

                                                              1 2 0

                                                              2 1 4

                                                              1 0 1

                                                              1 3 1

                                                              2 2 2

                                                              0 1 3

                                                              1 2 12 5 3

                                                              2 1 3

                                                              DTU Compute

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                                                              1 2 1

                                                              1 3 1

                                                              1 2 1

                                                              -1 -2 -1

                                                              0 0 0

                                                              1 2 1

                                                              Draw your filter

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                                                              Correlation on images ndash no normalisationA) 4B) 7C) 16D) 23E) 25

                                                              1 2 11 3 11 2 1

                                                              0 2 41 2 2

                                                              1 6 3

                                                              1 2 12 5 3

                                                              2 1 3

                                                              1 3 1

                                                              2 2 2

                                                              0 1 3

                                                              1 2 0

                                                              2 1 4

                                                              1 0 11 0

                                                              14

                                                              0 0

                                                              A B C D E

                                                              Chart1

                                                              1
                                                              0
                                                              14
                                                              0
                                                              0

                                                              Sheet1

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                                                              Correlation on images ndash no normalisation 2A) 010B) 3 3C) 6 2D) 10 15E) 11 32

                                                              13

                                                              0 0 0 0

                                                              A B C D E

                                                              -1 -2 -10 0 01 2 1

                                                              0 2 41 2 2

                                                              1 6 3

                                                              1 2 12 5 3

                                                              2 1 3

                                                              1 3 1

                                                              2 2 2

                                                              0 1 3

                                                              1 2 0

                                                              2 1 4

                                                              1 0 1

                                                              Chart1

                                                              13
                                                              0
                                                              0
                                                              0
                                                              0

                                                              Sheet1

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                                                              Mathematics of 2D Correlation

                                                              h

                                                              f

                                                              Correlation operator

                                                              1 2 11 3 11 2 1

                                                              0 2 4

                                                              1 2 2

                                                              1 6 3

                                                              1 2 1

                                                              2 5 3

                                                              2 1 3

                                                              1 3 1

                                                              2 2 2

                                                              0 1 3

                                                              1 2 0

                                                              2 1 4

                                                              1 0 1

                                                              119892119892 119909119909119910119910 = 119891119891 119909119909119910119910 ∘ ℎ(119909119909119910119910)

                                                              DTU Compute

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                                                              Mathematics of 2D Correlation

                                                              1 2 11 3 11 2 1

                                                              0 2 4

                                                              1 2 2

                                                              1 6 3

                                                              1 2 1

                                                              2 5 3

                                                              2 1 3

                                                              1 3 1

                                                              2 2 2

                                                              0 1 3

                                                              1 2 0

                                                              2 1 4

                                                              1 0 1

                                                              h

                                                              fh(00)

                                                              f(21)

                                                              Example g(21)

                                                              i = -1 j = -1

                                                              i = 1 j = 0

                                                              119892119892 119909119909119910119910 = 119895119895=minus119877119877

                                                              119877119877

                                                              119894119894=minus119877119877

                                                              119877119877

                                                              ℎ(119894119894 119895119895) 119891119891(119909119909 + 119894119894119910119910 + 119895119895)

                                                              DTU Compute

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                                                              Mathematics of 2D Correlation

                                                              1 2 11 3 11 2 1

                                                              0 2 4

                                                              1 2 2

                                                              1 6 3

                                                              1 2 1

                                                              2 5 3

                                                              2 1 3

                                                              1 3 1

                                                              2 2 2

                                                              0 1 3

                                                              1 2 0

                                                              2 1 4

                                                              1 0 1

                                                              h

                                                              f

                                                              119892119892 119909119909119910119910 = 119895119895=minus119877119877

                                                              119877119877

                                                              119894119894=minus119877119877

                                                              119877119877

                                                              ℎ(119894119894 119895119895) 119891119891(119909119909 + 119894119894119910119910 + 119895119895)

                                                              119892119892(119909119909119910119910 = 1 2 + 2 0 + 1 1 + 1 1 + 3 4 + 1 2 + 1 0 + 2 1 + 1 0

                                                              DTU Compute

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                                                              119892119892 119909119909 119910119910 = 119895119895=minus119877119877

                                                              119877119877

                                                              119894119894=minus119877119877

                                                              119877119877

                                                              ℎ(119894119894 119895119895) 119891119891(119909119909 + 119894119894119910119910 + 119895119895)

                                                              119892119892 22 =ℎ minus1minus1 sdot 119891119891 11 + ℎ 0minus1 sdot 119891119891 21 + ℎ 1minus1 sdot 119891119891 31 +ℎ minus10 sdot 119891119891 12 + ℎ 00 sdot 119891119891 22 + ℎ 10 sdot 119891119891 32 +ℎ minus11 sdot 119891119891 13 + ℎ 01 sdot 119891119891 23 + ℎ 11 sdot 119891119891 33

                                                              DTU Compute

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                                                              2D Kernel Normalisation

                                                              1 2 11 3 11 2 1

                                                              h

                                                              Normalisation factor

                                                              1 + 2 + 1 + 1 + 3 + 1 + 1 + 2 + 1 = 13

                                                              119909119909

                                                              119910119910

                                                              ℎ(119909119909119910119910)

                                                              DTU Compute

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                                                              CorrelationA) 50122B) 123001C) 11233D) 2550E) 90454

                                                              0 0 0 0

                                                              13

                                                              A B C D E

                                                              Chart1

                                                              0
                                                              0
                                                              0
                                                              0
                                                              13

                                                              Sheet1

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                                                              Smoothing filters

                                                              Also know as ndash Smoothing kernel Mean filter Low pass filter blurring

                                                              The simplest filter ndash Spatial low pass filterndash Removes high frequencies

                                                              Another mask ndash Gaussian filter

                                                              1 1 1

                                                              1 1 1

                                                              1 1 191

                                                              1 2 1

                                                              2 4 2

                                                              1 2 1161

                                                              Why Gaussian

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                                                              Use of smoothing

                                                              3x3 7x7 11x11 15x15

                                                              DTU Compute

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                                                              Use of smoothing Large kernels smooth more Removes high frequency information Good at enhancing big structures

                                                              3x3 15x15

                                                              DTU Compute

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                                                              Mean filterA) 166B) 113C) 12D) 51E) 245

                                                              0 0 0 0

                                                              A B C D E

                                                              Chart1

                                                              12
                                                              0
                                                              0
                                                              0
                                                              0

                                                              Sheet1

                                                              DTU Compute

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                                                              Border handling

                                                              0 2 41 2 2

                                                              1 6 3

                                                              1 2 12 5 3

                                                              2 1 3

                                                              1 3 1

                                                              2 2 2

                                                              0 1 3

                                                              1 2 0

                                                              2 1 4

                                                              1 0 1

                                                              Input Output

                                                              No values at the border

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                                                              Border handling ndash extend the input

                                                              0 2 41 2 2

                                                              1 6 3

                                                              1 2 12 5 3

                                                              2 1 3

                                                              1 3 1

                                                              2 2 2

                                                              0 1 3

                                                              1 2 0

                                                              2 1 4

                                                              1 0 1

                                                              Input

                                                              0 0 0 0 000000

                                                              bull Zero padding ndash what happens

                                                              bull Zero is black ndash creates dark border around the image

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                                                              Correlation with zero paddingA) 5 8B) 12 16C) 13 3D) 15 21E) 17 12

                                                              1 2 11 3 11 2 1

                                                              0 2 41 2 2

                                                              1 6 3

                                                              1 2 12 5 3

                                                              2 1 3

                                                              1 3 1

                                                              2 2 2

                                                              0 1 3

                                                              1 2 0

                                                              2 1 4

                                                              1 0 1

                                                              0

                                                              13

                                                              0 0 0

                                                              A B C D E

                                                              Chart1

                                                              0
                                                              13
                                                              0
                                                              0
                                                              0

                                                              Sheet1

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                                                              Border handling ndash extend the input

                                                              0 2 41 2 2

                                                              1 6 3

                                                              1 2 12 5 3

                                                              2 1 3

                                                              1 3 1

                                                              2 2 2

                                                              0 1 3

                                                              1 2 0

                                                              2 1 4

                                                              1 0 1

                                                              Input

                                                              1 2 0 1 311211

                                                              bull Reflection

                                                              bull Normally better than zero padding

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                                                              Template Matching Template

                                                              ndash Skabelon paring dansk Locates objects in images

                                                              Input

                                                              Template

                                                              Output Correlation image

                                                              DTU Compute

                                                              2122018Introduction to Medical Image Analysis55 DTU Compute Technical University of Denmark

                                                              Template Matching The correlation between the template and the input

                                                              image is computed for each pixel

                                                              Input

                                                              Template

                                                              Output Correlation image

                                                              DTU Compute

                                                              2122018Introduction to Medical Image Analysis56 DTU Compute Technical University of Denmark

                                                              Template Matching The pixel with the highest value is found in the

                                                              output imagendash Here is the highest correlation

                                                              Input

                                                              Template

                                                              Output Correlation image

                                                              DTU Compute

                                                              2122018Introduction to Medical Image Analysis57 DTU Compute Technical University of Denmark

                                                              Template Matching This corresponds to the found pattern in the input

                                                              image

                                                              Input

                                                              Template

                                                              Output Correlation image

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                                                              2122018Introduction to Medical Image Analysis58 DTU Compute Technical University of Denmark

                                                              Problematic Correlation Correlation matching has problem with light areas ndash

                                                              why

                                                              Input (f)

                                                              Template (h)

                                                              Output Correlation imageFake max

                                                              Real max

                                                              Very High119892119892 119909119909119910119910 = 119895119895=minus119877119877

                                                              119877119877

                                                              119894119894=minus119877119877

                                                              119877119877

                                                              ℎ(119894119894 119895119895) 119891119891(119909119909 + 119894119894119910119910 + 119895119895)

                                                              DTU Compute

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                                                              Normalised Cross Correlation

                                                              Input (f)

                                                              Template (h)

                                                              Output Correlation image

                                                              Real max

                                                              NCC x y =Correlation

                                                              Length of image patch sdot Length of template

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                                                              Length of template Vector length

                                                              ndash Put all pixel values into a vectorndash Compute the length of this vector

                                                              Describes the intensity of the templatendash Bright template has a large lengthndash Dark template has a small length

                                                              Template (h)

                                                              Length of template = 119895119895=minus119877119877

                                                              119877119877

                                                              119894119894=minus119877119877

                                                              119877119877

                                                              ℎ(119894119894 119895119895) ℎ(119894119894 119895119895)

                                                              DTU Compute

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                                                              Length of image patch Vector length based on pixel values in image patch Describes the intensity of the image patch

                                                              Template (h)

                                                              Input (f) with patch

                                                              DTU Compute

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                                                              Normalised Cross Correlation The length of the image patch and the length of

                                                              template normalise the NCC If the image is very bright the NCC will be ldquopulled

                                                              downrdquo

                                                              NCC x y =Correlation

                                                              Length of image patch sdot Length of template

                                                              DTU Compute

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                                                              Normalised Cross Correlation NCC will be between

                                                              ndash 0 No similarity between template and image patchndash 1 Template and image patch are identical

                                                              Input (f)

                                                              Template (h)

                                                              Output Correlation image

                                                              Real max

                                                              NCC x y =Correlation

                                                              Length of image patch sdot Length of template

                                                              DTU Compute

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                                                              Normalised Cross Correlation

                                                              A) 010B) 033C) 083D) 062E) 098

                                                              Der udfoslashres template matching med og normalized crosscorrelation (NCC) beregnes Hvad bliver NNC i den markerede pixel

                                                              1

                                                              2 2

                                                              3

                                                              2

                                                              A B C D E

                                                              Chart1

                                                              1
                                                              2
                                                              2
                                                              3
                                                              2

                                                              Sheet1

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                                                              Edges An edge is where there is a

                                                              high change in gray level values

                                                              Objects are often separated from the background by edgesGray level profile

                                                              DTU Compute

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                                                              Edges The profile as a function f(d) What value is high when there

                                                              is an edgendash The slope of fndash The slope of the tangent at d

                                                              f(d)

                                                              119891119891prime(119889119889)

                                                              DTU Compute

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                                                              Finite Difference Definition of slope

                                                              Approximation

                                                              Simpler approximationh = 1

                                                              119891119891prime 119889119889 = limℎrarr0

                                                              119891119891 119889119889 + ℎ minus 119891119891(119889119889)ℎ

                                                              119891119891prime 119889119889 asymp119891119891 119889119889 + ℎ minus 119891119891(119889119889)

                                                              ℎ

                                                              119891119891prime 119889119889 asymp 119891119891 119889119889 + 1 minus 119891119891(119889119889)

                                                              DTU Compute

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                                                              Edges Discrete approximation of frsquo(d) Can be implemented as a filter

                                                              -1 0 1

                                                              f(d-2) f(d-1) f(d) f(d+1) f(d+2) f(d+3)

                                                              f(d)

                                                              119891119891prime 119889119889 asymp 119891119891 119889119889 + 1 minus 119891119891(119889119889)

                                                              DTU Compute

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                                                              Edges in 2D Changes in gray level values

                                                              ndash Image gradientndash Gradient is the 2D derivative of a 2D function f(xy)ndash Equal to the slope of the imagendash A steep slope is equal to an edge

                                                              120571120571119891119891 119909119909119910119910 = 119866(119892119892119909119909119892119892119910119910)

                                                              DTU Compute

                                                              2122018Introduction to Medical Image Analysis71 DTU Compute Technical University of Denmark

                                                              Edge filter kernel The Prewitt filter is a typical

                                                              edge filter Output image has high

                                                              values where there are edges

                                                              -1 0 1

                                                              -1 0 1

                                                              -1 0 1Vertical Prewitt filter

                                                              DTU Compute

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                                                              Prewitt filter

                                                              Original Prewitt Prewitt

                                                              Hot colormapSmooth 15x15

                                                              Smooth 15x15

                                                              Prewitt

                                                              DTU Compute

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                                                              Edge detection Edge filter

                                                              ndash Prewitt for example Thresholding

                                                              ndash Separate edges from non-edges

                                                              Output is binary imagendash Edges are white

                                                              DTU Compute

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                                                              Edge filtering

                                                              A) MeanB) Horizontal SobelC) Vertical PrewittD) Horisontal PrewittE) Median

                                                              Der udfoslashres en filtrering (correlation) med et filter paring billedet Der bruges ikke coefficient normalization Den filtrerede vaeligrdi i den markerede pixel bliver -119 Hvilket et 3x3 filter blev benyttet

                                                              0

                                                              8

                                                              1 10

                                                              A B C D E

                                                              Chart1

                                                              0
                                                              8
                                                              1
                                                              1
                                                              0

                                                              Sheet1

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                                                              2122018Introduction to Medical Image Analysis76 DTU Compute Technical University of Denmark

                                                              02511 - Niveau af dagens emne forelaeligsingA) Meget letB) LetC) PassendeD) SvaeligrtE) Meget svaeligrt

                                                              23

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                                                              02512 - Niveau af dagens emne forelaeligsingA) Meget letB) LetC) PassendeD) SvaeligrtE) Meget svaeligrt

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                                                              02511 - Mit eget udbytte af dagenA) Jeg har laeligrt meget lidtB) Lidt laeligringC) PassendeD) God laeligringE) Jeg har laeligrt meget

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                                                              02512 - Mit eget udbytte af dagenA) Jeg har laeligrt meget lidtB) Lidt laeligringC) PassendeD) God laeligringE) Jeg har laeligrt meget

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                                                              02511 - Sidste uges oslashvelser (pixelwiseoperations)A) Meget letteB) LetteC) PassendeD) SvaeligreE) Meget svaeligre

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                                                              02512 - Sidste uges oslashvelser (pixelwiseoperations)A) Meget letteB) LetteC) PassendeD) SvaeligreE) Meget svaeligre

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                                                              Denne uges brug af clickersA) click click click ndash jeg bliver

                                                              sindssygB) For meget clickC) PassendeD) Jeg vil gerne have lidt mereE) Jeg kan ikrsquo faring nok

                                                              0 0

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                                                              What can you do after today Describe the difference between point processing and neighbourhood

                                                              processing Compute a rank filtered image using the min max median and

                                                              difference rank filters Compute a mean filtered image Decide if median or average filtering should be used for noise removal Choose the appropriate image border handling based on a given input

                                                              image Implement and apply template matching Compute the normalised cross correlation and explain why it should be

                                                              used Apply given image filter kernels to images Use edge filters on images Describe finite difference approximation of image gradients Describe the concept of edge detection

                                                              DTU Compute

                                                              2122018Introduction to Medical Image Analysis84 DTU Compute Technical University of Denmark

                                                              Oslashvelsesrapport over oslashvelse 4 - 02511 Oslashvelser taeligller cirka 30 af karakteren Skal afleveres senest den 7 marts kl 2359 Kan afleveres af 1 eller 2 personer

                                                              ndash I skal skrive jeres egen oslashvelsesrapportndash Brug mindst et af jeres egne billeder

                                                              Afleveres som PDF Lad vaeligre med at kopiere opgaveteksten ind i jeres

                                                              opgave Put Matlab kode i et Appendix og henvis fra teksten Eksempel rapport over oslashvelse findes paring

                                                              hjemmesiden under eksamen

                                                              DTU Compute

                                                              2122018Introduction to Medical Image Analysis85 DTU Compute Technical University of Denmark

                                                              Exercises

                                                              • Introduction to Medical Image Analysis
                                                              • Lecture 4 ndash Neighbourhood Processing
                                                              • What can you do after today
                                                              • Point processing
                                                              • Point processing
                                                              • Neighbourhood processing
                                                              • Use of filtering
                                                              • Salt and pepper noise
                                                              • Salt and pepper noise
                                                              • What is so special about noise
                                                              • Noise ndash go away
                                                              • What is the median Value
                                                              • The median value
                                                              • Noise away ndash the median filter
                                                              • Noise removal ndash average filter
                                                              • Noise removal ndash median filter
                                                              • Image Filtering
                                                              • Median filter
                                                              • Rank filters
                                                              • Median filter
                                                              • Correlation
                                                              • Why do we need similarity
                                                              • Correlation (1D)
                                                              • Correlation (1D)
                                                              • Normalisation
                                                              • Normalisation
                                                              • Correlation on images
                                                              • Correlation on images
                                                              • Correlation on images
                                                              • Draw your filter
                                                              • Correlation on images ndash no normalisation
                                                              • Correlation on images ndash no normalisation 2
                                                              • Mathematics of 2D Correlation
                                                              • Mathematics of 2D Correlation
                                                              • Mathematics of 2D Correlation
                                                              • Slide Number 40
                                                              • 2D Kernel Normalisation
                                                              • Correlation
                                                              • Smoothing filters
                                                              • Use of smoothing
                                                              • Use of smoothing
                                                              • Mean filter
                                                              • Border handling
                                                              • Border handling ndash extend the input
                                                              • Correlation with zero padding
                                                              • Border handling ndash extend the input
                                                              • Template Matching
                                                              • Template Matching
                                                              • Template Matching
                                                              • Template Matching
                                                              • Problematic Correlation
                                                              • Normalised Cross Correlation
                                                              • Length of template
                                                              • Length of image patch
                                                              • Normalised Cross Correlation
                                                              • Normalised Cross Correlation
                                                              • Normalised Cross Correlation
                                                              • Edges
                                                              • Edges
                                                              • Finite Difference
                                                              • Edges
                                                              • Edges in 2D
                                                              • Edge filter kernel
                                                              • Prewitt filter
                                                              • Edge detection
                                                              • Edge filtering
                                                              • 02511 - Niveau af dagens emne forelaeligsing
                                                              • 02512 - Niveau af dagens emne forelaeligsing
                                                              • 02511 - Mit eget udbytte af dagen
                                                              • 02512 - Mit eget udbytte af dagen
                                                              • 02511 - Sidste uges oslashvelser (pixelwise operations)
                                                              • 02512 - Sidste uges oslashvelser (pixelwise operations)
                                                              • Denne uges brug af clickers
                                                              • What can you do after today
                                                              • Oslashvelsesrapport over oslashvelse 4 - 02511
                                                              • Exercises
                                                                A0
                                                                B0
                                                                C5
                                                                D0
                                                                E6
                                                                A
                                                                B
                                                                C
                                                                D
                                                                E
                                                                A3
                                                                B0
                                                                C3
                                                                D0
                                                                E0
                                                                A
                                                                B
                                                                C
                                                                D
                                                                E
                                                                A0
                                                                B0
                                                                C1
                                                                D4
                                                                E1
                                                                A
                                                                B
                                                                C
                                                                D
                                                                E
                                                                A2
                                                                B1
                                                                C3
                                                                D2
                                                                E0
                                                                A
                                                                B
                                                                C
                                                                D
                                                                E
                                                                A0
                                                                B0
                                                                C2
                                                                D6
                                                                E0
                                                                A
                                                                B
                                                                C
                                                                D
                                                                E
                                                                A0
                                                                B0
                                                                C1
                                                                D0
                                                                E0
                                                                A
                                                                B
                                                                C
                                                                D
                                                                E
                                                                A2
                                                                B3
                                                                C6
                                                                D1
                                                                E0
                                                                A
                                                                B
                                                                C
                                                                D
                                                                E
                                                                A0
                                                                B8
                                                                C1
                                                                D1
                                                                E0
                                                                A
                                                                B
                                                                C
                                                                D
                                                                E
                                                                A1
                                                                B2
                                                                C2
                                                                D3
                                                                E2
                                                                A
                                                                B
                                                                C
                                                                D
                                                                E
                                                                A0
                                                                B13
                                                                C0
                                                                D0
                                                                E0
                                                                A
                                                                B
                                                                C
                                                                D
                                                                E
                                                                A12
                                                                B0
                                                                C0
                                                                D0
                                                                E0
                                                                A
                                                                B
                                                                C
                                                                D
                                                                E
                                                                A0
                                                                B0
                                                                C0
                                                                D0
                                                                E13
                                                                A
                                                                B
                                                                C
                                                                D
                                                                E
                                                                A13
                                                                B0
                                                                C0
                                                                D0
                                                                E0
                                                                A
                                                                B
                                                                C
                                                                D
                                                                E
                                                                A1
                                                                B0
                                                                C14
                                                                D0
                                                                E0
                                                                A
                                                                B
                                                                C
                                                                D
                                                                E

                                                                DTU Compute

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                                                                Normalisation Normalisation factor

                                                                ndash Sum of kernel coefficients

                                                                1 2 1h(x)

                                                                119909119909

                                                                ℎ 119909119909 = 1 + 2 + 1

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                                                                Correlation on images The filter is now 2D 1 1 1

                                                                1 1 1

                                                                1 1 1

                                                                0 2 4

                                                                1 2 2

                                                                1 6 3

                                                                1 2 12 5 3

                                                                2 1 3

                                                                1 3 1

                                                                2 2 2

                                                                0 1 3

                                                                1 2 0

                                                                2 1 4

                                                                1 0 1

                                                                912

                                                                91

                                                                Input OutputKernel

                                                                Kernel coefficients

                                                                DTU Compute

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                                                                Correlation on images

                                                                1 1 11 1 11 1 1

                                                                0 2 4

                                                                1 2 2

                                                                1 6 3

                                                                1 2 0

                                                                2 1 4

                                                                1 0 1

                                                                912

                                                                911

                                                                91

                                                                Input Output

                                                                1 3 1

                                                                2 2 2

                                                                0 1 3

                                                                1 2 12 5 3

                                                                2 1 3

                                                                DTU Compute

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                                                                Correlation on images

                                                                Input Output

                                                                The mask is moved row by row

                                                                No values at the border

                                                                0 2 4

                                                                1 2 2

                                                                1 6 3

                                                                1 2 0

                                                                2 1 4

                                                                1 0 1

                                                                1 3 1

                                                                2 2 2

                                                                0 1 3

                                                                1 2 12 5 3

                                                                2 1 3

                                                                DTU Compute

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                                                                1 2 1

                                                                1 3 1

                                                                1 2 1

                                                                -1 -2 -1

                                                                0 0 0

                                                                1 2 1

                                                                Draw your filter

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                                                                Correlation on images ndash no normalisationA) 4B) 7C) 16D) 23E) 25

                                                                1 2 11 3 11 2 1

                                                                0 2 41 2 2

                                                                1 6 3

                                                                1 2 12 5 3

                                                                2 1 3

                                                                1 3 1

                                                                2 2 2

                                                                0 1 3

                                                                1 2 0

                                                                2 1 4

                                                                1 0 11 0

                                                                14

                                                                0 0

                                                                A B C D E

                                                                Chart1

                                                                1
                                                                0
                                                                14
                                                                0
                                                                0

                                                                Sheet1

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                                                                Correlation on images ndash no normalisation 2A) 010B) 3 3C) 6 2D) 10 15E) 11 32

                                                                13

                                                                0 0 0 0

                                                                A B C D E

                                                                -1 -2 -10 0 01 2 1

                                                                0 2 41 2 2

                                                                1 6 3

                                                                1 2 12 5 3

                                                                2 1 3

                                                                1 3 1

                                                                2 2 2

                                                                0 1 3

                                                                1 2 0

                                                                2 1 4

                                                                1 0 1

                                                                Chart1

                                                                13
                                                                0
                                                                0
                                                                0
                                                                0

                                                                Sheet1

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                                                                Mathematics of 2D Correlation

                                                                h

                                                                f

                                                                Correlation operator

                                                                1 2 11 3 11 2 1

                                                                0 2 4

                                                                1 2 2

                                                                1 6 3

                                                                1 2 1

                                                                2 5 3

                                                                2 1 3

                                                                1 3 1

                                                                2 2 2

                                                                0 1 3

                                                                1 2 0

                                                                2 1 4

                                                                1 0 1

                                                                119892119892 119909119909119910119910 = 119891119891 119909119909119910119910 ∘ ℎ(119909119909119910119910)

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                                                                Mathematics of 2D Correlation

                                                                1 2 11 3 11 2 1

                                                                0 2 4

                                                                1 2 2

                                                                1 6 3

                                                                1 2 1

                                                                2 5 3

                                                                2 1 3

                                                                1 3 1

                                                                2 2 2

                                                                0 1 3

                                                                1 2 0

                                                                2 1 4

                                                                1 0 1

                                                                h

                                                                fh(00)

                                                                f(21)

                                                                Example g(21)

                                                                i = -1 j = -1

                                                                i = 1 j = 0

                                                                119892119892 119909119909119910119910 = 119895119895=minus119877119877

                                                                119877119877

                                                                119894119894=minus119877119877

                                                                119877119877

                                                                ℎ(119894119894 119895119895) 119891119891(119909119909 + 119894119894119910119910 + 119895119895)

                                                                DTU Compute

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                                                                Mathematics of 2D Correlation

                                                                1 2 11 3 11 2 1

                                                                0 2 4

                                                                1 2 2

                                                                1 6 3

                                                                1 2 1

                                                                2 5 3

                                                                2 1 3

                                                                1 3 1

                                                                2 2 2

                                                                0 1 3

                                                                1 2 0

                                                                2 1 4

                                                                1 0 1

                                                                h

                                                                f

                                                                119892119892 119909119909119910119910 = 119895119895=minus119877119877

                                                                119877119877

                                                                119894119894=minus119877119877

                                                                119877119877

                                                                ℎ(119894119894 119895119895) 119891119891(119909119909 + 119894119894119910119910 + 119895119895)

                                                                119892119892(119909119909119910119910 = 1 2 + 2 0 + 1 1 + 1 1 + 3 4 + 1 2 + 1 0 + 2 1 + 1 0

                                                                DTU Compute

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                                                                119892119892 119909119909 119910119910 = 119895119895=minus119877119877

                                                                119877119877

                                                                119894119894=minus119877119877

                                                                119877119877

                                                                ℎ(119894119894 119895119895) 119891119891(119909119909 + 119894119894119910119910 + 119895119895)

                                                                119892119892 22 =ℎ minus1minus1 sdot 119891119891 11 + ℎ 0minus1 sdot 119891119891 21 + ℎ 1minus1 sdot 119891119891 31 +ℎ minus10 sdot 119891119891 12 + ℎ 00 sdot 119891119891 22 + ℎ 10 sdot 119891119891 32 +ℎ minus11 sdot 119891119891 13 + ℎ 01 sdot 119891119891 23 + ℎ 11 sdot 119891119891 33

                                                                DTU Compute

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                                                                2D Kernel Normalisation

                                                                1 2 11 3 11 2 1

                                                                h

                                                                Normalisation factor

                                                                1 + 2 + 1 + 1 + 3 + 1 + 1 + 2 + 1 = 13

                                                                119909119909

                                                                119910119910

                                                                ℎ(119909119909119910119910)

                                                                DTU Compute

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                                                                CorrelationA) 50122B) 123001C) 11233D) 2550E) 90454

                                                                0 0 0 0

                                                                13

                                                                A B C D E

                                                                Chart1

                                                                0
                                                                0
                                                                0
                                                                0
                                                                13

                                                                Sheet1

                                                                DTU Compute

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                                                                Smoothing filters

                                                                Also know as ndash Smoothing kernel Mean filter Low pass filter blurring

                                                                The simplest filter ndash Spatial low pass filterndash Removes high frequencies

                                                                Another mask ndash Gaussian filter

                                                                1 1 1

                                                                1 1 1

                                                                1 1 191

                                                                1 2 1

                                                                2 4 2

                                                                1 2 1161

                                                                Why Gaussian

                                                                DTU Compute

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                                                                Use of smoothing

                                                                3x3 7x7 11x11 15x15

                                                                DTU Compute

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                                                                Use of smoothing Large kernels smooth more Removes high frequency information Good at enhancing big structures

                                                                3x3 15x15

                                                                DTU Compute

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                                                                Mean filterA) 166B) 113C) 12D) 51E) 245

                                                                0 0 0 0

                                                                A B C D E

                                                                Chart1

                                                                12
                                                                0
                                                                0
                                                                0
                                                                0

                                                                Sheet1

                                                                DTU Compute

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                                                                Border handling

                                                                0 2 41 2 2

                                                                1 6 3

                                                                1 2 12 5 3

                                                                2 1 3

                                                                1 3 1

                                                                2 2 2

                                                                0 1 3

                                                                1 2 0

                                                                2 1 4

                                                                1 0 1

                                                                Input Output

                                                                No values at the border

                                                                DTU Compute

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                                                                Border handling ndash extend the input

                                                                0 2 41 2 2

                                                                1 6 3

                                                                1 2 12 5 3

                                                                2 1 3

                                                                1 3 1

                                                                2 2 2

                                                                0 1 3

                                                                1 2 0

                                                                2 1 4

                                                                1 0 1

                                                                Input

                                                                0 0 0 0 000000

                                                                bull Zero padding ndash what happens

                                                                bull Zero is black ndash creates dark border around the image

                                                                DTU Compute

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                                                                Correlation with zero paddingA) 5 8B) 12 16C) 13 3D) 15 21E) 17 12

                                                                1 2 11 3 11 2 1

                                                                0 2 41 2 2

                                                                1 6 3

                                                                1 2 12 5 3

                                                                2 1 3

                                                                1 3 1

                                                                2 2 2

                                                                0 1 3

                                                                1 2 0

                                                                2 1 4

                                                                1 0 1

                                                                0

                                                                13

                                                                0 0 0

                                                                A B C D E

                                                                Chart1

                                                                0
                                                                13
                                                                0
                                                                0
                                                                0

                                                                Sheet1

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                                                                Border handling ndash extend the input

                                                                0 2 41 2 2

                                                                1 6 3

                                                                1 2 12 5 3

                                                                2 1 3

                                                                1 3 1

                                                                2 2 2

                                                                0 1 3

                                                                1 2 0

                                                                2 1 4

                                                                1 0 1

                                                                Input

                                                                1 2 0 1 311211

                                                                bull Reflection

                                                                bull Normally better than zero padding

                                                                DTU Compute

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                                                                Template Matching Template

                                                                ndash Skabelon paring dansk Locates objects in images

                                                                Input

                                                                Template

                                                                Output Correlation image

                                                                DTU Compute

                                                                2122018Introduction to Medical Image Analysis55 DTU Compute Technical University of Denmark

                                                                Template Matching The correlation between the template and the input

                                                                image is computed for each pixel

                                                                Input

                                                                Template

                                                                Output Correlation image

                                                                DTU Compute

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                                                                Template Matching The pixel with the highest value is found in the

                                                                output imagendash Here is the highest correlation

                                                                Input

                                                                Template

                                                                Output Correlation image

                                                                DTU Compute

                                                                2122018Introduction to Medical Image Analysis57 DTU Compute Technical University of Denmark

                                                                Template Matching This corresponds to the found pattern in the input

                                                                image

                                                                Input

                                                                Template

                                                                Output Correlation image

                                                                DTU Compute

                                                                2122018Introduction to Medical Image Analysis58 DTU Compute Technical University of Denmark

                                                                Problematic Correlation Correlation matching has problem with light areas ndash

                                                                why

                                                                Input (f)

                                                                Template (h)

                                                                Output Correlation imageFake max

                                                                Real max

                                                                Very High119892119892 119909119909119910119910 = 119895119895=minus119877119877

                                                                119877119877

                                                                119894119894=minus119877119877

                                                                119877119877

                                                                ℎ(119894119894 119895119895) 119891119891(119909119909 + 119894119894119910119910 + 119895119895)

                                                                DTU Compute

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                                                                Normalised Cross Correlation

                                                                Input (f)

                                                                Template (h)

                                                                Output Correlation image

                                                                Real max

                                                                NCC x y =Correlation

                                                                Length of image patch sdot Length of template

                                                                DTU Compute

                                                                2122018Introduction to Medical Image Analysis60 DTU Compute Technical University of Denmark

                                                                Length of template Vector length

                                                                ndash Put all pixel values into a vectorndash Compute the length of this vector

                                                                Describes the intensity of the templatendash Bright template has a large lengthndash Dark template has a small length

                                                                Template (h)

                                                                Length of template = 119895119895=minus119877119877

                                                                119877119877

                                                                119894119894=minus119877119877

                                                                119877119877

                                                                ℎ(119894119894 119895119895) ℎ(119894119894 119895119895)

                                                                DTU Compute

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                                                                Length of image patch Vector length based on pixel values in image patch Describes the intensity of the image patch

                                                                Template (h)

                                                                Input (f) with patch

                                                                DTU Compute

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                                                                Normalised Cross Correlation The length of the image patch and the length of

                                                                template normalise the NCC If the image is very bright the NCC will be ldquopulled

                                                                downrdquo

                                                                NCC x y =Correlation

                                                                Length of image patch sdot Length of template

                                                                DTU Compute

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                                                                Normalised Cross Correlation NCC will be between

                                                                ndash 0 No similarity between template and image patchndash 1 Template and image patch are identical

                                                                Input (f)

                                                                Template (h)

                                                                Output Correlation image

                                                                Real max

                                                                NCC x y =Correlation

                                                                Length of image patch sdot Length of template

                                                                DTU Compute

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                                                                Normalised Cross Correlation

                                                                A) 010B) 033C) 083D) 062E) 098

                                                                Der udfoslashres template matching med og normalized crosscorrelation (NCC) beregnes Hvad bliver NNC i den markerede pixel

                                                                1

                                                                2 2

                                                                3

                                                                2

                                                                A B C D E

                                                                Chart1

                                                                1
                                                                2
                                                                2
                                                                3
                                                                2

                                                                Sheet1

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                                                                Edges An edge is where there is a

                                                                high change in gray level values

                                                                Objects are often separated from the background by edgesGray level profile

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                                                                Edges The profile as a function f(d) What value is high when there

                                                                is an edgendash The slope of fndash The slope of the tangent at d

                                                                f(d)

                                                                119891119891prime(119889119889)

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                                                                Finite Difference Definition of slope

                                                                Approximation

                                                                Simpler approximationh = 1

                                                                119891119891prime 119889119889 = limℎrarr0

                                                                119891119891 119889119889 + ℎ minus 119891119891(119889119889)ℎ

                                                                119891119891prime 119889119889 asymp119891119891 119889119889 + ℎ minus 119891119891(119889119889)

                                                                ℎ

                                                                119891119891prime 119889119889 asymp 119891119891 119889119889 + 1 minus 119891119891(119889119889)

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                                                                Edges Discrete approximation of frsquo(d) Can be implemented as a filter

                                                                -1 0 1

                                                                f(d-2) f(d-1) f(d) f(d+1) f(d+2) f(d+3)

                                                                f(d)

                                                                119891119891prime 119889119889 asymp 119891119891 119889119889 + 1 minus 119891119891(119889119889)

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                                                                Edges in 2D Changes in gray level values

                                                                ndash Image gradientndash Gradient is the 2D derivative of a 2D function f(xy)ndash Equal to the slope of the imagendash A steep slope is equal to an edge

                                                                120571120571119891119891 119909119909119910119910 = 119866(119892119892119909119909119892119892119910119910)

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                                                                Edge filter kernel The Prewitt filter is a typical

                                                                edge filter Output image has high

                                                                values where there are edges

                                                                -1 0 1

                                                                -1 0 1

                                                                -1 0 1Vertical Prewitt filter

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                                                                Prewitt filter

                                                                Original Prewitt Prewitt

                                                                Hot colormapSmooth 15x15

                                                                Smooth 15x15

                                                                Prewitt

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                                                                Edge detection Edge filter

                                                                ndash Prewitt for example Thresholding

                                                                ndash Separate edges from non-edges

                                                                Output is binary imagendash Edges are white

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                                                                Edge filtering

                                                                A) MeanB) Horizontal SobelC) Vertical PrewittD) Horisontal PrewittE) Median

                                                                Der udfoslashres en filtrering (correlation) med et filter paring billedet Der bruges ikke coefficient normalization Den filtrerede vaeligrdi i den markerede pixel bliver -119 Hvilket et 3x3 filter blev benyttet

                                                                0

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                                                                02511 - Niveau af dagens emne forelaeligsingA) Meget letB) LetC) PassendeD) SvaeligrtE) Meget svaeligrt

                                                                23

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                                                                02512 - Niveau af dagens emne forelaeligsingA) Meget letB) LetC) PassendeD) SvaeligrtE) Meget svaeligrt

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                                                                02511 - Mit eget udbytte af dagenA) Jeg har laeligrt meget lidtB) Lidt laeligringC) PassendeD) God laeligringE) Jeg har laeligrt meget

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                                                                02512 - Mit eget udbytte af dagenA) Jeg har laeligrt meget lidtB) Lidt laeligringC) PassendeD) God laeligringE) Jeg har laeligrt meget

                                                                2

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                                                                02511 - Sidste uges oslashvelser (pixelwiseoperations)A) Meget letteB) LetteC) PassendeD) SvaeligreE) Meget svaeligre

                                                                0 0

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                                                                02512 - Sidste uges oslashvelser (pixelwiseoperations)A) Meget letteB) LetteC) PassendeD) SvaeligreE) Meget svaeligre

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                                                                Denne uges brug af clickersA) click click click ndash jeg bliver

                                                                sindssygB) For meget clickC) PassendeD) Jeg vil gerne have lidt mereE) Jeg kan ikrsquo faring nok

                                                                0 0

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                                                                What can you do after today Describe the difference between point processing and neighbourhood

                                                                processing Compute a rank filtered image using the min max median and

                                                                difference rank filters Compute a mean filtered image Decide if median or average filtering should be used for noise removal Choose the appropriate image border handling based on a given input

                                                                image Implement and apply template matching Compute the normalised cross correlation and explain why it should be

                                                                used Apply given image filter kernels to images Use edge filters on images Describe finite difference approximation of image gradients Describe the concept of edge detection

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                                                                Oslashvelsesrapport over oslashvelse 4 - 02511 Oslashvelser taeligller cirka 30 af karakteren Skal afleveres senest den 7 marts kl 2359 Kan afleveres af 1 eller 2 personer

                                                                ndash I skal skrive jeres egen oslashvelsesrapportndash Brug mindst et af jeres egne billeder

                                                                Afleveres som PDF Lad vaeligre med at kopiere opgaveteksten ind i jeres

                                                                opgave Put Matlab kode i et Appendix og henvis fra teksten Eksempel rapport over oslashvelse findes paring

                                                                hjemmesiden under eksamen

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                                                                2122018Introduction to Medical Image Analysis85 DTU Compute Technical University of Denmark

                                                                Exercises

                                                                • Introduction to Medical Image Analysis
                                                                • Lecture 4 ndash Neighbourhood Processing
                                                                • What can you do after today
                                                                • Point processing
                                                                • Point processing
                                                                • Neighbourhood processing
                                                                • Use of filtering
                                                                • Salt and pepper noise
                                                                • Salt and pepper noise
                                                                • What is so special about noise
                                                                • Noise ndash go away
                                                                • What is the median Value
                                                                • The median value
                                                                • Noise away ndash the median filter
                                                                • Noise removal ndash average filter
                                                                • Noise removal ndash median filter
                                                                • Image Filtering
                                                                • Median filter
                                                                • Rank filters
                                                                • Median filter
                                                                • Correlation
                                                                • Why do we need similarity
                                                                • Correlation (1D)
                                                                • Correlation (1D)
                                                                • Normalisation
                                                                • Normalisation
                                                                • Correlation on images
                                                                • Correlation on images
                                                                • Correlation on images
                                                                • Draw your filter
                                                                • Correlation on images ndash no normalisation
                                                                • Correlation on images ndash no normalisation 2
                                                                • Mathematics of 2D Correlation
                                                                • Mathematics of 2D Correlation
                                                                • Mathematics of 2D Correlation
                                                                • Slide Number 40
                                                                • 2D Kernel Normalisation
                                                                • Correlation
                                                                • Smoothing filters
                                                                • Use of smoothing
                                                                • Use of smoothing
                                                                • Mean filter
                                                                • Border handling
                                                                • Border handling ndash extend the input
                                                                • Correlation with zero padding
                                                                • Border handling ndash extend the input
                                                                • Template Matching
                                                                • Template Matching
                                                                • Template Matching
                                                                • Template Matching
                                                                • Problematic Correlation
                                                                • Normalised Cross Correlation
                                                                • Length of template
                                                                • Length of image patch
                                                                • Normalised Cross Correlation
                                                                • Normalised Cross Correlation
                                                                • Normalised Cross Correlation
                                                                • Edges
                                                                • Edges
                                                                • Finite Difference
                                                                • Edges
                                                                • Edges in 2D
                                                                • Edge filter kernel
                                                                • Prewitt filter
                                                                • Edge detection
                                                                • Edge filtering
                                                                • 02511 - Niveau af dagens emne forelaeligsing
                                                                • 02512 - Niveau af dagens emne forelaeligsing
                                                                • 02511 - Mit eget udbytte af dagen
                                                                • 02512 - Mit eget udbytte af dagen
                                                                • 02511 - Sidste uges oslashvelser (pixelwise operations)
                                                                • 02512 - Sidste uges oslashvelser (pixelwise operations)
                                                                • Denne uges brug af clickers
                                                                • What can you do after today
                                                                • Oslashvelsesrapport over oslashvelse 4 - 02511
                                                                • Exercises
                                                                  A0
                                                                  B0
                                                                  C5
                                                                  D0
                                                                  E6
                                                                  A
                                                                  B
                                                                  C
                                                                  D
                                                                  E
                                                                  A3
                                                                  B0
                                                                  C3
                                                                  D0
                                                                  E0
                                                                  A
                                                                  B
                                                                  C
                                                                  D
                                                                  E
                                                                  A0
                                                                  B0
                                                                  C1
                                                                  D4
                                                                  E1
                                                                  A
                                                                  B
                                                                  C
                                                                  D
                                                                  E
                                                                  A2
                                                                  B1
                                                                  C3
                                                                  D2
                                                                  E0
                                                                  A
                                                                  B
                                                                  C
                                                                  D
                                                                  E
                                                                  A0
                                                                  B0
                                                                  C2
                                                                  D6
                                                                  E0
                                                                  A
                                                                  B
                                                                  C
                                                                  D
                                                                  E
                                                                  A0
                                                                  B0
                                                                  C1
                                                                  D0
                                                                  E0
                                                                  A
                                                                  B
                                                                  C
                                                                  D
                                                                  E
                                                                  A2
                                                                  B3
                                                                  C6
                                                                  D1
                                                                  E0
                                                                  A
                                                                  B
                                                                  C
                                                                  D
                                                                  E
                                                                  A0
                                                                  B8
                                                                  C1
                                                                  D1
                                                                  E0
                                                                  A
                                                                  B
                                                                  C
                                                                  D
                                                                  E
                                                                  A1
                                                                  B2
                                                                  C2
                                                                  D3
                                                                  E2
                                                                  A
                                                                  B
                                                                  C
                                                                  D
                                                                  E
                                                                  A0
                                                                  B13
                                                                  C0
                                                                  D0
                                                                  E0
                                                                  A
                                                                  B
                                                                  C
                                                                  D
                                                                  E
                                                                  A12
                                                                  B0
                                                                  C0
                                                                  D0
                                                                  E0
                                                                  A
                                                                  B
                                                                  C
                                                                  D
                                                                  E
                                                                  A0
                                                                  B0
                                                                  C0
                                                                  D0
                                                                  E13
                                                                  A
                                                                  B
                                                                  C
                                                                  D
                                                                  E
                                                                  A13
                                                                  B0
                                                                  C0
                                                                  D0
                                                                  E0
                                                                  A
                                                                  B
                                                                  C
                                                                  D
                                                                  E
                                                                  A1
                                                                  B0
                                                                  C14
                                                                  D0
                                                                  E0
                                                                  A
                                                                  B
                                                                  C
                                                                  D
                                                                  E

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                                                                  Correlation on images The filter is now 2D 1 1 1

                                                                  1 1 1

                                                                  1 1 1

                                                                  0 2 4

                                                                  1 2 2

                                                                  1 6 3

                                                                  1 2 12 5 3

                                                                  2 1 3

                                                                  1 3 1

                                                                  2 2 2

                                                                  0 1 3

                                                                  1 2 0

                                                                  2 1 4

                                                                  1 0 1

                                                                  912

                                                                  91

                                                                  Input OutputKernel

                                                                  Kernel coefficients

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                                                                  Correlation on images

                                                                  1 1 11 1 11 1 1

                                                                  0 2 4

                                                                  1 2 2

                                                                  1 6 3

                                                                  1 2 0

                                                                  2 1 4

                                                                  1 0 1

                                                                  912

                                                                  911

                                                                  91

                                                                  Input Output

                                                                  1 3 1

                                                                  2 2 2

                                                                  0 1 3

                                                                  1 2 12 5 3

                                                                  2 1 3

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                                                                  Correlation on images

                                                                  Input Output

                                                                  The mask is moved row by row

                                                                  No values at the border

                                                                  0 2 4

                                                                  1 2 2

                                                                  1 6 3

                                                                  1 2 0

                                                                  2 1 4

                                                                  1 0 1

                                                                  1 3 1

                                                                  2 2 2

                                                                  0 1 3

                                                                  1 2 12 5 3

                                                                  2 1 3

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                                                                  1 2 1

                                                                  1 3 1

                                                                  1 2 1

                                                                  -1 -2 -1

                                                                  0 0 0

                                                                  1 2 1

                                                                  Draw your filter

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                                                                  Correlation on images ndash no normalisationA) 4B) 7C) 16D) 23E) 25

                                                                  1 2 11 3 11 2 1

                                                                  0 2 41 2 2

                                                                  1 6 3

                                                                  1 2 12 5 3

                                                                  2 1 3

                                                                  1 3 1

                                                                  2 2 2

                                                                  0 1 3

                                                                  1 2 0

                                                                  2 1 4

                                                                  1 0 11 0

                                                                  14

                                                                  0 0

                                                                  A B C D E

                                                                  Chart1

                                                                  1
                                                                  0
                                                                  14
                                                                  0
                                                                  0

                                                                  Sheet1

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                                                                  Correlation on images ndash no normalisation 2A) 010B) 3 3C) 6 2D) 10 15E) 11 32

                                                                  13

                                                                  0 0 0 0

                                                                  A B C D E

                                                                  -1 -2 -10 0 01 2 1

                                                                  0 2 41 2 2

                                                                  1 6 3

                                                                  1 2 12 5 3

                                                                  2 1 3

                                                                  1 3 1

                                                                  2 2 2

                                                                  0 1 3

                                                                  1 2 0

                                                                  2 1 4

                                                                  1 0 1

                                                                  Chart1

                                                                  13
                                                                  0
                                                                  0
                                                                  0
                                                                  0

                                                                  Sheet1

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                                                                  Mathematics of 2D Correlation

                                                                  h

                                                                  f

                                                                  Correlation operator

                                                                  1 2 11 3 11 2 1

                                                                  0 2 4

                                                                  1 2 2

                                                                  1 6 3

                                                                  1 2 1

                                                                  2 5 3

                                                                  2 1 3

                                                                  1 3 1

                                                                  2 2 2

                                                                  0 1 3

                                                                  1 2 0

                                                                  2 1 4

                                                                  1 0 1

                                                                  119892119892 119909119909119910119910 = 119891119891 119909119909119910119910 ∘ ℎ(119909119909119910119910)

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                                                                  Mathematics of 2D Correlation

                                                                  1 2 11 3 11 2 1

                                                                  0 2 4

                                                                  1 2 2

                                                                  1 6 3

                                                                  1 2 1

                                                                  2 5 3

                                                                  2 1 3

                                                                  1 3 1

                                                                  2 2 2

                                                                  0 1 3

                                                                  1 2 0

                                                                  2 1 4

                                                                  1 0 1

                                                                  h

                                                                  fh(00)

                                                                  f(21)

                                                                  Example g(21)

                                                                  i = -1 j = -1

                                                                  i = 1 j = 0

                                                                  119892119892 119909119909119910119910 = 119895119895=minus119877119877

                                                                  119877119877

                                                                  119894119894=minus119877119877

                                                                  119877119877

                                                                  ℎ(119894119894 119895119895) 119891119891(119909119909 + 119894119894119910119910 + 119895119895)

                                                                  DTU Compute

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                                                                  Mathematics of 2D Correlation

                                                                  1 2 11 3 11 2 1

                                                                  0 2 4

                                                                  1 2 2

                                                                  1 6 3

                                                                  1 2 1

                                                                  2 5 3

                                                                  2 1 3

                                                                  1 3 1

                                                                  2 2 2

                                                                  0 1 3

                                                                  1 2 0

                                                                  2 1 4

                                                                  1 0 1

                                                                  h

                                                                  f

                                                                  119892119892 119909119909119910119910 = 119895119895=minus119877119877

                                                                  119877119877

                                                                  119894119894=minus119877119877

                                                                  119877119877

                                                                  ℎ(119894119894 119895119895) 119891119891(119909119909 + 119894119894119910119910 + 119895119895)

                                                                  119892119892(119909119909119910119910 = 1 2 + 2 0 + 1 1 + 1 1 + 3 4 + 1 2 + 1 0 + 2 1 + 1 0

                                                                  DTU Compute

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                                                                  119892119892 119909119909 119910119910 = 119895119895=minus119877119877

                                                                  119877119877

                                                                  119894119894=minus119877119877

                                                                  119877119877

                                                                  ℎ(119894119894 119895119895) 119891119891(119909119909 + 119894119894119910119910 + 119895119895)

                                                                  119892119892 22 =ℎ minus1minus1 sdot 119891119891 11 + ℎ 0minus1 sdot 119891119891 21 + ℎ 1minus1 sdot 119891119891 31 +ℎ minus10 sdot 119891119891 12 + ℎ 00 sdot 119891119891 22 + ℎ 10 sdot 119891119891 32 +ℎ minus11 sdot 119891119891 13 + ℎ 01 sdot 119891119891 23 + ℎ 11 sdot 119891119891 33

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                                                                  2D Kernel Normalisation

                                                                  1 2 11 3 11 2 1

                                                                  h

                                                                  Normalisation factor

                                                                  1 + 2 + 1 + 1 + 3 + 1 + 1 + 2 + 1 = 13

                                                                  119909119909

                                                                  119910119910

                                                                  ℎ(119909119909119910119910)

                                                                  DTU Compute

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                                                                  CorrelationA) 50122B) 123001C) 11233D) 2550E) 90454

                                                                  0 0 0 0

                                                                  13

                                                                  A B C D E

                                                                  Chart1

                                                                  0
                                                                  0
                                                                  0
                                                                  0
                                                                  13

                                                                  Sheet1

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                                                                  Smoothing filters

                                                                  Also know as ndash Smoothing kernel Mean filter Low pass filter blurring

                                                                  The simplest filter ndash Spatial low pass filterndash Removes high frequencies

                                                                  Another mask ndash Gaussian filter

                                                                  1 1 1

                                                                  1 1 1

                                                                  1 1 191

                                                                  1 2 1

                                                                  2 4 2

                                                                  1 2 1161

                                                                  Why Gaussian

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                                                                  Use of smoothing

                                                                  3x3 7x7 11x11 15x15

                                                                  DTU Compute

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                                                                  Use of smoothing Large kernels smooth more Removes high frequency information Good at enhancing big structures

                                                                  3x3 15x15

                                                                  DTU Compute

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                                                                  Mean filterA) 166B) 113C) 12D) 51E) 245

                                                                  0 0 0 0

                                                                  A B C D E

                                                                  Chart1

                                                                  12
                                                                  0
                                                                  0
                                                                  0
                                                                  0

                                                                  Sheet1

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                                                                  Border handling

                                                                  0 2 41 2 2

                                                                  1 6 3

                                                                  1 2 12 5 3

                                                                  2 1 3

                                                                  1 3 1

                                                                  2 2 2

                                                                  0 1 3

                                                                  1 2 0

                                                                  2 1 4

                                                                  1 0 1

                                                                  Input Output

                                                                  No values at the border

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                                                                  Border handling ndash extend the input

                                                                  0 2 41 2 2

                                                                  1 6 3

                                                                  1 2 12 5 3

                                                                  2 1 3

                                                                  1 3 1

                                                                  2 2 2

                                                                  0 1 3

                                                                  1 2 0

                                                                  2 1 4

                                                                  1 0 1

                                                                  Input

                                                                  0 0 0 0 000000

                                                                  bull Zero padding ndash what happens

                                                                  bull Zero is black ndash creates dark border around the image

                                                                  DTU Compute

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                                                                  Correlation with zero paddingA) 5 8B) 12 16C) 13 3D) 15 21E) 17 12

                                                                  1 2 11 3 11 2 1

                                                                  0 2 41 2 2

                                                                  1 6 3

                                                                  1 2 12 5 3

                                                                  2 1 3

                                                                  1 3 1

                                                                  2 2 2

                                                                  0 1 3

                                                                  1 2 0

                                                                  2 1 4

                                                                  1 0 1

                                                                  0

                                                                  13

                                                                  0 0 0

                                                                  A B C D E

                                                                  Chart1

                                                                  0
                                                                  13
                                                                  0
                                                                  0
                                                                  0

                                                                  Sheet1

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                                                                  Border handling ndash extend the input

                                                                  0 2 41 2 2

                                                                  1 6 3

                                                                  1 2 12 5 3

                                                                  2 1 3

                                                                  1 3 1

                                                                  2 2 2

                                                                  0 1 3

                                                                  1 2 0

                                                                  2 1 4

                                                                  1 0 1

                                                                  Input

                                                                  1 2 0 1 311211

                                                                  bull Reflection

                                                                  bull Normally better than zero padding

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                                                                  Template Matching Template

                                                                  ndash Skabelon paring dansk Locates objects in images

                                                                  Input

                                                                  Template

                                                                  Output Correlation image

                                                                  DTU Compute

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                                                                  Template Matching The correlation between the template and the input

                                                                  image is computed for each pixel

                                                                  Input

                                                                  Template

                                                                  Output Correlation image

                                                                  DTU Compute

                                                                  2122018Introduction to Medical Image Analysis56 DTU Compute Technical University of Denmark

                                                                  Template Matching The pixel with the highest value is found in the

                                                                  output imagendash Here is the highest correlation

                                                                  Input

                                                                  Template

                                                                  Output Correlation image

                                                                  DTU Compute

                                                                  2122018Introduction to Medical Image Analysis57 DTU Compute Technical University of Denmark

                                                                  Template Matching This corresponds to the found pattern in the input

                                                                  image

                                                                  Input

                                                                  Template

                                                                  Output Correlation image

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                                                                  Problematic Correlation Correlation matching has problem with light areas ndash

                                                                  why

                                                                  Input (f)

                                                                  Template (h)

                                                                  Output Correlation imageFake max

                                                                  Real max

                                                                  Very High119892119892 119909119909119910119910 = 119895119895=minus119877119877

                                                                  119877119877

                                                                  119894119894=minus119877119877

                                                                  119877119877

                                                                  ℎ(119894119894 119895119895) 119891119891(119909119909 + 119894119894119910119910 + 119895119895)

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                                                                  Normalised Cross Correlation

                                                                  Input (f)

                                                                  Template (h)

                                                                  Output Correlation image

                                                                  Real max

                                                                  NCC x y =Correlation

                                                                  Length of image patch sdot Length of template

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                                                                  Length of template Vector length

                                                                  ndash Put all pixel values into a vectorndash Compute the length of this vector

                                                                  Describes the intensity of the templatendash Bright template has a large lengthndash Dark template has a small length

                                                                  Template (h)

                                                                  Length of template = 119895119895=minus119877119877

                                                                  119877119877

                                                                  119894119894=minus119877119877

                                                                  119877119877

                                                                  ℎ(119894119894 119895119895) ℎ(119894119894 119895119895)

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                                                                  Length of image patch Vector length based on pixel values in image patch Describes the intensity of the image patch

                                                                  Template (h)

                                                                  Input (f) with patch

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                                                                  Normalised Cross Correlation The length of the image patch and the length of

                                                                  template normalise the NCC If the image is very bright the NCC will be ldquopulled

                                                                  downrdquo

                                                                  NCC x y =Correlation

                                                                  Length of image patch sdot Length of template

                                                                  DTU Compute

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                                                                  Normalised Cross Correlation NCC will be between

                                                                  ndash 0 No similarity between template and image patchndash 1 Template and image patch are identical

                                                                  Input (f)

                                                                  Template (h)

                                                                  Output Correlation image

                                                                  Real max

                                                                  NCC x y =Correlation

                                                                  Length of image patch sdot Length of template

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                                                                  Normalised Cross Correlation

                                                                  A) 010B) 033C) 083D) 062E) 098

                                                                  Der udfoslashres template matching med og normalized crosscorrelation (NCC) beregnes Hvad bliver NNC i den markerede pixel

                                                                  1

                                                                  2 2

                                                                  3

                                                                  2

                                                                  A B C D E

                                                                  Chart1

                                                                  1
                                                                  2
                                                                  2
                                                                  3
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                                                                  Edges An edge is where there is a

                                                                  high change in gray level values

                                                                  Objects are often separated from the background by edgesGray level profile

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                                                                  Edges The profile as a function f(d) What value is high when there

                                                                  is an edgendash The slope of fndash The slope of the tangent at d

                                                                  f(d)

                                                                  119891119891prime(119889119889)

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                                                                  Finite Difference Definition of slope

                                                                  Approximation

                                                                  Simpler approximationh = 1

                                                                  119891119891prime 119889119889 = limℎrarr0

                                                                  119891119891 119889119889 + ℎ minus 119891119891(119889119889)ℎ

                                                                  119891119891prime 119889119889 asymp119891119891 119889119889 + ℎ minus 119891119891(119889119889)

                                                                  ℎ

                                                                  119891119891prime 119889119889 asymp 119891119891 119889119889 + 1 minus 119891119891(119889119889)

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                                                                  Edges Discrete approximation of frsquo(d) Can be implemented as a filter

                                                                  -1 0 1

                                                                  f(d-2) f(d-1) f(d) f(d+1) f(d+2) f(d+3)

                                                                  f(d)

                                                                  119891119891prime 119889119889 asymp 119891119891 119889119889 + 1 minus 119891119891(119889119889)

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                                                                  Edges in 2D Changes in gray level values

                                                                  ndash Image gradientndash Gradient is the 2D derivative of a 2D function f(xy)ndash Equal to the slope of the imagendash A steep slope is equal to an edge

                                                                  120571120571119891119891 119909119909119910119910 = 119866(119892119892119909119909119892119892119910119910)

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                                                                  Edge filter kernel The Prewitt filter is a typical

                                                                  edge filter Output image has high

                                                                  values where there are edges

                                                                  -1 0 1

                                                                  -1 0 1

                                                                  -1 0 1Vertical Prewitt filter

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                                                                  Prewitt filter

                                                                  Original Prewitt Prewitt

                                                                  Hot colormapSmooth 15x15

                                                                  Smooth 15x15

                                                                  Prewitt

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                                                                  Edge detection Edge filter

                                                                  ndash Prewitt for example Thresholding

                                                                  ndash Separate edges from non-edges

                                                                  Output is binary imagendash Edges are white

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                                                                  Edge filtering

                                                                  A) MeanB) Horizontal SobelC) Vertical PrewittD) Horisontal PrewittE) Median

                                                                  Der udfoslashres en filtrering (correlation) med et filter paring billedet Der bruges ikke coefficient normalization Den filtrerede vaeligrdi i den markerede pixel bliver -119 Hvilket et 3x3 filter blev benyttet

                                                                  0

                                                                  8

                                                                  1 10

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                                                                  02511 - Niveau af dagens emne forelaeligsingA) Meget letB) LetC) PassendeD) SvaeligrtE) Meget svaeligrt

                                                                  23

                                                                  6

                                                                  10

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                                                                  02512 - Niveau af dagens emne forelaeligsingA) Meget letB) LetC) PassendeD) SvaeligrtE) Meget svaeligrt

                                                                  0 0

                                                                  1

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                                                                  02511 - Mit eget udbytte af dagenA) Jeg har laeligrt meget lidtB) Lidt laeligringC) PassendeD) God laeligringE) Jeg har laeligrt meget

                                                                  0 0

                                                                  2

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                                                                  02512 - Mit eget udbytte af dagenA) Jeg har laeligrt meget lidtB) Lidt laeligringC) PassendeD) God laeligringE) Jeg har laeligrt meget

                                                                  2

                                                                  1

                                                                  3

                                                                  2

                                                                  0

                                                                  A B C D E

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                                                                  2
                                                                  1
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                                                                  02511 - Sidste uges oslashvelser (pixelwiseoperations)A) Meget letteB) LetteC) PassendeD) SvaeligreE) Meget svaeligre

                                                                  0 0

                                                                  1

                                                                  4

                                                                  1

                                                                  A B C D E

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                                                                  0
                                                                  1
                                                                  4
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                                                                  02512 - Sidste uges oslashvelser (pixelwiseoperations)A) Meget letteB) LetteC) PassendeD) SvaeligreE) Meget svaeligre

                                                                  3

                                                                  0

                                                                  3

                                                                  0 0

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                                                                  Denne uges brug af clickersA) click click click ndash jeg bliver

                                                                  sindssygB) For meget clickC) PassendeD) Jeg vil gerne have lidt mereE) Jeg kan ikrsquo faring nok

                                                                  0 0

                                                                  5

                                                                  0

                                                                  6

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                                                                  What can you do after today Describe the difference between point processing and neighbourhood

                                                                  processing Compute a rank filtered image using the min max median and

                                                                  difference rank filters Compute a mean filtered image Decide if median or average filtering should be used for noise removal Choose the appropriate image border handling based on a given input

                                                                  image Implement and apply template matching Compute the normalised cross correlation and explain why it should be

                                                                  used Apply given image filter kernels to images Use edge filters on images Describe finite difference approximation of image gradients Describe the concept of edge detection

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                                                                  Oslashvelsesrapport over oslashvelse 4 - 02511 Oslashvelser taeligller cirka 30 af karakteren Skal afleveres senest den 7 marts kl 2359 Kan afleveres af 1 eller 2 personer

                                                                  ndash I skal skrive jeres egen oslashvelsesrapportndash Brug mindst et af jeres egne billeder

                                                                  Afleveres som PDF Lad vaeligre med at kopiere opgaveteksten ind i jeres

                                                                  opgave Put Matlab kode i et Appendix og henvis fra teksten Eksempel rapport over oslashvelse findes paring

                                                                  hjemmesiden under eksamen

                                                                  DTU Compute

                                                                  2122018Introduction to Medical Image Analysis85 DTU Compute Technical University of Denmark

                                                                  Exercises

                                                                  • Introduction to Medical Image Analysis
                                                                  • Lecture 4 ndash Neighbourhood Processing
                                                                  • What can you do after today
                                                                  • Point processing
                                                                  • Point processing
                                                                  • Neighbourhood processing
                                                                  • Use of filtering
                                                                  • Salt and pepper noise
                                                                  • Salt and pepper noise
                                                                  • What is so special about noise
                                                                  • Noise ndash go away
                                                                  • What is the median Value
                                                                  • The median value
                                                                  • Noise away ndash the median filter
                                                                  • Noise removal ndash average filter
                                                                  • Noise removal ndash median filter
                                                                  • Image Filtering
                                                                  • Median filter
                                                                  • Rank filters
                                                                  • Median filter
                                                                  • Correlation
                                                                  • Why do we need similarity
                                                                  • Correlation (1D)
                                                                  • Correlation (1D)
                                                                  • Normalisation
                                                                  • Normalisation
                                                                  • Correlation on images
                                                                  • Correlation on images
                                                                  • Correlation on images
                                                                  • Draw your filter
                                                                  • Correlation on images ndash no normalisation
                                                                  • Correlation on images ndash no normalisation 2
                                                                  • Mathematics of 2D Correlation
                                                                  • Mathematics of 2D Correlation
                                                                  • Mathematics of 2D Correlation
                                                                  • Slide Number 40
                                                                  • 2D Kernel Normalisation
                                                                  • Correlation
                                                                  • Smoothing filters
                                                                  • Use of smoothing
                                                                  • Use of smoothing
                                                                  • Mean filter
                                                                  • Border handling
                                                                  • Border handling ndash extend the input
                                                                  • Correlation with zero padding
                                                                  • Border handling ndash extend the input
                                                                  • Template Matching
                                                                  • Template Matching
                                                                  • Template Matching
                                                                  • Template Matching
                                                                  • Problematic Correlation
                                                                  • Normalised Cross Correlation
                                                                  • Length of template
                                                                  • Length of image patch
                                                                  • Normalised Cross Correlation
                                                                  • Normalised Cross Correlation
                                                                  • Normalised Cross Correlation
                                                                  • Edges
                                                                  • Edges
                                                                  • Finite Difference
                                                                  • Edges
                                                                  • Edges in 2D
                                                                  • Edge filter kernel
                                                                  • Prewitt filter
                                                                  • Edge detection
                                                                  • Edge filtering
                                                                  • 02511 - Niveau af dagens emne forelaeligsing
                                                                  • 02512 - Niveau af dagens emne forelaeligsing
                                                                  • 02511 - Mit eget udbytte af dagen
                                                                  • 02512 - Mit eget udbytte af dagen
                                                                  • 02511 - Sidste uges oslashvelser (pixelwise operations)
                                                                  • 02512 - Sidste uges oslashvelser (pixelwise operations)
                                                                  • Denne uges brug af clickers
                                                                  • What can you do after today
                                                                  • Oslashvelsesrapport over oslashvelse 4 - 02511
                                                                  • Exercises
                                                                    A0
                                                                    B0
                                                                    C5
                                                                    D0
                                                                    E6
                                                                    A
                                                                    B
                                                                    C
                                                                    D
                                                                    E
                                                                    A3
                                                                    B0
                                                                    C3
                                                                    D0
                                                                    E0
                                                                    A
                                                                    B
                                                                    C
                                                                    D
                                                                    E
                                                                    A0
                                                                    B0
                                                                    C1
                                                                    D4
                                                                    E1
                                                                    A
                                                                    B
                                                                    C
                                                                    D
                                                                    E
                                                                    A2
                                                                    B1
                                                                    C3
                                                                    D2
                                                                    E0
                                                                    A
                                                                    B
                                                                    C
                                                                    D
                                                                    E
                                                                    A0
                                                                    B0
                                                                    C2
                                                                    D6
                                                                    E0
                                                                    A
                                                                    B
                                                                    C
                                                                    D
                                                                    E
                                                                    A0
                                                                    B0
                                                                    C1
                                                                    D0
                                                                    E0
                                                                    A
                                                                    B
                                                                    C
                                                                    D
                                                                    E
                                                                    A2
                                                                    B3
                                                                    C6
                                                                    D1
                                                                    E0
                                                                    A
                                                                    B
                                                                    C
                                                                    D
                                                                    E
                                                                    A0
                                                                    B8
                                                                    C1
                                                                    D1
                                                                    E0
                                                                    A
                                                                    B
                                                                    C
                                                                    D
                                                                    E
                                                                    A1
                                                                    B2
                                                                    C2
                                                                    D3
                                                                    E2
                                                                    A
                                                                    B
                                                                    C
                                                                    D
                                                                    E
                                                                    A0
                                                                    B13
                                                                    C0
                                                                    D0
                                                                    E0
                                                                    A
                                                                    B
                                                                    C
                                                                    D
                                                                    E
                                                                    A12
                                                                    B0
                                                                    C0
                                                                    D0
                                                                    E0
                                                                    A
                                                                    B
                                                                    C
                                                                    D
                                                                    E
                                                                    A0
                                                                    B0
                                                                    C0
                                                                    D0
                                                                    E13
                                                                    A
                                                                    B
                                                                    C
                                                                    D
                                                                    E
                                                                    A13
                                                                    B0
                                                                    C0
                                                                    D0
                                                                    E0
                                                                    A
                                                                    B
                                                                    C
                                                                    D
                                                                    E
                                                                    A1
                                                                    B0
                                                                    C14
                                                                    D0
                                                                    E0
                                                                    A
                                                                    B
                                                                    C
                                                                    D
                                                                    E

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                                                                    Correlation on images

                                                                    1 1 11 1 11 1 1

                                                                    0 2 4

                                                                    1 2 2

                                                                    1 6 3

                                                                    1 2 0

                                                                    2 1 4

                                                                    1 0 1

                                                                    912

                                                                    911

                                                                    91

                                                                    Input Output

                                                                    1 3 1

                                                                    2 2 2

                                                                    0 1 3

                                                                    1 2 12 5 3

                                                                    2 1 3

                                                                    DTU Compute

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                                                                    Correlation on images

                                                                    Input Output

                                                                    The mask is moved row by row

                                                                    No values at the border

                                                                    0 2 4

                                                                    1 2 2

                                                                    1 6 3

                                                                    1 2 0

                                                                    2 1 4

                                                                    1 0 1

                                                                    1 3 1

                                                                    2 2 2

                                                                    0 1 3

                                                                    1 2 12 5 3

                                                                    2 1 3

                                                                    DTU Compute

                                                                    2122018Introduction to Medical Image Analysis32 DTU Compute Technical University of Denmark

                                                                    1 2 1

                                                                    1 3 1

                                                                    1 2 1

                                                                    -1 -2 -1

                                                                    0 0 0

                                                                    1 2 1

                                                                    Draw your filter

                                                                    DTU Compute

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                                                                    Correlation on images ndash no normalisationA) 4B) 7C) 16D) 23E) 25

                                                                    1 2 11 3 11 2 1

                                                                    0 2 41 2 2

                                                                    1 6 3

                                                                    1 2 12 5 3

                                                                    2 1 3

                                                                    1 3 1

                                                                    2 2 2

                                                                    0 1 3

                                                                    1 2 0

                                                                    2 1 4

                                                                    1 0 11 0

                                                                    14

                                                                    0 0

                                                                    A B C D E

                                                                    Chart1

                                                                    1
                                                                    0
                                                                    14
                                                                    0
                                                                    0

                                                                    Sheet1

                                                                    DTU Compute

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                                                                    Correlation on images ndash no normalisation 2A) 010B) 3 3C) 6 2D) 10 15E) 11 32

                                                                    13

                                                                    0 0 0 0

                                                                    A B C D E

                                                                    -1 -2 -10 0 01 2 1

                                                                    0 2 41 2 2

                                                                    1 6 3

                                                                    1 2 12 5 3

                                                                    2 1 3

                                                                    1 3 1

                                                                    2 2 2

                                                                    0 1 3

                                                                    1 2 0

                                                                    2 1 4

                                                                    1 0 1

                                                                    Chart1

                                                                    13
                                                                    0
                                                                    0
                                                                    0
                                                                    0

                                                                    Sheet1

                                                                    DTU Compute

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                                                                    Mathematics of 2D Correlation

                                                                    h

                                                                    f

                                                                    Correlation operator

                                                                    1 2 11 3 11 2 1

                                                                    0 2 4

                                                                    1 2 2

                                                                    1 6 3

                                                                    1 2 1

                                                                    2 5 3

                                                                    2 1 3

                                                                    1 3 1

                                                                    2 2 2

                                                                    0 1 3

                                                                    1 2 0

                                                                    2 1 4

                                                                    1 0 1

                                                                    119892119892 119909119909119910119910 = 119891119891 119909119909119910119910 ∘ ℎ(119909119909119910119910)

                                                                    DTU Compute

                                                                    2122018Introduction to Medical Image Analysis38 DTU Compute Technical University of Denmark

                                                                    Mathematics of 2D Correlation

                                                                    1 2 11 3 11 2 1

                                                                    0 2 4

                                                                    1 2 2

                                                                    1 6 3

                                                                    1 2 1

                                                                    2 5 3

                                                                    2 1 3

                                                                    1 3 1

                                                                    2 2 2

                                                                    0 1 3

                                                                    1 2 0

                                                                    2 1 4

                                                                    1 0 1

                                                                    h

                                                                    fh(00)

                                                                    f(21)

                                                                    Example g(21)

                                                                    i = -1 j = -1

                                                                    i = 1 j = 0

                                                                    119892119892 119909119909119910119910 = 119895119895=minus119877119877

                                                                    119877119877

                                                                    119894119894=minus119877119877

                                                                    119877119877

                                                                    ℎ(119894119894 119895119895) 119891119891(119909119909 + 119894119894119910119910 + 119895119895)

                                                                    DTU Compute

                                                                    2122018Introduction to Medical Image Analysis39 DTU Compute Technical University of Denmark

                                                                    Mathematics of 2D Correlation

                                                                    1 2 11 3 11 2 1

                                                                    0 2 4

                                                                    1 2 2

                                                                    1 6 3

                                                                    1 2 1

                                                                    2 5 3

                                                                    2 1 3

                                                                    1 3 1

                                                                    2 2 2

                                                                    0 1 3

                                                                    1 2 0

                                                                    2 1 4

                                                                    1 0 1

                                                                    h

                                                                    f

                                                                    119892119892 119909119909119910119910 = 119895119895=minus119877119877

                                                                    119877119877

                                                                    119894119894=minus119877119877

                                                                    119877119877

                                                                    ℎ(119894119894 119895119895) 119891119891(119909119909 + 119894119894119910119910 + 119895119895)

                                                                    119892119892(119909119909119910119910 = 1 2 + 2 0 + 1 1 + 1 1 + 3 4 + 1 2 + 1 0 + 2 1 + 1 0

                                                                    DTU Compute

                                                                    2122018Introduction to Medical Image Analysis40 DTU Compute Technical University of Denmark

                                                                    119892119892 119909119909 119910119910 = 119895119895=minus119877119877

                                                                    119877119877

                                                                    119894119894=minus119877119877

                                                                    119877119877

                                                                    ℎ(119894119894 119895119895) 119891119891(119909119909 + 119894119894119910119910 + 119895119895)

                                                                    119892119892 22 =ℎ minus1minus1 sdot 119891119891 11 + ℎ 0minus1 sdot 119891119891 21 + ℎ 1minus1 sdot 119891119891 31 +ℎ minus10 sdot 119891119891 12 + ℎ 00 sdot 119891119891 22 + ℎ 10 sdot 119891119891 32 +ℎ minus11 sdot 119891119891 13 + ℎ 01 sdot 119891119891 23 + ℎ 11 sdot 119891119891 33

                                                                    DTU Compute

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                                                                    2D Kernel Normalisation

                                                                    1 2 11 3 11 2 1

                                                                    h

                                                                    Normalisation factor

                                                                    1 + 2 + 1 + 1 + 3 + 1 + 1 + 2 + 1 = 13

                                                                    119909119909

                                                                    119910119910

                                                                    ℎ(119909119909119910119910)

                                                                    DTU Compute

                                                                    2122018Introduction to Medical Image Analysis42 DTU Compute Technical University of Denmark

                                                                    CorrelationA) 50122B) 123001C) 11233D) 2550E) 90454

                                                                    0 0 0 0

                                                                    13

                                                                    A B C D E

                                                                    Chart1

                                                                    0
                                                                    0
                                                                    0
                                                                    0
                                                                    13

                                                                    Sheet1

                                                                    DTU Compute

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                                                                    Smoothing filters

                                                                    Also know as ndash Smoothing kernel Mean filter Low pass filter blurring

                                                                    The simplest filter ndash Spatial low pass filterndash Removes high frequencies

                                                                    Another mask ndash Gaussian filter

                                                                    1 1 1

                                                                    1 1 1

                                                                    1 1 191

                                                                    1 2 1

                                                                    2 4 2

                                                                    1 2 1161

                                                                    Why Gaussian

                                                                    DTU Compute

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                                                                    Use of smoothing

                                                                    3x3 7x7 11x11 15x15

                                                                    DTU Compute

                                                                    2122018Introduction to Medical Image Analysis46 DTU Compute Technical University of Denmark

                                                                    Use of smoothing Large kernels smooth more Removes high frequency information Good at enhancing big structures

                                                                    3x3 15x15

                                                                    DTU Compute

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                                                                    Mean filterA) 166B) 113C) 12D) 51E) 245

                                                                    0 0 0 0

                                                                    A B C D E

                                                                    Chart1

                                                                    12
                                                                    0
                                                                    0
                                                                    0
                                                                    0

                                                                    Sheet1

                                                                    DTU Compute

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                                                                    Border handling

                                                                    0 2 41 2 2

                                                                    1 6 3

                                                                    1 2 12 5 3

                                                                    2 1 3

                                                                    1 3 1

                                                                    2 2 2

                                                                    0 1 3

                                                                    1 2 0

                                                                    2 1 4

                                                                    1 0 1

                                                                    Input Output

                                                                    No values at the border

                                                                    DTU Compute

                                                                    2122018Introduction to Medical Image Analysis50 DTU Compute Technical University of Denmark

                                                                    Border handling ndash extend the input

                                                                    0 2 41 2 2

                                                                    1 6 3

                                                                    1 2 12 5 3

                                                                    2 1 3

                                                                    1 3 1

                                                                    2 2 2

                                                                    0 1 3

                                                                    1 2 0

                                                                    2 1 4

                                                                    1 0 1

                                                                    Input

                                                                    0 0 0 0 000000

                                                                    bull Zero padding ndash what happens

                                                                    bull Zero is black ndash creates dark border around the image

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                                                                    Correlation with zero paddingA) 5 8B) 12 16C) 13 3D) 15 21E) 17 12

                                                                    1 2 11 3 11 2 1

                                                                    0 2 41 2 2

                                                                    1 6 3

                                                                    1 2 12 5 3

                                                                    2 1 3

                                                                    1 3 1

                                                                    2 2 2

                                                                    0 1 3

                                                                    1 2 0

                                                                    2 1 4

                                                                    1 0 1

                                                                    0

                                                                    13

                                                                    0 0 0

                                                                    A B C D E

                                                                    Chart1

                                                                    0
                                                                    13
                                                                    0
                                                                    0
                                                                    0

                                                                    Sheet1

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                                                                    Border handling ndash extend the input

                                                                    0 2 41 2 2

                                                                    1 6 3

                                                                    1 2 12 5 3

                                                                    2 1 3

                                                                    1 3 1

                                                                    2 2 2

                                                                    0 1 3

                                                                    1 2 0

                                                                    2 1 4

                                                                    1 0 1

                                                                    Input

                                                                    1 2 0 1 311211

                                                                    bull Reflection

                                                                    bull Normally better than zero padding

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                                                                    Template Matching Template

                                                                    ndash Skabelon paring dansk Locates objects in images

                                                                    Input

                                                                    Template

                                                                    Output Correlation image

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                                                                    Template Matching The correlation between the template and the input

                                                                    image is computed for each pixel

                                                                    Input

                                                                    Template

                                                                    Output Correlation image

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                                                                    Template Matching The pixel with the highest value is found in the

                                                                    output imagendash Here is the highest correlation

                                                                    Input

                                                                    Template

                                                                    Output Correlation image

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                                                                    Template Matching This corresponds to the found pattern in the input

                                                                    image

                                                                    Input

                                                                    Template

                                                                    Output Correlation image

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                                                                    Problematic Correlation Correlation matching has problem with light areas ndash

                                                                    why

                                                                    Input (f)

                                                                    Template (h)

                                                                    Output Correlation imageFake max

                                                                    Real max

                                                                    Very High119892119892 119909119909119910119910 = 119895119895=minus119877119877

                                                                    119877119877

                                                                    119894119894=minus119877119877

                                                                    119877119877

                                                                    ℎ(119894119894 119895119895) 119891119891(119909119909 + 119894119894119910119910 + 119895119895)

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                                                                    Normalised Cross Correlation

                                                                    Input (f)

                                                                    Template (h)

                                                                    Output Correlation image

                                                                    Real max

                                                                    NCC x y =Correlation

                                                                    Length of image patch sdot Length of template

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                                                                    Length of template Vector length

                                                                    ndash Put all pixel values into a vectorndash Compute the length of this vector

                                                                    Describes the intensity of the templatendash Bright template has a large lengthndash Dark template has a small length

                                                                    Template (h)

                                                                    Length of template = 119895119895=minus119877119877

                                                                    119877119877

                                                                    119894119894=minus119877119877

                                                                    119877119877

                                                                    ℎ(119894119894 119895119895) ℎ(119894119894 119895119895)

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                                                                    Length of image patch Vector length based on pixel values in image patch Describes the intensity of the image patch

                                                                    Template (h)

                                                                    Input (f) with patch

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                                                                    Normalised Cross Correlation The length of the image patch and the length of

                                                                    template normalise the NCC If the image is very bright the NCC will be ldquopulled

                                                                    downrdquo

                                                                    NCC x y =Correlation

                                                                    Length of image patch sdot Length of template

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                                                                    Normalised Cross Correlation NCC will be between

                                                                    ndash 0 No similarity between template and image patchndash 1 Template and image patch are identical

                                                                    Input (f)

                                                                    Template (h)

                                                                    Output Correlation image

                                                                    Real max

                                                                    NCC x y =Correlation

                                                                    Length of image patch sdot Length of template

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                                                                    Normalised Cross Correlation

                                                                    A) 010B) 033C) 083D) 062E) 098

                                                                    Der udfoslashres template matching med og normalized crosscorrelation (NCC) beregnes Hvad bliver NNC i den markerede pixel

                                                                    1

                                                                    2 2

                                                                    3

                                                                    2

                                                                    A B C D E

                                                                    Chart1

                                                                    1
                                                                    2
                                                                    2
                                                                    3
                                                                    2

                                                                    Sheet1

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                                                                    Edges An edge is where there is a

                                                                    high change in gray level values

                                                                    Objects are often separated from the background by edgesGray level profile

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                                                                    Edges The profile as a function f(d) What value is high when there

                                                                    is an edgendash The slope of fndash The slope of the tangent at d

                                                                    f(d)

                                                                    119891119891prime(119889119889)

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                                                                    Finite Difference Definition of slope

                                                                    Approximation

                                                                    Simpler approximationh = 1

                                                                    119891119891prime 119889119889 = limℎrarr0

                                                                    119891119891 119889119889 + ℎ minus 119891119891(119889119889)ℎ

                                                                    119891119891prime 119889119889 asymp119891119891 119889119889 + ℎ minus 119891119891(119889119889)

                                                                    ℎ

                                                                    119891119891prime 119889119889 asymp 119891119891 119889119889 + 1 minus 119891119891(119889119889)

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                                                                    Edges Discrete approximation of frsquo(d) Can be implemented as a filter

                                                                    -1 0 1

                                                                    f(d-2) f(d-1) f(d) f(d+1) f(d+2) f(d+3)

                                                                    f(d)

                                                                    119891119891prime 119889119889 asymp 119891119891 119889119889 + 1 minus 119891119891(119889119889)

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                                                                    Edges in 2D Changes in gray level values

                                                                    ndash Image gradientndash Gradient is the 2D derivative of a 2D function f(xy)ndash Equal to the slope of the imagendash A steep slope is equal to an edge

                                                                    120571120571119891119891 119909119909119910119910 = 119866(119892119892119909119909119892119892119910119910)

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                                                                    Edge filter kernel The Prewitt filter is a typical

                                                                    edge filter Output image has high

                                                                    values where there are edges

                                                                    -1 0 1

                                                                    -1 0 1

                                                                    -1 0 1Vertical Prewitt filter

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                                                                    Prewitt filter

                                                                    Original Prewitt Prewitt

                                                                    Hot colormapSmooth 15x15

                                                                    Smooth 15x15

                                                                    Prewitt

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                                                                    Edge detection Edge filter

                                                                    ndash Prewitt for example Thresholding

                                                                    ndash Separate edges from non-edges

                                                                    Output is binary imagendash Edges are white

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                                                                    Edge filtering

                                                                    A) MeanB) Horizontal SobelC) Vertical PrewittD) Horisontal PrewittE) Median

                                                                    Der udfoslashres en filtrering (correlation) med et filter paring billedet Der bruges ikke coefficient normalization Den filtrerede vaeligrdi i den markerede pixel bliver -119 Hvilket et 3x3 filter blev benyttet

                                                                    0

                                                                    8

                                                                    1 10

                                                                    A B C D E

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                                                                    0
                                                                    8
                                                                    1
                                                                    1
                                                                    0

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                                                                    02511 - Niveau af dagens emne forelaeligsingA) Meget letB) LetC) PassendeD) SvaeligrtE) Meget svaeligrt

                                                                    23

                                                                    6

                                                                    10

                                                                    A B C D E

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                                                                    2
                                                                    3
                                                                    6
                                                                    1
                                                                    0

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                                                                    02512 - Niveau af dagens emne forelaeligsingA) Meget letB) LetC) PassendeD) SvaeligrtE) Meget svaeligrt

                                                                    0 0

                                                                    1

                                                                    0 0

                                                                    A B C D E

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                                                                    0
                                                                    0
                                                                    1
                                                                    0
                                                                    0

                                                                    Sheet1

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                                                                    02511 - Mit eget udbytte af dagenA) Jeg har laeligrt meget lidtB) Lidt laeligringC) PassendeD) God laeligringE) Jeg har laeligrt meget

                                                                    0 0

                                                                    2

                                                                    6

                                                                    0

                                                                    A B C D E

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                                                                    0
                                                                    0
                                                                    2
                                                                    6
                                                                    0

                                                                    Sheet1

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                                                                    02512 - Mit eget udbytte af dagenA) Jeg har laeligrt meget lidtB) Lidt laeligringC) PassendeD) God laeligringE) Jeg har laeligrt meget

                                                                    2

                                                                    1

                                                                    3

                                                                    2

                                                                    0

                                                                    A B C D E

                                                                    Chart1

                                                                    2
                                                                    1
                                                                    3
                                                                    2
                                                                    0

                                                                    Sheet1

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                                                                    02511 - Sidste uges oslashvelser (pixelwiseoperations)A) Meget letteB) LetteC) PassendeD) SvaeligreE) Meget svaeligre

                                                                    0 0

                                                                    1

                                                                    4

                                                                    1

                                                                    A B C D E

                                                                    Chart1

                                                                    0
                                                                    0
                                                                    1
                                                                    4
                                                                    1

                                                                    Sheet1

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                                                                    02512 - Sidste uges oslashvelser (pixelwiseoperations)A) Meget letteB) LetteC) PassendeD) SvaeligreE) Meget svaeligre

                                                                    3

                                                                    0

                                                                    3

                                                                    0 0

                                                                    A B C D E

                                                                    Chart1

                                                                    3
                                                                    0
                                                                    3
                                                                    0
                                                                    0

                                                                    Sheet1

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                                                                    Denne uges brug af clickersA) click click click ndash jeg bliver

                                                                    sindssygB) For meget clickC) PassendeD) Jeg vil gerne have lidt mereE) Jeg kan ikrsquo faring nok

                                                                    0 0

                                                                    5

                                                                    0

                                                                    6

                                                                    A B C D E

                                                                    Chart1

                                                                    0
                                                                    0
                                                                    5
                                                                    0
                                                                    6

                                                                    Sheet1

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                                                                    What can you do after today Describe the difference between point processing and neighbourhood

                                                                    processing Compute a rank filtered image using the min max median and

                                                                    difference rank filters Compute a mean filtered image Decide if median or average filtering should be used for noise removal Choose the appropriate image border handling based on a given input

                                                                    image Implement and apply template matching Compute the normalised cross correlation and explain why it should be

                                                                    used Apply given image filter kernels to images Use edge filters on images Describe finite difference approximation of image gradients Describe the concept of edge detection

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                                                                    Oslashvelsesrapport over oslashvelse 4 - 02511 Oslashvelser taeligller cirka 30 af karakteren Skal afleveres senest den 7 marts kl 2359 Kan afleveres af 1 eller 2 personer

                                                                    ndash I skal skrive jeres egen oslashvelsesrapportndash Brug mindst et af jeres egne billeder

                                                                    Afleveres som PDF Lad vaeligre med at kopiere opgaveteksten ind i jeres

                                                                    opgave Put Matlab kode i et Appendix og henvis fra teksten Eksempel rapport over oslashvelse findes paring

                                                                    hjemmesiden under eksamen

                                                                    DTU Compute

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                                                                    Exercises

                                                                    • Introduction to Medical Image Analysis
                                                                    • Lecture 4 ndash Neighbourhood Processing
                                                                    • What can you do after today
                                                                    • Point processing
                                                                    • Point processing
                                                                    • Neighbourhood processing
                                                                    • Use of filtering
                                                                    • Salt and pepper noise
                                                                    • Salt and pepper noise
                                                                    • What is so special about noise
                                                                    • Noise ndash go away
                                                                    • What is the median Value
                                                                    • The median value
                                                                    • Noise away ndash the median filter
                                                                    • Noise removal ndash average filter
                                                                    • Noise removal ndash median filter
                                                                    • Image Filtering
                                                                    • Median filter
                                                                    • Rank filters
                                                                    • Median filter
                                                                    • Correlation
                                                                    • Why do we need similarity
                                                                    • Correlation (1D)
                                                                    • Correlation (1D)
                                                                    • Normalisation
                                                                    • Normalisation
                                                                    • Correlation on images
                                                                    • Correlation on images
                                                                    • Correlation on images
                                                                    • Draw your filter
                                                                    • Correlation on images ndash no normalisation
                                                                    • Correlation on images ndash no normalisation 2
                                                                    • Mathematics of 2D Correlation
                                                                    • Mathematics of 2D Correlation
                                                                    • Mathematics of 2D Correlation
                                                                    • Slide Number 40
                                                                    • 2D Kernel Normalisation
                                                                    • Correlation
                                                                    • Smoothing filters
                                                                    • Use of smoothing
                                                                    • Use of smoothing
                                                                    • Mean filter
                                                                    • Border handling
                                                                    • Border handling ndash extend the input
                                                                    • Correlation with zero padding
                                                                    • Border handling ndash extend the input
                                                                    • Template Matching
                                                                    • Template Matching
                                                                    • Template Matching
                                                                    • Template Matching
                                                                    • Problematic Correlation
                                                                    • Normalised Cross Correlation
                                                                    • Length of template
                                                                    • Length of image patch
                                                                    • Normalised Cross Correlation
                                                                    • Normalised Cross Correlation
                                                                    • Normalised Cross Correlation
                                                                    • Edges
                                                                    • Edges
                                                                    • Finite Difference
                                                                    • Edges
                                                                    • Edges in 2D
                                                                    • Edge filter kernel
                                                                    • Prewitt filter
                                                                    • Edge detection
                                                                    • Edge filtering
                                                                    • 02511 - Niveau af dagens emne forelaeligsing
                                                                    • 02512 - Niveau af dagens emne forelaeligsing
                                                                    • 02511 - Mit eget udbytte af dagen
                                                                    • 02512 - Mit eget udbytte af dagen
                                                                    • 02511 - Sidste uges oslashvelser (pixelwise operations)
                                                                    • 02512 - Sidste uges oslashvelser (pixelwise operations)
                                                                    • Denne uges brug af clickers
                                                                    • What can you do after today
                                                                    • Oslashvelsesrapport over oslashvelse 4 - 02511
                                                                    • Exercises
                                                                      A0
                                                                      B0
                                                                      C5
                                                                      D0
                                                                      E6
                                                                      A
                                                                      B
                                                                      C
                                                                      D
                                                                      E
                                                                      A3
                                                                      B0
                                                                      C3
                                                                      D0
                                                                      E0
                                                                      A
                                                                      B
                                                                      C
                                                                      D
                                                                      E
                                                                      A0
                                                                      B0
                                                                      C1
                                                                      D4
                                                                      E1
                                                                      A
                                                                      B
                                                                      C
                                                                      D
                                                                      E
                                                                      A2
                                                                      B1
                                                                      C3
                                                                      D2
                                                                      E0
                                                                      A
                                                                      B
                                                                      C
                                                                      D
                                                                      E
                                                                      A0
                                                                      B0
                                                                      C2
                                                                      D6
                                                                      E0
                                                                      A
                                                                      B
                                                                      C
                                                                      D
                                                                      E
                                                                      A0
                                                                      B0
                                                                      C1
                                                                      D0
                                                                      E0
                                                                      A
                                                                      B
                                                                      C
                                                                      D
                                                                      E
                                                                      A2
                                                                      B3
                                                                      C6
                                                                      D1
                                                                      E0
                                                                      A
                                                                      B
                                                                      C
                                                                      D
                                                                      E
                                                                      A0
                                                                      B8
                                                                      C1
                                                                      D1
                                                                      E0
                                                                      A
                                                                      B
                                                                      C
                                                                      D
                                                                      E
                                                                      A1
                                                                      B2
                                                                      C2
                                                                      D3
                                                                      E2
                                                                      A
                                                                      B
                                                                      C
                                                                      D
                                                                      E
                                                                      A0
                                                                      B13
                                                                      C0
                                                                      D0
                                                                      E0
                                                                      A
                                                                      B
                                                                      C
                                                                      D
                                                                      E
                                                                      A12
                                                                      B0
                                                                      C0
                                                                      D0
                                                                      E0
                                                                      A
                                                                      B
                                                                      C
                                                                      D
                                                                      E
                                                                      A0
                                                                      B0
                                                                      C0
                                                                      D0
                                                                      E13
                                                                      A
                                                                      B
                                                                      C
                                                                      D
                                                                      E
                                                                      A13
                                                                      B0
                                                                      C0
                                                                      D0
                                                                      E0
                                                                      A
                                                                      B
                                                                      C
                                                                      D
                                                                      E
                                                                      A1
                                                                      B0
                                                                      C14
                                                                      D0
                                                                      E0
                                                                      A
                                                                      B
                                                                      C
                                                                      D
                                                                      E

                                                                      DTU Compute

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                                                                      Correlation on images

                                                                      Input Output

                                                                      The mask is moved row by row

                                                                      No values at the border

                                                                      0 2 4

                                                                      1 2 2

                                                                      1 6 3

                                                                      1 2 0

                                                                      2 1 4

                                                                      1 0 1

                                                                      1 3 1

                                                                      2 2 2

                                                                      0 1 3

                                                                      1 2 12 5 3

                                                                      2 1 3

                                                                      DTU Compute

                                                                      2122018Introduction to Medical Image Analysis32 DTU Compute Technical University of Denmark

                                                                      1 2 1

                                                                      1 3 1

                                                                      1 2 1

                                                                      -1 -2 -1

                                                                      0 0 0

                                                                      1 2 1

                                                                      Draw your filter

                                                                      DTU Compute

                                                                      2122018Introduction to Medical Image Analysis33 DTU Compute Technical University of Denmark

                                                                      Correlation on images ndash no normalisationA) 4B) 7C) 16D) 23E) 25

                                                                      1 2 11 3 11 2 1

                                                                      0 2 41 2 2

                                                                      1 6 3

                                                                      1 2 12 5 3

                                                                      2 1 3

                                                                      1 3 1

                                                                      2 2 2

                                                                      0 1 3

                                                                      1 2 0

                                                                      2 1 4

                                                                      1 0 11 0

                                                                      14

                                                                      0 0

                                                                      A B C D E

                                                                      Chart1

                                                                      1
                                                                      0
                                                                      14
                                                                      0
                                                                      0

                                                                      Sheet1

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                                                                      Correlation on images ndash no normalisation 2A) 010B) 3 3C) 6 2D) 10 15E) 11 32

                                                                      13

                                                                      0 0 0 0

                                                                      A B C D E

                                                                      -1 -2 -10 0 01 2 1

                                                                      0 2 41 2 2

                                                                      1 6 3

                                                                      1 2 12 5 3

                                                                      2 1 3

                                                                      1 3 1

                                                                      2 2 2

                                                                      0 1 3

                                                                      1 2 0

                                                                      2 1 4

                                                                      1 0 1

                                                                      Chart1

                                                                      13
                                                                      0
                                                                      0
                                                                      0
                                                                      0

                                                                      Sheet1

                                                                      DTU Compute

                                                                      2122018Introduction to Medical Image Analysis37 DTU Compute Technical University of Denmark

                                                                      Mathematics of 2D Correlation

                                                                      h

                                                                      f

                                                                      Correlation operator

                                                                      1 2 11 3 11 2 1

                                                                      0 2 4

                                                                      1 2 2

                                                                      1 6 3

                                                                      1 2 1

                                                                      2 5 3

                                                                      2 1 3

                                                                      1 3 1

                                                                      2 2 2

                                                                      0 1 3

                                                                      1 2 0

                                                                      2 1 4

                                                                      1 0 1

                                                                      119892119892 119909119909119910119910 = 119891119891 119909119909119910119910 ∘ ℎ(119909119909119910119910)

                                                                      DTU Compute

                                                                      2122018Introduction to Medical Image Analysis38 DTU Compute Technical University of Denmark

                                                                      Mathematics of 2D Correlation

                                                                      1 2 11 3 11 2 1

                                                                      0 2 4

                                                                      1 2 2

                                                                      1 6 3

                                                                      1 2 1

                                                                      2 5 3

                                                                      2 1 3

                                                                      1 3 1

                                                                      2 2 2

                                                                      0 1 3

                                                                      1 2 0

                                                                      2 1 4

                                                                      1 0 1

                                                                      h

                                                                      fh(00)

                                                                      f(21)

                                                                      Example g(21)

                                                                      i = -1 j = -1

                                                                      i = 1 j = 0

                                                                      119892119892 119909119909119910119910 = 119895119895=minus119877119877

                                                                      119877119877

                                                                      119894119894=minus119877119877

                                                                      119877119877

                                                                      ℎ(119894119894 119895119895) 119891119891(119909119909 + 119894119894119910119910 + 119895119895)

                                                                      DTU Compute

                                                                      2122018Introduction to Medical Image Analysis39 DTU Compute Technical University of Denmark

                                                                      Mathematics of 2D Correlation

                                                                      1 2 11 3 11 2 1

                                                                      0 2 4

                                                                      1 2 2

                                                                      1 6 3

                                                                      1 2 1

                                                                      2 5 3

                                                                      2 1 3

                                                                      1 3 1

                                                                      2 2 2

                                                                      0 1 3

                                                                      1 2 0

                                                                      2 1 4

                                                                      1 0 1

                                                                      h

                                                                      f

                                                                      119892119892 119909119909119910119910 = 119895119895=minus119877119877

                                                                      119877119877

                                                                      119894119894=minus119877119877

                                                                      119877119877

                                                                      ℎ(119894119894 119895119895) 119891119891(119909119909 + 119894119894119910119910 + 119895119895)

                                                                      119892119892(119909119909119910119910 = 1 2 + 2 0 + 1 1 + 1 1 + 3 4 + 1 2 + 1 0 + 2 1 + 1 0

                                                                      DTU Compute

                                                                      2122018Introduction to Medical Image Analysis40 DTU Compute Technical University of Denmark

                                                                      119892119892 119909119909 119910119910 = 119895119895=minus119877119877

                                                                      119877119877

                                                                      119894119894=minus119877119877

                                                                      119877119877

                                                                      ℎ(119894119894 119895119895) 119891119891(119909119909 + 119894119894119910119910 + 119895119895)

                                                                      119892119892 22 =ℎ minus1minus1 sdot 119891119891 11 + ℎ 0minus1 sdot 119891119891 21 + ℎ 1minus1 sdot 119891119891 31 +ℎ minus10 sdot 119891119891 12 + ℎ 00 sdot 119891119891 22 + ℎ 10 sdot 119891119891 32 +ℎ minus11 sdot 119891119891 13 + ℎ 01 sdot 119891119891 23 + ℎ 11 sdot 119891119891 33

                                                                      DTU Compute

                                                                      2122018Introduction to Medical Image Analysis41 DTU Compute Technical University of Denmark

                                                                      2D Kernel Normalisation

                                                                      1 2 11 3 11 2 1

                                                                      h

                                                                      Normalisation factor

                                                                      1 + 2 + 1 + 1 + 3 + 1 + 1 + 2 + 1 = 13

                                                                      119909119909

                                                                      119910119910

                                                                      ℎ(119909119909119910119910)

                                                                      DTU Compute

                                                                      2122018Introduction to Medical Image Analysis42 DTU Compute Technical University of Denmark

                                                                      CorrelationA) 50122B) 123001C) 11233D) 2550E) 90454

                                                                      0 0 0 0

                                                                      13

                                                                      A B C D E

                                                                      Chart1

                                                                      0
                                                                      0
                                                                      0
                                                                      0
                                                                      13

                                                                      Sheet1

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                                                                      Smoothing filters

                                                                      Also know as ndash Smoothing kernel Mean filter Low pass filter blurring

                                                                      The simplest filter ndash Spatial low pass filterndash Removes high frequencies

                                                                      Another mask ndash Gaussian filter

                                                                      1 1 1

                                                                      1 1 1

                                                                      1 1 191

                                                                      1 2 1

                                                                      2 4 2

                                                                      1 2 1161

                                                                      Why Gaussian

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                                                                      Use of smoothing

                                                                      3x3 7x7 11x11 15x15

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                                                                      Use of smoothing Large kernels smooth more Removes high frequency information Good at enhancing big structures

                                                                      3x3 15x15

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                                                                      Mean filterA) 166B) 113C) 12D) 51E) 245

                                                                      0 0 0 0

                                                                      A B C D E

                                                                      Chart1

                                                                      12
                                                                      0
                                                                      0
                                                                      0
                                                                      0

                                                                      Sheet1

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                                                                      Border handling

                                                                      0 2 41 2 2

                                                                      1 6 3

                                                                      1 2 12 5 3

                                                                      2 1 3

                                                                      1 3 1

                                                                      2 2 2

                                                                      0 1 3

                                                                      1 2 0

                                                                      2 1 4

                                                                      1 0 1

                                                                      Input Output

                                                                      No values at the border

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                                                                      Border handling ndash extend the input

                                                                      0 2 41 2 2

                                                                      1 6 3

                                                                      1 2 12 5 3

                                                                      2 1 3

                                                                      1 3 1

                                                                      2 2 2

                                                                      0 1 3

                                                                      1 2 0

                                                                      2 1 4

                                                                      1 0 1

                                                                      Input

                                                                      0 0 0 0 000000

                                                                      bull Zero padding ndash what happens

                                                                      bull Zero is black ndash creates dark border around the image

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                                                                      Correlation with zero paddingA) 5 8B) 12 16C) 13 3D) 15 21E) 17 12

                                                                      1 2 11 3 11 2 1

                                                                      0 2 41 2 2

                                                                      1 6 3

                                                                      1 2 12 5 3

                                                                      2 1 3

                                                                      1 3 1

                                                                      2 2 2

                                                                      0 1 3

                                                                      1 2 0

                                                                      2 1 4

                                                                      1 0 1

                                                                      0

                                                                      13

                                                                      0 0 0

                                                                      A B C D E

                                                                      Chart1

                                                                      0
                                                                      13
                                                                      0
                                                                      0
                                                                      0

                                                                      Sheet1

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                                                                      Border handling ndash extend the input

                                                                      0 2 41 2 2

                                                                      1 6 3

                                                                      1 2 12 5 3

                                                                      2 1 3

                                                                      1 3 1

                                                                      2 2 2

                                                                      0 1 3

                                                                      1 2 0

                                                                      2 1 4

                                                                      1 0 1

                                                                      Input

                                                                      1 2 0 1 311211

                                                                      bull Reflection

                                                                      bull Normally better than zero padding

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                                                                      Template Matching Template

                                                                      ndash Skabelon paring dansk Locates objects in images

                                                                      Input

                                                                      Template

                                                                      Output Correlation image

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                                                                      Template Matching The correlation between the template and the input

                                                                      image is computed for each pixel

                                                                      Input

                                                                      Template

                                                                      Output Correlation image

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                                                                      Template Matching The pixel with the highest value is found in the

                                                                      output imagendash Here is the highest correlation

                                                                      Input

                                                                      Template

                                                                      Output Correlation image

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                                                                      Template Matching This corresponds to the found pattern in the input

                                                                      image

                                                                      Input

                                                                      Template

                                                                      Output Correlation image

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                                                                      Problematic Correlation Correlation matching has problem with light areas ndash

                                                                      why

                                                                      Input (f)

                                                                      Template (h)

                                                                      Output Correlation imageFake max

                                                                      Real max

                                                                      Very High119892119892 119909119909119910119910 = 119895119895=minus119877119877

                                                                      119877119877

                                                                      119894119894=minus119877119877

                                                                      119877119877

                                                                      ℎ(119894119894 119895119895) 119891119891(119909119909 + 119894119894119910119910 + 119895119895)

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                                                                      Normalised Cross Correlation

                                                                      Input (f)

                                                                      Template (h)

                                                                      Output Correlation image

                                                                      Real max

                                                                      NCC x y =Correlation

                                                                      Length of image patch sdot Length of template

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                                                                      Length of template Vector length

                                                                      ndash Put all pixel values into a vectorndash Compute the length of this vector

                                                                      Describes the intensity of the templatendash Bright template has a large lengthndash Dark template has a small length

                                                                      Template (h)

                                                                      Length of template = 119895119895=minus119877119877

                                                                      119877119877

                                                                      119894119894=minus119877119877

                                                                      119877119877

                                                                      ℎ(119894119894 119895119895) ℎ(119894119894 119895119895)

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                                                                      Length of image patch Vector length based on pixel values in image patch Describes the intensity of the image patch

                                                                      Template (h)

                                                                      Input (f) with patch

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                                                                      Normalised Cross Correlation The length of the image patch and the length of

                                                                      template normalise the NCC If the image is very bright the NCC will be ldquopulled

                                                                      downrdquo

                                                                      NCC x y =Correlation

                                                                      Length of image patch sdot Length of template

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                                                                      Normalised Cross Correlation NCC will be between

                                                                      ndash 0 No similarity between template and image patchndash 1 Template and image patch are identical

                                                                      Input (f)

                                                                      Template (h)

                                                                      Output Correlation image

                                                                      Real max

                                                                      NCC x y =Correlation

                                                                      Length of image patch sdot Length of template

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                                                                      Normalised Cross Correlation

                                                                      A) 010B) 033C) 083D) 062E) 098

                                                                      Der udfoslashres template matching med og normalized crosscorrelation (NCC) beregnes Hvad bliver NNC i den markerede pixel

                                                                      1

                                                                      2 2

                                                                      3

                                                                      2

                                                                      A B C D E

                                                                      Chart1

                                                                      1
                                                                      2
                                                                      2
                                                                      3
                                                                      2

                                                                      Sheet1

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                                                                      Edges An edge is where there is a

                                                                      high change in gray level values

                                                                      Objects are often separated from the background by edgesGray level profile

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                                                                      Edges The profile as a function f(d) What value is high when there

                                                                      is an edgendash The slope of fndash The slope of the tangent at d

                                                                      f(d)

                                                                      119891119891prime(119889119889)

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                                                                      Finite Difference Definition of slope

                                                                      Approximation

                                                                      Simpler approximationh = 1

                                                                      119891119891prime 119889119889 = limℎrarr0

                                                                      119891119891 119889119889 + ℎ minus 119891119891(119889119889)ℎ

                                                                      119891119891prime 119889119889 asymp119891119891 119889119889 + ℎ minus 119891119891(119889119889)

                                                                      ℎ

                                                                      119891119891prime 119889119889 asymp 119891119891 119889119889 + 1 minus 119891119891(119889119889)

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                                                                      Edges Discrete approximation of frsquo(d) Can be implemented as a filter

                                                                      -1 0 1

                                                                      f(d-2) f(d-1) f(d) f(d+1) f(d+2) f(d+3)

                                                                      f(d)

                                                                      119891119891prime 119889119889 asymp 119891119891 119889119889 + 1 minus 119891119891(119889119889)

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                                                                      Edges in 2D Changes in gray level values

                                                                      ndash Image gradientndash Gradient is the 2D derivative of a 2D function f(xy)ndash Equal to the slope of the imagendash A steep slope is equal to an edge

                                                                      120571120571119891119891 119909119909119910119910 = 119866(119892119892119909119909119892119892119910119910)

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                                                                      Edge filter kernel The Prewitt filter is a typical

                                                                      edge filter Output image has high

                                                                      values where there are edges

                                                                      -1 0 1

                                                                      -1 0 1

                                                                      -1 0 1Vertical Prewitt filter

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                                                                      Prewitt filter

                                                                      Original Prewitt Prewitt

                                                                      Hot colormapSmooth 15x15

                                                                      Smooth 15x15

                                                                      Prewitt

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                                                                      Edge detection Edge filter

                                                                      ndash Prewitt for example Thresholding

                                                                      ndash Separate edges from non-edges

                                                                      Output is binary imagendash Edges are white

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                                                                      Edge filtering

                                                                      A) MeanB) Horizontal SobelC) Vertical PrewittD) Horisontal PrewittE) Median

                                                                      Der udfoslashres en filtrering (correlation) med et filter paring billedet Der bruges ikke coefficient normalization Den filtrerede vaeligrdi i den markerede pixel bliver -119 Hvilket et 3x3 filter blev benyttet

                                                                      0

                                                                      8

                                                                      1 10

                                                                      A B C D E

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                                                                      1
                                                                      1
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                                                                      02511 - Niveau af dagens emne forelaeligsingA) Meget letB) LetC) PassendeD) SvaeligrtE) Meget svaeligrt

                                                                      23

                                                                      6

                                                                      10

                                                                      A B C D E

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                                                                      02512 - Niveau af dagens emne forelaeligsingA) Meget letB) LetC) PassendeD) SvaeligrtE) Meget svaeligrt

                                                                      0 0

                                                                      1

                                                                      0 0

                                                                      A B C D E

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                                                                      0
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                                                                      1
                                                                      0
                                                                      0

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                                                                      02511 - Mit eget udbytte af dagenA) Jeg har laeligrt meget lidtB) Lidt laeligringC) PassendeD) God laeligringE) Jeg har laeligrt meget

                                                                      0 0

                                                                      2

                                                                      6

                                                                      0

                                                                      A B C D E

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                                                                      0
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                                                                      2
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                                                                      02512 - Mit eget udbytte af dagenA) Jeg har laeligrt meget lidtB) Lidt laeligringC) PassendeD) God laeligringE) Jeg har laeligrt meget

                                                                      2

                                                                      1

                                                                      3

                                                                      2

                                                                      0

                                                                      A B C D E

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                                                                      2
                                                                      1
                                                                      3
                                                                      2
                                                                      0

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                                                                      02511 - Sidste uges oslashvelser (pixelwiseoperations)A) Meget letteB) LetteC) PassendeD) SvaeligreE) Meget svaeligre

                                                                      0 0

                                                                      1

                                                                      4

                                                                      1

                                                                      A B C D E

                                                                      Chart1

                                                                      0
                                                                      0
                                                                      1
                                                                      4
                                                                      1

                                                                      Sheet1

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                                                                      02512 - Sidste uges oslashvelser (pixelwiseoperations)A) Meget letteB) LetteC) PassendeD) SvaeligreE) Meget svaeligre

                                                                      3

                                                                      0

                                                                      3

                                                                      0 0

                                                                      A B C D E

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                                                                      0

                                                                      Sheet1

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                                                                      Denne uges brug af clickersA) click click click ndash jeg bliver

                                                                      sindssygB) For meget clickC) PassendeD) Jeg vil gerne have lidt mereE) Jeg kan ikrsquo faring nok

                                                                      0 0

                                                                      5

                                                                      0

                                                                      6

                                                                      A B C D E

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                                                                      5
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                                                                      What can you do after today Describe the difference between point processing and neighbourhood

                                                                      processing Compute a rank filtered image using the min max median and

                                                                      difference rank filters Compute a mean filtered image Decide if median or average filtering should be used for noise removal Choose the appropriate image border handling based on a given input

                                                                      image Implement and apply template matching Compute the normalised cross correlation and explain why it should be

                                                                      used Apply given image filter kernels to images Use edge filters on images Describe finite difference approximation of image gradients Describe the concept of edge detection

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                                                                      Oslashvelsesrapport over oslashvelse 4 - 02511 Oslashvelser taeligller cirka 30 af karakteren Skal afleveres senest den 7 marts kl 2359 Kan afleveres af 1 eller 2 personer

                                                                      ndash I skal skrive jeres egen oslashvelsesrapportndash Brug mindst et af jeres egne billeder

                                                                      Afleveres som PDF Lad vaeligre med at kopiere opgaveteksten ind i jeres

                                                                      opgave Put Matlab kode i et Appendix og henvis fra teksten Eksempel rapport over oslashvelse findes paring

                                                                      hjemmesiden under eksamen

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                                                                      2122018Introduction to Medical Image Analysis85 DTU Compute Technical University of Denmark

                                                                      Exercises

                                                                      • Introduction to Medical Image Analysis
                                                                      • Lecture 4 ndash Neighbourhood Processing
                                                                      • What can you do after today
                                                                      • Point processing
                                                                      • Point processing
                                                                      • Neighbourhood processing
                                                                      • Use of filtering
                                                                      • Salt and pepper noise
                                                                      • Salt and pepper noise
                                                                      • What is so special about noise
                                                                      • Noise ndash go away
                                                                      • What is the median Value
                                                                      • The median value
                                                                      • Noise away ndash the median filter
                                                                      • Noise removal ndash average filter
                                                                      • Noise removal ndash median filter
                                                                      • Image Filtering
                                                                      • Median filter
                                                                      • Rank filters
                                                                      • Median filter
                                                                      • Correlation
                                                                      • Why do we need similarity
                                                                      • Correlation (1D)
                                                                      • Correlation (1D)
                                                                      • Normalisation
                                                                      • Normalisation
                                                                      • Correlation on images
                                                                      • Correlation on images
                                                                      • Correlation on images
                                                                      • Draw your filter
                                                                      • Correlation on images ndash no normalisation
                                                                      • Correlation on images ndash no normalisation 2
                                                                      • Mathematics of 2D Correlation
                                                                      • Mathematics of 2D Correlation
                                                                      • Mathematics of 2D Correlation
                                                                      • Slide Number 40
                                                                      • 2D Kernel Normalisation
                                                                      • Correlation
                                                                      • Smoothing filters
                                                                      • Use of smoothing
                                                                      • Use of smoothing
                                                                      • Mean filter
                                                                      • Border handling
                                                                      • Border handling ndash extend the input
                                                                      • Correlation with zero padding
                                                                      • Border handling ndash extend the input
                                                                      • Template Matching
                                                                      • Template Matching
                                                                      • Template Matching
                                                                      • Template Matching
                                                                      • Problematic Correlation
                                                                      • Normalised Cross Correlation
                                                                      • Length of template
                                                                      • Length of image patch
                                                                      • Normalised Cross Correlation
                                                                      • Normalised Cross Correlation
                                                                      • Normalised Cross Correlation
                                                                      • Edges
                                                                      • Edges
                                                                      • Finite Difference
                                                                      • Edges
                                                                      • Edges in 2D
                                                                      • Edge filter kernel
                                                                      • Prewitt filter
                                                                      • Edge detection
                                                                      • Edge filtering
                                                                      • 02511 - Niveau af dagens emne forelaeligsing
                                                                      • 02512 - Niveau af dagens emne forelaeligsing
                                                                      • 02511 - Mit eget udbytte af dagen
                                                                      • 02512 - Mit eget udbytte af dagen
                                                                      • 02511 - Sidste uges oslashvelser (pixelwise operations)
                                                                      • 02512 - Sidste uges oslashvelser (pixelwise operations)
                                                                      • Denne uges brug af clickers
                                                                      • What can you do after today
                                                                      • Oslashvelsesrapport over oslashvelse 4 - 02511
                                                                      • Exercises
                                                                        A0
                                                                        B0
                                                                        C5
                                                                        D0
                                                                        E6
                                                                        A
                                                                        B
                                                                        C
                                                                        D
                                                                        E
                                                                        A3
                                                                        B0
                                                                        C3
                                                                        D0
                                                                        E0
                                                                        A
                                                                        B
                                                                        C
                                                                        D
                                                                        E
                                                                        A0
                                                                        B0
                                                                        C1
                                                                        D4
                                                                        E1
                                                                        A
                                                                        B
                                                                        C
                                                                        D
                                                                        E
                                                                        A2
                                                                        B1
                                                                        C3
                                                                        D2
                                                                        E0
                                                                        A
                                                                        B
                                                                        C
                                                                        D
                                                                        E
                                                                        A0
                                                                        B0
                                                                        C2
                                                                        D6
                                                                        E0
                                                                        A
                                                                        B
                                                                        C
                                                                        D
                                                                        E
                                                                        A0
                                                                        B0
                                                                        C1
                                                                        D0
                                                                        E0
                                                                        A
                                                                        B
                                                                        C
                                                                        D
                                                                        E
                                                                        A2
                                                                        B3
                                                                        C6
                                                                        D1
                                                                        E0
                                                                        A
                                                                        B
                                                                        C
                                                                        D
                                                                        E
                                                                        A0
                                                                        B8
                                                                        C1
                                                                        D1
                                                                        E0
                                                                        A
                                                                        B
                                                                        C
                                                                        D
                                                                        E
                                                                        A1
                                                                        B2
                                                                        C2
                                                                        D3
                                                                        E2
                                                                        A
                                                                        B
                                                                        C
                                                                        D
                                                                        E
                                                                        A0
                                                                        B13
                                                                        C0
                                                                        D0
                                                                        E0
                                                                        A
                                                                        B
                                                                        C
                                                                        D
                                                                        E
                                                                        A12
                                                                        B0
                                                                        C0
                                                                        D0
                                                                        E0
                                                                        A
                                                                        B
                                                                        C
                                                                        D
                                                                        E
                                                                        A0
                                                                        B0
                                                                        C0
                                                                        D0
                                                                        E13
                                                                        A
                                                                        B
                                                                        C
                                                                        D
                                                                        E
                                                                        A13
                                                                        B0
                                                                        C0
                                                                        D0
                                                                        E0
                                                                        A
                                                                        B
                                                                        C
                                                                        D
                                                                        E
                                                                        A1
                                                                        B0
                                                                        C14
                                                                        D0
                                                                        E0
                                                                        A
                                                                        B
                                                                        C
                                                                        D
                                                                        E

                                                                        DTU Compute

                                                                        2122018Introduction to Medical Image Analysis32 DTU Compute Technical University of Denmark

                                                                        1 2 1

                                                                        1 3 1

                                                                        1 2 1

                                                                        -1 -2 -1

                                                                        0 0 0

                                                                        1 2 1

                                                                        Draw your filter

                                                                        DTU Compute

                                                                        2122018Introduction to Medical Image Analysis33 DTU Compute Technical University of Denmark

                                                                        Correlation on images ndash no normalisationA) 4B) 7C) 16D) 23E) 25

                                                                        1 2 11 3 11 2 1

                                                                        0 2 41 2 2

                                                                        1 6 3

                                                                        1 2 12 5 3

                                                                        2 1 3

                                                                        1 3 1

                                                                        2 2 2

                                                                        0 1 3

                                                                        1 2 0

                                                                        2 1 4

                                                                        1 0 11 0

                                                                        14

                                                                        0 0

                                                                        A B C D E

                                                                        Chart1

                                                                        1
                                                                        0
                                                                        14
                                                                        0
                                                                        0

                                                                        Sheet1

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                                                                        Correlation on images ndash no normalisation 2A) 010B) 3 3C) 6 2D) 10 15E) 11 32

                                                                        13

                                                                        0 0 0 0

                                                                        A B C D E

                                                                        -1 -2 -10 0 01 2 1

                                                                        0 2 41 2 2

                                                                        1 6 3

                                                                        1 2 12 5 3

                                                                        2 1 3

                                                                        1 3 1

                                                                        2 2 2

                                                                        0 1 3

                                                                        1 2 0

                                                                        2 1 4

                                                                        1 0 1

                                                                        Chart1

                                                                        13
                                                                        0
                                                                        0
                                                                        0
                                                                        0

                                                                        Sheet1

                                                                        DTU Compute

                                                                        2122018Introduction to Medical Image Analysis37 DTU Compute Technical University of Denmark

                                                                        Mathematics of 2D Correlation

                                                                        h

                                                                        f

                                                                        Correlation operator

                                                                        1 2 11 3 11 2 1

                                                                        0 2 4

                                                                        1 2 2

                                                                        1 6 3

                                                                        1 2 1

                                                                        2 5 3

                                                                        2 1 3

                                                                        1 3 1

                                                                        2 2 2

                                                                        0 1 3

                                                                        1 2 0

                                                                        2 1 4

                                                                        1 0 1

                                                                        119892119892 119909119909119910119910 = 119891119891 119909119909119910119910 ∘ ℎ(119909119909119910119910)

                                                                        DTU Compute

                                                                        2122018Introduction to Medical Image Analysis38 DTU Compute Technical University of Denmark

                                                                        Mathematics of 2D Correlation

                                                                        1 2 11 3 11 2 1

                                                                        0 2 4

                                                                        1 2 2

                                                                        1 6 3

                                                                        1 2 1

                                                                        2 5 3

                                                                        2 1 3

                                                                        1 3 1

                                                                        2 2 2

                                                                        0 1 3

                                                                        1 2 0

                                                                        2 1 4

                                                                        1 0 1

                                                                        h

                                                                        fh(00)

                                                                        f(21)

                                                                        Example g(21)

                                                                        i = -1 j = -1

                                                                        i = 1 j = 0

                                                                        119892119892 119909119909119910119910 = 119895119895=minus119877119877

                                                                        119877119877

                                                                        119894119894=minus119877119877

                                                                        119877119877

                                                                        ℎ(119894119894 119895119895) 119891119891(119909119909 + 119894119894119910119910 + 119895119895)

                                                                        DTU Compute

                                                                        2122018Introduction to Medical Image Analysis39 DTU Compute Technical University of Denmark

                                                                        Mathematics of 2D Correlation

                                                                        1 2 11 3 11 2 1

                                                                        0 2 4

                                                                        1 2 2

                                                                        1 6 3

                                                                        1 2 1

                                                                        2 5 3

                                                                        2 1 3

                                                                        1 3 1

                                                                        2 2 2

                                                                        0 1 3

                                                                        1 2 0

                                                                        2 1 4

                                                                        1 0 1

                                                                        h

                                                                        f

                                                                        119892119892 119909119909119910119910 = 119895119895=minus119877119877

                                                                        119877119877

                                                                        119894119894=minus119877119877

                                                                        119877119877

                                                                        ℎ(119894119894 119895119895) 119891119891(119909119909 + 119894119894119910119910 + 119895119895)

                                                                        119892119892(119909119909119910119910 = 1 2 + 2 0 + 1 1 + 1 1 + 3 4 + 1 2 + 1 0 + 2 1 + 1 0

                                                                        DTU Compute

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                                                                        119892119892 119909119909 119910119910 = 119895119895=minus119877119877

                                                                        119877119877

                                                                        119894119894=minus119877119877

                                                                        119877119877

                                                                        ℎ(119894119894 119895119895) 119891119891(119909119909 + 119894119894119910119910 + 119895119895)

                                                                        119892119892 22 =ℎ minus1minus1 sdot 119891119891 11 + ℎ 0minus1 sdot 119891119891 21 + ℎ 1minus1 sdot 119891119891 31 +ℎ minus10 sdot 119891119891 12 + ℎ 00 sdot 119891119891 22 + ℎ 10 sdot 119891119891 32 +ℎ minus11 sdot 119891119891 13 + ℎ 01 sdot 119891119891 23 + ℎ 11 sdot 119891119891 33

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                                                                        2D Kernel Normalisation

                                                                        1 2 11 3 11 2 1

                                                                        h

                                                                        Normalisation factor

                                                                        1 + 2 + 1 + 1 + 3 + 1 + 1 + 2 + 1 = 13

                                                                        119909119909

                                                                        119910119910

                                                                        ℎ(119909119909119910119910)

                                                                        DTU Compute

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                                                                        CorrelationA) 50122B) 123001C) 11233D) 2550E) 90454

                                                                        0 0 0 0

                                                                        13

                                                                        A B C D E

                                                                        Chart1

                                                                        0
                                                                        0
                                                                        0
                                                                        0
                                                                        13

                                                                        Sheet1

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                                                                        Smoothing filters

                                                                        Also know as ndash Smoothing kernel Mean filter Low pass filter blurring

                                                                        The simplest filter ndash Spatial low pass filterndash Removes high frequencies

                                                                        Another mask ndash Gaussian filter

                                                                        1 1 1

                                                                        1 1 1

                                                                        1 1 191

                                                                        1 2 1

                                                                        2 4 2

                                                                        1 2 1161

                                                                        Why Gaussian

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                                                                        Use of smoothing

                                                                        3x3 7x7 11x11 15x15

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                                                                        Use of smoothing Large kernels smooth more Removes high frequency information Good at enhancing big structures

                                                                        3x3 15x15

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                                                                        Mean filterA) 166B) 113C) 12D) 51E) 245

                                                                        0 0 0 0

                                                                        A B C D E

                                                                        Chart1

                                                                        12
                                                                        0
                                                                        0
                                                                        0
                                                                        0

                                                                        Sheet1

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                                                                        Border handling

                                                                        0 2 41 2 2

                                                                        1 6 3

                                                                        1 2 12 5 3

                                                                        2 1 3

                                                                        1 3 1

                                                                        2 2 2

                                                                        0 1 3

                                                                        1 2 0

                                                                        2 1 4

                                                                        1 0 1

                                                                        Input Output

                                                                        No values at the border

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                                                                        Border handling ndash extend the input

                                                                        0 2 41 2 2

                                                                        1 6 3

                                                                        1 2 12 5 3

                                                                        2 1 3

                                                                        1 3 1

                                                                        2 2 2

                                                                        0 1 3

                                                                        1 2 0

                                                                        2 1 4

                                                                        1 0 1

                                                                        Input

                                                                        0 0 0 0 000000

                                                                        bull Zero padding ndash what happens

                                                                        bull Zero is black ndash creates dark border around the image

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                                                                        Correlation with zero paddingA) 5 8B) 12 16C) 13 3D) 15 21E) 17 12

                                                                        1 2 11 3 11 2 1

                                                                        0 2 41 2 2

                                                                        1 6 3

                                                                        1 2 12 5 3

                                                                        2 1 3

                                                                        1 3 1

                                                                        2 2 2

                                                                        0 1 3

                                                                        1 2 0

                                                                        2 1 4

                                                                        1 0 1

                                                                        0

                                                                        13

                                                                        0 0 0

                                                                        A B C D E

                                                                        Chart1

                                                                        0
                                                                        13
                                                                        0
                                                                        0
                                                                        0

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                                                                        Border handling ndash extend the input

                                                                        0 2 41 2 2

                                                                        1 6 3

                                                                        1 2 12 5 3

                                                                        2 1 3

                                                                        1 3 1

                                                                        2 2 2

                                                                        0 1 3

                                                                        1 2 0

                                                                        2 1 4

                                                                        1 0 1

                                                                        Input

                                                                        1 2 0 1 311211

                                                                        bull Reflection

                                                                        bull Normally better than zero padding

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                                                                        Template Matching Template

                                                                        ndash Skabelon paring dansk Locates objects in images

                                                                        Input

                                                                        Template

                                                                        Output Correlation image

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                                                                        Template Matching The correlation between the template and the input

                                                                        image is computed for each pixel

                                                                        Input

                                                                        Template

                                                                        Output Correlation image

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                                                                        Template Matching The pixel with the highest value is found in the

                                                                        output imagendash Here is the highest correlation

                                                                        Input

                                                                        Template

                                                                        Output Correlation image

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                                                                        Template Matching This corresponds to the found pattern in the input

                                                                        image

                                                                        Input

                                                                        Template

                                                                        Output Correlation image

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                                                                        Problematic Correlation Correlation matching has problem with light areas ndash

                                                                        why

                                                                        Input (f)

                                                                        Template (h)

                                                                        Output Correlation imageFake max

                                                                        Real max

                                                                        Very High119892119892 119909119909119910119910 = 119895119895=minus119877119877

                                                                        119877119877

                                                                        119894119894=minus119877119877

                                                                        119877119877

                                                                        ℎ(119894119894 119895119895) 119891119891(119909119909 + 119894119894119910119910 + 119895119895)

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                                                                        Normalised Cross Correlation

                                                                        Input (f)

                                                                        Template (h)

                                                                        Output Correlation image

                                                                        Real max

                                                                        NCC x y =Correlation

                                                                        Length of image patch sdot Length of template

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                                                                        Length of template Vector length

                                                                        ndash Put all pixel values into a vectorndash Compute the length of this vector

                                                                        Describes the intensity of the templatendash Bright template has a large lengthndash Dark template has a small length

                                                                        Template (h)

                                                                        Length of template = 119895119895=minus119877119877

                                                                        119877119877

                                                                        119894119894=minus119877119877

                                                                        119877119877

                                                                        ℎ(119894119894 119895119895) ℎ(119894119894 119895119895)

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                                                                        Length of image patch Vector length based on pixel values in image patch Describes the intensity of the image patch

                                                                        Template (h)

                                                                        Input (f) with patch

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                                                                        Normalised Cross Correlation The length of the image patch and the length of

                                                                        template normalise the NCC If the image is very bright the NCC will be ldquopulled

                                                                        downrdquo

                                                                        NCC x y =Correlation

                                                                        Length of image patch sdot Length of template

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                                                                        Normalised Cross Correlation NCC will be between

                                                                        ndash 0 No similarity between template and image patchndash 1 Template and image patch are identical

                                                                        Input (f)

                                                                        Template (h)

                                                                        Output Correlation image

                                                                        Real max

                                                                        NCC x y =Correlation

                                                                        Length of image patch sdot Length of template

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                                                                        Normalised Cross Correlation

                                                                        A) 010B) 033C) 083D) 062E) 098

                                                                        Der udfoslashres template matching med og normalized crosscorrelation (NCC) beregnes Hvad bliver NNC i den markerede pixel

                                                                        1

                                                                        2 2

                                                                        3

                                                                        2

                                                                        A B C D E

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                                                                        1
                                                                        2
                                                                        2
                                                                        3
                                                                        2

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                                                                        Edges An edge is where there is a

                                                                        high change in gray level values

                                                                        Objects are often separated from the background by edgesGray level profile

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                                                                        Edges The profile as a function f(d) What value is high when there

                                                                        is an edgendash The slope of fndash The slope of the tangent at d

                                                                        f(d)

                                                                        119891119891prime(119889119889)

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                                                                        Finite Difference Definition of slope

                                                                        Approximation

                                                                        Simpler approximationh = 1

                                                                        119891119891prime 119889119889 = limℎrarr0

                                                                        119891119891 119889119889 + ℎ minus 119891119891(119889119889)ℎ

                                                                        119891119891prime 119889119889 asymp119891119891 119889119889 + ℎ minus 119891119891(119889119889)

                                                                        ℎ

                                                                        119891119891prime 119889119889 asymp 119891119891 119889119889 + 1 minus 119891119891(119889119889)

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                                                                        Edges Discrete approximation of frsquo(d) Can be implemented as a filter

                                                                        -1 0 1

                                                                        f(d-2) f(d-1) f(d) f(d+1) f(d+2) f(d+3)

                                                                        f(d)

                                                                        119891119891prime 119889119889 asymp 119891119891 119889119889 + 1 minus 119891119891(119889119889)

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                                                                        Edges in 2D Changes in gray level values

                                                                        ndash Image gradientndash Gradient is the 2D derivative of a 2D function f(xy)ndash Equal to the slope of the imagendash A steep slope is equal to an edge

                                                                        120571120571119891119891 119909119909119910119910 = 119866(119892119892119909119909119892119892119910119910)

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                                                                        Edge filter kernel The Prewitt filter is a typical

                                                                        edge filter Output image has high

                                                                        values where there are edges

                                                                        -1 0 1

                                                                        -1 0 1

                                                                        -1 0 1Vertical Prewitt filter

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                                                                        Prewitt filter

                                                                        Original Prewitt Prewitt

                                                                        Hot colormapSmooth 15x15

                                                                        Smooth 15x15

                                                                        Prewitt

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                                                                        Edge detection Edge filter

                                                                        ndash Prewitt for example Thresholding

                                                                        ndash Separate edges from non-edges

                                                                        Output is binary imagendash Edges are white

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                                                                        Edge filtering

                                                                        A) MeanB) Horizontal SobelC) Vertical PrewittD) Horisontal PrewittE) Median

                                                                        Der udfoslashres en filtrering (correlation) med et filter paring billedet Der bruges ikke coefficient normalization Den filtrerede vaeligrdi i den markerede pixel bliver -119 Hvilket et 3x3 filter blev benyttet

                                                                        0

                                                                        8

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                                                                        02511 - Niveau af dagens emne forelaeligsingA) Meget letB) LetC) PassendeD) SvaeligrtE) Meget svaeligrt

                                                                        23

                                                                        6

                                                                        10

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                                                                        02512 - Niveau af dagens emne forelaeligsingA) Meget letB) LetC) PassendeD) SvaeligrtE) Meget svaeligrt

                                                                        0 0

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                                                                        02511 - Mit eget udbytte af dagenA) Jeg har laeligrt meget lidtB) Lidt laeligringC) PassendeD) God laeligringE) Jeg har laeligrt meget

                                                                        0 0

                                                                        2

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                                                                        02512 - Mit eget udbytte af dagenA) Jeg har laeligrt meget lidtB) Lidt laeligringC) PassendeD) God laeligringE) Jeg har laeligrt meget

                                                                        2

                                                                        1

                                                                        3

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                                                                        02511 - Sidste uges oslashvelser (pixelwiseoperations)A) Meget letteB) LetteC) PassendeD) SvaeligreE) Meget svaeligre

                                                                        0 0

                                                                        1

                                                                        4

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                                                                        02512 - Sidste uges oslashvelser (pixelwiseoperations)A) Meget letteB) LetteC) PassendeD) SvaeligreE) Meget svaeligre

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                                                                        Denne uges brug af clickersA) click click click ndash jeg bliver

                                                                        sindssygB) For meget clickC) PassendeD) Jeg vil gerne have lidt mereE) Jeg kan ikrsquo faring nok

                                                                        0 0

                                                                        5

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                                                                        What can you do after today Describe the difference between point processing and neighbourhood

                                                                        processing Compute a rank filtered image using the min max median and

                                                                        difference rank filters Compute a mean filtered image Decide if median or average filtering should be used for noise removal Choose the appropriate image border handling based on a given input

                                                                        image Implement and apply template matching Compute the normalised cross correlation and explain why it should be

                                                                        used Apply given image filter kernels to images Use edge filters on images Describe finite difference approximation of image gradients Describe the concept of edge detection

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                                                                        2122018Introduction to Medical Image Analysis84 DTU Compute Technical University of Denmark

                                                                        Oslashvelsesrapport over oslashvelse 4 - 02511 Oslashvelser taeligller cirka 30 af karakteren Skal afleveres senest den 7 marts kl 2359 Kan afleveres af 1 eller 2 personer

                                                                        ndash I skal skrive jeres egen oslashvelsesrapportndash Brug mindst et af jeres egne billeder

                                                                        Afleveres som PDF Lad vaeligre med at kopiere opgaveteksten ind i jeres

                                                                        opgave Put Matlab kode i et Appendix og henvis fra teksten Eksempel rapport over oslashvelse findes paring

                                                                        hjemmesiden under eksamen

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                                                                        2122018Introduction to Medical Image Analysis85 DTU Compute Technical University of Denmark

                                                                        Exercises

                                                                        • Introduction to Medical Image Analysis
                                                                        • Lecture 4 ndash Neighbourhood Processing
                                                                        • What can you do after today
                                                                        • Point processing
                                                                        • Point processing
                                                                        • Neighbourhood processing
                                                                        • Use of filtering
                                                                        • Salt and pepper noise
                                                                        • Salt and pepper noise
                                                                        • What is so special about noise
                                                                        • Noise ndash go away
                                                                        • What is the median Value
                                                                        • The median value
                                                                        • Noise away ndash the median filter
                                                                        • Noise removal ndash average filter
                                                                        • Noise removal ndash median filter
                                                                        • Image Filtering
                                                                        • Median filter
                                                                        • Rank filters
                                                                        • Median filter
                                                                        • Correlation
                                                                        • Why do we need similarity
                                                                        • Correlation (1D)
                                                                        • Correlation (1D)
                                                                        • Normalisation
                                                                        • Normalisation
                                                                        • Correlation on images
                                                                        • Correlation on images
                                                                        • Correlation on images
                                                                        • Draw your filter
                                                                        • Correlation on images ndash no normalisation
                                                                        • Correlation on images ndash no normalisation 2
                                                                        • Mathematics of 2D Correlation
                                                                        • Mathematics of 2D Correlation
                                                                        • Mathematics of 2D Correlation
                                                                        • Slide Number 40
                                                                        • 2D Kernel Normalisation
                                                                        • Correlation
                                                                        • Smoothing filters
                                                                        • Use of smoothing
                                                                        • Use of smoothing
                                                                        • Mean filter
                                                                        • Border handling
                                                                        • Border handling ndash extend the input
                                                                        • Correlation with zero padding
                                                                        • Border handling ndash extend the input
                                                                        • Template Matching
                                                                        • Template Matching
                                                                        • Template Matching
                                                                        • Template Matching
                                                                        • Problematic Correlation
                                                                        • Normalised Cross Correlation
                                                                        • Length of template
                                                                        • Length of image patch
                                                                        • Normalised Cross Correlation
                                                                        • Normalised Cross Correlation
                                                                        • Normalised Cross Correlation
                                                                        • Edges
                                                                        • Edges
                                                                        • Finite Difference
                                                                        • Edges
                                                                        • Edges in 2D
                                                                        • Edge filter kernel
                                                                        • Prewitt filter
                                                                        • Edge detection
                                                                        • Edge filtering
                                                                        • 02511 - Niveau af dagens emne forelaeligsing
                                                                        • 02512 - Niveau af dagens emne forelaeligsing
                                                                        • 02511 - Mit eget udbytte af dagen
                                                                        • 02512 - Mit eget udbytte af dagen
                                                                        • 02511 - Sidste uges oslashvelser (pixelwise operations)
                                                                        • 02512 - Sidste uges oslashvelser (pixelwise operations)
                                                                        • Denne uges brug af clickers
                                                                        • What can you do after today
                                                                        • Oslashvelsesrapport over oslashvelse 4 - 02511
                                                                        • Exercises
                                                                          A0
                                                                          B0
                                                                          C5
                                                                          D0
                                                                          E6
                                                                          A
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                                                                          D
                                                                          E
                                                                          A3
                                                                          B0
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                                                                          A
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                                                                          A0
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                                                                          D4
                                                                          E1
                                                                          A
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                                                                          A2
                                                                          B1
                                                                          C3
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                                                                          E0
                                                                          A
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                                                                          C2
                                                                          D6
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                                                                          A
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                                                                          D0
                                                                          E0
                                                                          A
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                                                                          A2
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                                                                          C6
                                                                          D1
                                                                          E0
                                                                          A
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                                                                          A0
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                                                                          E0
                                                                          A
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                                                                          A1
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                                                                          C2
                                                                          D3
                                                                          E2
                                                                          A
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                                                                          C
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                                                                          A0
                                                                          B13
                                                                          C0
                                                                          D0
                                                                          E0
                                                                          A
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                                                                          A12
                                                                          B0
                                                                          C0
                                                                          D0
                                                                          E0
                                                                          A
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                                                                          A0
                                                                          B0
                                                                          C0
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                                                                          E13
                                                                          A
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                                                                          A13
                                                                          B0
                                                                          C0
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                                                                          E0
                                                                          A
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                                                                          A1
                                                                          B0
                                                                          C14
                                                                          D0
                                                                          E0
                                                                          A
                                                                          B
                                                                          C
                                                                          D
                                                                          E

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                                                                          2122018Introduction to Medical Image Analysis33 DTU Compute Technical University of Denmark

                                                                          Correlation on images ndash no normalisationA) 4B) 7C) 16D) 23E) 25

                                                                          1 2 11 3 11 2 1

                                                                          0 2 41 2 2

                                                                          1 6 3

                                                                          1 2 12 5 3

                                                                          2 1 3

                                                                          1 3 1

                                                                          2 2 2

                                                                          0 1 3

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                                                                          1 0 11 0

                                                                          14

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                                                                          Correlation on images ndash no normalisation 2A) 010B) 3 3C) 6 2D) 10 15E) 11 32

                                                                          13

                                                                          0 0 0 0

                                                                          A B C D E

                                                                          -1 -2 -10 0 01 2 1

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                                                                          1 2 12 5 3

                                                                          2 1 3

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                                                                          Mathematics of 2D Correlation

                                                                          h

                                                                          f

                                                                          Correlation operator

                                                                          1 2 11 3 11 2 1

                                                                          0 2 4

                                                                          1 2 2

                                                                          1 6 3

                                                                          1 2 1

                                                                          2 5 3

                                                                          2 1 3

                                                                          1 3 1

                                                                          2 2 2

                                                                          0 1 3

                                                                          1 2 0

                                                                          2 1 4

                                                                          1 0 1

                                                                          119892119892 119909119909119910119910 = 119891119891 119909119909119910119910 ∘ ℎ(119909119909119910119910)

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                                                                          Mathematics of 2D Correlation

                                                                          1 2 11 3 11 2 1

                                                                          0 2 4

                                                                          1 2 2

                                                                          1 6 3

                                                                          1 2 1

                                                                          2 5 3

                                                                          2 1 3

                                                                          1 3 1

                                                                          2 2 2

                                                                          0 1 3

                                                                          1 2 0

                                                                          2 1 4

                                                                          1 0 1

                                                                          h

                                                                          fh(00)

                                                                          f(21)

                                                                          Example g(21)

                                                                          i = -1 j = -1

                                                                          i = 1 j = 0

                                                                          119892119892 119909119909119910119910 = 119895119895=minus119877119877

                                                                          119877119877

                                                                          119894119894=minus119877119877

                                                                          119877119877

                                                                          ℎ(119894119894 119895119895) 119891119891(119909119909 + 119894119894119910119910 + 119895119895)

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                                                                          Mathematics of 2D Correlation

                                                                          1 2 11 3 11 2 1

                                                                          0 2 4

                                                                          1 2 2

                                                                          1 6 3

                                                                          1 2 1

                                                                          2 5 3

                                                                          2 1 3

                                                                          1 3 1

                                                                          2 2 2

                                                                          0 1 3

                                                                          1 2 0

                                                                          2 1 4

                                                                          1 0 1

                                                                          h

                                                                          f

                                                                          119892119892 119909119909119910119910 = 119895119895=minus119877119877

                                                                          119877119877

                                                                          119894119894=minus119877119877

                                                                          119877119877

                                                                          ℎ(119894119894 119895119895) 119891119891(119909119909 + 119894119894119910119910 + 119895119895)

                                                                          119892119892(119909119909119910119910 = 1 2 + 2 0 + 1 1 + 1 1 + 3 4 + 1 2 + 1 0 + 2 1 + 1 0

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                                                                          119892119892 119909119909 119910119910 = 119895119895=minus119877119877

                                                                          119877119877

                                                                          119894119894=minus119877119877

                                                                          119877119877

                                                                          ℎ(119894119894 119895119895) 119891119891(119909119909 + 119894119894119910119910 + 119895119895)

                                                                          119892119892 22 =ℎ minus1minus1 sdot 119891119891 11 + ℎ 0minus1 sdot 119891119891 21 + ℎ 1minus1 sdot 119891119891 31 +ℎ minus10 sdot 119891119891 12 + ℎ 00 sdot 119891119891 22 + ℎ 10 sdot 119891119891 32 +ℎ minus11 sdot 119891119891 13 + ℎ 01 sdot 119891119891 23 + ℎ 11 sdot 119891119891 33

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                                                                          2D Kernel Normalisation

                                                                          1 2 11 3 11 2 1

                                                                          h

                                                                          Normalisation factor

                                                                          1 + 2 + 1 + 1 + 3 + 1 + 1 + 2 + 1 = 13

                                                                          119909119909

                                                                          119910119910

                                                                          ℎ(119909119909119910119910)

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                                                                          CorrelationA) 50122B) 123001C) 11233D) 2550E) 90454

                                                                          0 0 0 0

                                                                          13

                                                                          A B C D E

                                                                          Chart1

                                                                          0
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                                                                          0
                                                                          0
                                                                          13

                                                                          Sheet1

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                                                                          Smoothing filters

                                                                          Also know as ndash Smoothing kernel Mean filter Low pass filter blurring

                                                                          The simplest filter ndash Spatial low pass filterndash Removes high frequencies

                                                                          Another mask ndash Gaussian filter

                                                                          1 1 1

                                                                          1 1 1

                                                                          1 1 191

                                                                          1 2 1

                                                                          2 4 2

                                                                          1 2 1161

                                                                          Why Gaussian

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                                                                          Use of smoothing

                                                                          3x3 7x7 11x11 15x15

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                                                                          Use of smoothing Large kernels smooth more Removes high frequency information Good at enhancing big structures

                                                                          3x3 15x15

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                                                                          Mean filterA) 166B) 113C) 12D) 51E) 245

                                                                          0 0 0 0

                                                                          A B C D E

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                                                                          12
                                                                          0
                                                                          0
                                                                          0
                                                                          0

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                                                                          Border handling

                                                                          0 2 41 2 2

                                                                          1 6 3

                                                                          1 2 12 5 3

                                                                          2 1 3

                                                                          1 3 1

                                                                          2 2 2

                                                                          0 1 3

                                                                          1 2 0

                                                                          2 1 4

                                                                          1 0 1

                                                                          Input Output

                                                                          No values at the border

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                                                                          Border handling ndash extend the input

                                                                          0 2 41 2 2

                                                                          1 6 3

                                                                          1 2 12 5 3

                                                                          2 1 3

                                                                          1 3 1

                                                                          2 2 2

                                                                          0 1 3

                                                                          1 2 0

                                                                          2 1 4

                                                                          1 0 1

                                                                          Input

                                                                          0 0 0 0 000000

                                                                          bull Zero padding ndash what happens

                                                                          bull Zero is black ndash creates dark border around the image

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                                                                          Correlation with zero paddingA) 5 8B) 12 16C) 13 3D) 15 21E) 17 12

                                                                          1 2 11 3 11 2 1

                                                                          0 2 41 2 2

                                                                          1 6 3

                                                                          1 2 12 5 3

                                                                          2 1 3

                                                                          1 3 1

                                                                          2 2 2

                                                                          0 1 3

                                                                          1 2 0

                                                                          2 1 4

                                                                          1 0 1

                                                                          0

                                                                          13

                                                                          0 0 0

                                                                          A B C D E

                                                                          Chart1

                                                                          0
                                                                          13
                                                                          0
                                                                          0
                                                                          0

                                                                          Sheet1

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                                                                          Border handling ndash extend the input

                                                                          0 2 41 2 2

                                                                          1 6 3

                                                                          1 2 12 5 3

                                                                          2 1 3

                                                                          1 3 1

                                                                          2 2 2

                                                                          0 1 3

                                                                          1 2 0

                                                                          2 1 4

                                                                          1 0 1

                                                                          Input

                                                                          1 2 0 1 311211

                                                                          bull Reflection

                                                                          bull Normally better than zero padding

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                                                                          Template Matching Template

                                                                          ndash Skabelon paring dansk Locates objects in images

                                                                          Input

                                                                          Template

                                                                          Output Correlation image

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                                                                          Template Matching The correlation between the template and the input

                                                                          image is computed for each pixel

                                                                          Input

                                                                          Template

                                                                          Output Correlation image

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                                                                          Template Matching The pixel with the highest value is found in the

                                                                          output imagendash Here is the highest correlation

                                                                          Input

                                                                          Template

                                                                          Output Correlation image

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                                                                          Template Matching This corresponds to the found pattern in the input

                                                                          image

                                                                          Input

                                                                          Template

                                                                          Output Correlation image

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                                                                          Problematic Correlation Correlation matching has problem with light areas ndash

                                                                          why

                                                                          Input (f)

                                                                          Template (h)

                                                                          Output Correlation imageFake max

                                                                          Real max

                                                                          Very High119892119892 119909119909119910119910 = 119895119895=minus119877119877

                                                                          119877119877

                                                                          119894119894=minus119877119877

                                                                          119877119877

                                                                          ℎ(119894119894 119895119895) 119891119891(119909119909 + 119894119894119910119910 + 119895119895)

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                                                                          Normalised Cross Correlation

                                                                          Input (f)

                                                                          Template (h)

                                                                          Output Correlation image

                                                                          Real max

                                                                          NCC x y =Correlation

                                                                          Length of image patch sdot Length of template

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                                                                          Length of template Vector length

                                                                          ndash Put all pixel values into a vectorndash Compute the length of this vector

                                                                          Describes the intensity of the templatendash Bright template has a large lengthndash Dark template has a small length

                                                                          Template (h)

                                                                          Length of template = 119895119895=minus119877119877

                                                                          119877119877

                                                                          119894119894=minus119877119877

                                                                          119877119877

                                                                          ℎ(119894119894 119895119895) ℎ(119894119894 119895119895)

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                                                                          Length of image patch Vector length based on pixel values in image patch Describes the intensity of the image patch

                                                                          Template (h)

                                                                          Input (f) with patch

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                                                                          Normalised Cross Correlation The length of the image patch and the length of

                                                                          template normalise the NCC If the image is very bright the NCC will be ldquopulled

                                                                          downrdquo

                                                                          NCC x y =Correlation

                                                                          Length of image patch sdot Length of template

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                                                                          Normalised Cross Correlation NCC will be between

                                                                          ndash 0 No similarity between template and image patchndash 1 Template and image patch are identical

                                                                          Input (f)

                                                                          Template (h)

                                                                          Output Correlation image

                                                                          Real max

                                                                          NCC x y =Correlation

                                                                          Length of image patch sdot Length of template

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                                                                          Normalised Cross Correlation

                                                                          A) 010B) 033C) 083D) 062E) 098

                                                                          Der udfoslashres template matching med og normalized crosscorrelation (NCC) beregnes Hvad bliver NNC i den markerede pixel

                                                                          1

                                                                          2 2

                                                                          3

                                                                          2

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                                                                          Edges An edge is where there is a

                                                                          high change in gray level values

                                                                          Objects are often separated from the background by edgesGray level profile

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                                                                          Edges The profile as a function f(d) What value is high when there

                                                                          is an edgendash The slope of fndash The slope of the tangent at d

                                                                          f(d)

                                                                          119891119891prime(119889119889)

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                                                                          Finite Difference Definition of slope

                                                                          Approximation

                                                                          Simpler approximationh = 1

                                                                          119891119891prime 119889119889 = limℎrarr0

                                                                          119891119891 119889119889 + ℎ minus 119891119891(119889119889)ℎ

                                                                          119891119891prime 119889119889 asymp119891119891 119889119889 + ℎ minus 119891119891(119889119889)

                                                                          ℎ

                                                                          119891119891prime 119889119889 asymp 119891119891 119889119889 + 1 minus 119891119891(119889119889)

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                                                                          Edges Discrete approximation of frsquo(d) Can be implemented as a filter

                                                                          -1 0 1

                                                                          f(d-2) f(d-1) f(d) f(d+1) f(d+2) f(d+3)

                                                                          f(d)

                                                                          119891119891prime 119889119889 asymp 119891119891 119889119889 + 1 minus 119891119891(119889119889)

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                                                                          Edges in 2D Changes in gray level values

                                                                          ndash Image gradientndash Gradient is the 2D derivative of a 2D function f(xy)ndash Equal to the slope of the imagendash A steep slope is equal to an edge

                                                                          120571120571119891119891 119909119909119910119910 = 119866(119892119892119909119909119892119892119910119910)

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                                                                          Edge filter kernel The Prewitt filter is a typical

                                                                          edge filter Output image has high

                                                                          values where there are edges

                                                                          -1 0 1

                                                                          -1 0 1

                                                                          -1 0 1Vertical Prewitt filter

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                                                                          Prewitt filter

                                                                          Original Prewitt Prewitt

                                                                          Hot colormapSmooth 15x15

                                                                          Smooth 15x15

                                                                          Prewitt

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                                                                          Edge detection Edge filter

                                                                          ndash Prewitt for example Thresholding

                                                                          ndash Separate edges from non-edges

                                                                          Output is binary imagendash Edges are white

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                                                                          Edge filtering

                                                                          A) MeanB) Horizontal SobelC) Vertical PrewittD) Horisontal PrewittE) Median

                                                                          Der udfoslashres en filtrering (correlation) med et filter paring billedet Der bruges ikke coefficient normalization Den filtrerede vaeligrdi i den markerede pixel bliver -119 Hvilket et 3x3 filter blev benyttet

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                                                                          02511 - Niveau af dagens emne forelaeligsingA) Meget letB) LetC) PassendeD) SvaeligrtE) Meget svaeligrt

                                                                          23

                                                                          6

                                                                          10

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                                                                          02512 - Niveau af dagens emne forelaeligsingA) Meget letB) LetC) PassendeD) SvaeligrtE) Meget svaeligrt

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                                                                          02511 - Mit eget udbytte af dagenA) Jeg har laeligrt meget lidtB) Lidt laeligringC) PassendeD) God laeligringE) Jeg har laeligrt meget

                                                                          0 0

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                                                                          02512 - Mit eget udbytte af dagenA) Jeg har laeligrt meget lidtB) Lidt laeligringC) PassendeD) God laeligringE) Jeg har laeligrt meget

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                                                                          02511 - Sidste uges oslashvelser (pixelwiseoperations)A) Meget letteB) LetteC) PassendeD) SvaeligreE) Meget svaeligre

                                                                          0 0

                                                                          1

                                                                          4

                                                                          1

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                                                                          02512 - Sidste uges oslashvelser (pixelwiseoperations)A) Meget letteB) LetteC) PassendeD) SvaeligreE) Meget svaeligre

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                                                                          0

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                                                                          Denne uges brug af clickersA) click click click ndash jeg bliver

                                                                          sindssygB) For meget clickC) PassendeD) Jeg vil gerne have lidt mereE) Jeg kan ikrsquo faring nok

                                                                          0 0

                                                                          5

                                                                          0

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                                                                          What can you do after today Describe the difference between point processing and neighbourhood

                                                                          processing Compute a rank filtered image using the min max median and

                                                                          difference rank filters Compute a mean filtered image Decide if median or average filtering should be used for noise removal Choose the appropriate image border handling based on a given input

                                                                          image Implement and apply template matching Compute the normalised cross correlation and explain why it should be

                                                                          used Apply given image filter kernels to images Use edge filters on images Describe finite difference approximation of image gradients Describe the concept of edge detection

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                                                                          Oslashvelsesrapport over oslashvelse 4 - 02511 Oslashvelser taeligller cirka 30 af karakteren Skal afleveres senest den 7 marts kl 2359 Kan afleveres af 1 eller 2 personer

                                                                          ndash I skal skrive jeres egen oslashvelsesrapportndash Brug mindst et af jeres egne billeder

                                                                          Afleveres som PDF Lad vaeligre med at kopiere opgaveteksten ind i jeres

                                                                          opgave Put Matlab kode i et Appendix og henvis fra teksten Eksempel rapport over oslashvelse findes paring

                                                                          hjemmesiden under eksamen

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                                                                          Exercises

                                                                          • Introduction to Medical Image Analysis
                                                                          • Lecture 4 ndash Neighbourhood Processing
                                                                          • What can you do after today
                                                                          • Point processing
                                                                          • Point processing
                                                                          • Neighbourhood processing
                                                                          • Use of filtering
                                                                          • Salt and pepper noise
                                                                          • Salt and pepper noise
                                                                          • What is so special about noise
                                                                          • Noise ndash go away
                                                                          • What is the median Value
                                                                          • The median value
                                                                          • Noise away ndash the median filter
                                                                          • Noise removal ndash average filter
                                                                          • Noise removal ndash median filter
                                                                          • Image Filtering
                                                                          • Median filter
                                                                          • Rank filters
                                                                          • Median filter
                                                                          • Correlation
                                                                          • Why do we need similarity
                                                                          • Correlation (1D)
                                                                          • Correlation (1D)
                                                                          • Normalisation
                                                                          • Normalisation
                                                                          • Correlation on images
                                                                          • Correlation on images
                                                                          • Correlation on images
                                                                          • Draw your filter
                                                                          • Correlation on images ndash no normalisation
                                                                          • Correlation on images ndash no normalisation 2
                                                                          • Mathematics of 2D Correlation
                                                                          • Mathematics of 2D Correlation
                                                                          • Mathematics of 2D Correlation
                                                                          • Slide Number 40
                                                                          • 2D Kernel Normalisation
                                                                          • Correlation
                                                                          • Smoothing filters
                                                                          • Use of smoothing
                                                                          • Use of smoothing
                                                                          • Mean filter
                                                                          • Border handling
                                                                          • Border handling ndash extend the input
                                                                          • Correlation with zero padding
                                                                          • Border handling ndash extend the input
                                                                          • Template Matching
                                                                          • Template Matching
                                                                          • Template Matching
                                                                          • Template Matching
                                                                          • Problematic Correlation
                                                                          • Normalised Cross Correlation
                                                                          • Length of template
                                                                          • Length of image patch
                                                                          • Normalised Cross Correlation
                                                                          • Normalised Cross Correlation
                                                                          • Normalised Cross Correlation
                                                                          • Edges
                                                                          • Edges
                                                                          • Finite Difference
                                                                          • Edges
                                                                          • Edges in 2D
                                                                          • Edge filter kernel
                                                                          • Prewitt filter
                                                                          • Edge detection
                                                                          • Edge filtering
                                                                          • 02511 - Niveau af dagens emne forelaeligsing
                                                                          • 02512 - Niveau af dagens emne forelaeligsing
                                                                          • 02511 - Mit eget udbytte af dagen
                                                                          • 02512 - Mit eget udbytte af dagen
                                                                          • 02511 - Sidste uges oslashvelser (pixelwise operations)
                                                                          • 02512 - Sidste uges oslashvelser (pixelwise operations)
                                                                          • Denne uges brug af clickers
                                                                          • What can you do after today
                                                                          • Oslashvelsesrapport over oslashvelse 4 - 02511
                                                                          • Exercises
                                                                            A0
                                                                            B0
                                                                            C5
                                                                            D0
                                                                            E6
                                                                            A
                                                                            B
                                                                            C
                                                                            D
                                                                            E
                                                                            A3
                                                                            B0
                                                                            C3
                                                                            D0
                                                                            E0
                                                                            A
                                                                            B
                                                                            C
                                                                            D
                                                                            E
                                                                            A0
                                                                            B0
                                                                            C1
                                                                            D4
                                                                            E1
                                                                            A
                                                                            B
                                                                            C
                                                                            D
                                                                            E
                                                                            A2
                                                                            B1
                                                                            C3
                                                                            D2
                                                                            E0
                                                                            A
                                                                            B
                                                                            C
                                                                            D
                                                                            E
                                                                            A0
                                                                            B0
                                                                            C2
                                                                            D6
                                                                            E0
                                                                            A
                                                                            B
                                                                            C
                                                                            D
                                                                            E
                                                                            A0
                                                                            B0
                                                                            C1
                                                                            D0
                                                                            E0
                                                                            A
                                                                            B
                                                                            C
                                                                            D
                                                                            E
                                                                            A2
                                                                            B3
                                                                            C6
                                                                            D1
                                                                            E0
                                                                            A
                                                                            B
                                                                            C
                                                                            D
                                                                            E
                                                                            A0
                                                                            B8
                                                                            C1
                                                                            D1
                                                                            E0
                                                                            A
                                                                            B
                                                                            C
                                                                            D
                                                                            E
                                                                            A1
                                                                            B2
                                                                            C2
                                                                            D3
                                                                            E2
                                                                            A
                                                                            B
                                                                            C
                                                                            D
                                                                            E
                                                                            A0
                                                                            B13
                                                                            C0
                                                                            D0
                                                                            E0
                                                                            A
                                                                            B
                                                                            C
                                                                            D
                                                                            E
                                                                            A12
                                                                            B0
                                                                            C0
                                                                            D0
                                                                            E0
                                                                            A
                                                                            B
                                                                            C
                                                                            D
                                                                            E
                                                                            A0
                                                                            B0
                                                                            C0
                                                                            D0
                                                                            E13
                                                                            A
                                                                            B
                                                                            C
                                                                            D
                                                                            E
                                                                            A13
                                                                            B0
                                                                            C0
                                                                            D0
                                                                            E0
                                                                            A
                                                                            B
                                                                            C
                                                                            D
                                                                            E
                                                                            A1
                                                                            B0
                                                                            C14
                                                                            D0
                                                                            E0
                                                                            A
                                                                            B
                                                                            C
                                                                            D
                                                                            E

                                                                            Chart1

                                                                            1
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                                                                            14
                                                                            0
                                                                            0

                                                                            Sheet1

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                                                                            Correlation on images ndash no normalisation 2A) 010B) 3 3C) 6 2D) 10 15E) 11 32

                                                                            13

                                                                            0 0 0 0

                                                                            A B C D E

                                                                            -1 -2 -10 0 01 2 1

                                                                            0 2 41 2 2

                                                                            1 6 3

                                                                            1 2 12 5 3

                                                                            2 1 3

                                                                            1 3 1

                                                                            2 2 2

                                                                            0 1 3

                                                                            1 2 0

                                                                            2 1 4

                                                                            1 0 1

                                                                            Chart1

                                                                            13
                                                                            0
                                                                            0
                                                                            0
                                                                            0

                                                                            Sheet1

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                                                                            Mathematics of 2D Correlation

                                                                            h

                                                                            f

                                                                            Correlation operator

                                                                            1 2 11 3 11 2 1

                                                                            0 2 4

                                                                            1 2 2

                                                                            1 6 3

                                                                            1 2 1

                                                                            2 5 3

                                                                            2 1 3

                                                                            1 3 1

                                                                            2 2 2

                                                                            0 1 3

                                                                            1 2 0

                                                                            2 1 4

                                                                            1 0 1

                                                                            119892119892 119909119909119910119910 = 119891119891 119909119909119910119910 ∘ ℎ(119909119909119910119910)

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                                                                            Mathematics of 2D Correlation

                                                                            1 2 11 3 11 2 1

                                                                            0 2 4

                                                                            1 2 2

                                                                            1 6 3

                                                                            1 2 1

                                                                            2 5 3

                                                                            2 1 3

                                                                            1 3 1

                                                                            2 2 2

                                                                            0 1 3

                                                                            1 2 0

                                                                            2 1 4

                                                                            1 0 1

                                                                            h

                                                                            fh(00)

                                                                            f(21)

                                                                            Example g(21)

                                                                            i = -1 j = -1

                                                                            i = 1 j = 0

                                                                            119892119892 119909119909119910119910 = 119895119895=minus119877119877

                                                                            119877119877

                                                                            119894119894=minus119877119877

                                                                            119877119877

                                                                            ℎ(119894119894 119895119895) 119891119891(119909119909 + 119894119894119910119910 + 119895119895)

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                                                                            Mathematics of 2D Correlation

                                                                            1 2 11 3 11 2 1

                                                                            0 2 4

                                                                            1 2 2

                                                                            1 6 3

                                                                            1 2 1

                                                                            2 5 3

                                                                            2 1 3

                                                                            1 3 1

                                                                            2 2 2

                                                                            0 1 3

                                                                            1 2 0

                                                                            2 1 4

                                                                            1 0 1

                                                                            h

                                                                            f

                                                                            119892119892 119909119909119910119910 = 119895119895=minus119877119877

                                                                            119877119877

                                                                            119894119894=minus119877119877

                                                                            119877119877

                                                                            ℎ(119894119894 119895119895) 119891119891(119909119909 + 119894119894119910119910 + 119895119895)

                                                                            119892119892(119909119909119910119910 = 1 2 + 2 0 + 1 1 + 1 1 + 3 4 + 1 2 + 1 0 + 2 1 + 1 0

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                                                                            119892119892 119909119909 119910119910 = 119895119895=minus119877119877

                                                                            119877119877

                                                                            119894119894=minus119877119877

                                                                            119877119877

                                                                            ℎ(119894119894 119895119895) 119891119891(119909119909 + 119894119894119910119910 + 119895119895)

                                                                            119892119892 22 =ℎ minus1minus1 sdot 119891119891 11 + ℎ 0minus1 sdot 119891119891 21 + ℎ 1minus1 sdot 119891119891 31 +ℎ minus10 sdot 119891119891 12 + ℎ 00 sdot 119891119891 22 + ℎ 10 sdot 119891119891 32 +ℎ minus11 sdot 119891119891 13 + ℎ 01 sdot 119891119891 23 + ℎ 11 sdot 119891119891 33

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                                                                            2D Kernel Normalisation

                                                                            1 2 11 3 11 2 1

                                                                            h

                                                                            Normalisation factor

                                                                            1 + 2 + 1 + 1 + 3 + 1 + 1 + 2 + 1 = 13

                                                                            119909119909

                                                                            119910119910

                                                                            ℎ(119909119909119910119910)

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                                                                            CorrelationA) 50122B) 123001C) 11233D) 2550E) 90454

                                                                            0 0 0 0

                                                                            13

                                                                            A B C D E

                                                                            Chart1

                                                                            0
                                                                            0
                                                                            0
                                                                            0
                                                                            13

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                                                                            Smoothing filters

                                                                            Also know as ndash Smoothing kernel Mean filter Low pass filter blurring

                                                                            The simplest filter ndash Spatial low pass filterndash Removes high frequencies

                                                                            Another mask ndash Gaussian filter

                                                                            1 1 1

                                                                            1 1 1

                                                                            1 1 191

                                                                            1 2 1

                                                                            2 4 2

                                                                            1 2 1161

                                                                            Why Gaussian

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                                                                            Use of smoothing

                                                                            3x3 7x7 11x11 15x15

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                                                                            Use of smoothing Large kernels smooth more Removes high frequency information Good at enhancing big structures

                                                                            3x3 15x15

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                                                                            Mean filterA) 166B) 113C) 12D) 51E) 245

                                                                            0 0 0 0

                                                                            A B C D E

                                                                            Chart1

                                                                            12
                                                                            0
                                                                            0
                                                                            0
                                                                            0

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                                                                            Border handling

                                                                            0 2 41 2 2

                                                                            1 6 3

                                                                            1 2 12 5 3

                                                                            2 1 3

                                                                            1 3 1

                                                                            2 2 2

                                                                            0 1 3

                                                                            1 2 0

                                                                            2 1 4

                                                                            1 0 1

                                                                            Input Output

                                                                            No values at the border

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                                                                            Border handling ndash extend the input

                                                                            0 2 41 2 2

                                                                            1 6 3

                                                                            1 2 12 5 3

                                                                            2 1 3

                                                                            1 3 1

                                                                            2 2 2

                                                                            0 1 3

                                                                            1 2 0

                                                                            2 1 4

                                                                            1 0 1

                                                                            Input

                                                                            0 0 0 0 000000

                                                                            bull Zero padding ndash what happens

                                                                            bull Zero is black ndash creates dark border around the image

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                                                                            Correlation with zero paddingA) 5 8B) 12 16C) 13 3D) 15 21E) 17 12

                                                                            1 2 11 3 11 2 1

                                                                            0 2 41 2 2

                                                                            1 6 3

                                                                            1 2 12 5 3

                                                                            2 1 3

                                                                            1 3 1

                                                                            2 2 2

                                                                            0 1 3

                                                                            1 2 0

                                                                            2 1 4

                                                                            1 0 1

                                                                            0

                                                                            13

                                                                            0 0 0

                                                                            A B C D E

                                                                            Chart1

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                                                                            13
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                                                                            0
                                                                            0

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                                                                            Border handling ndash extend the input

                                                                            0 2 41 2 2

                                                                            1 6 3

                                                                            1 2 12 5 3

                                                                            2 1 3

                                                                            1 3 1

                                                                            2 2 2

                                                                            0 1 3

                                                                            1 2 0

                                                                            2 1 4

                                                                            1 0 1

                                                                            Input

                                                                            1 2 0 1 311211

                                                                            bull Reflection

                                                                            bull Normally better than zero padding

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                                                                            Template Matching Template

                                                                            ndash Skabelon paring dansk Locates objects in images

                                                                            Input

                                                                            Template

                                                                            Output Correlation image

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                                                                            Template Matching The correlation between the template and the input

                                                                            image is computed for each pixel

                                                                            Input

                                                                            Template

                                                                            Output Correlation image

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                                                                            Template Matching The pixel with the highest value is found in the

                                                                            output imagendash Here is the highest correlation

                                                                            Input

                                                                            Template

                                                                            Output Correlation image

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                                                                            Template Matching This corresponds to the found pattern in the input

                                                                            image

                                                                            Input

                                                                            Template

                                                                            Output Correlation image

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                                                                            Problematic Correlation Correlation matching has problem with light areas ndash

                                                                            why

                                                                            Input (f)

                                                                            Template (h)

                                                                            Output Correlation imageFake max

                                                                            Real max

                                                                            Very High119892119892 119909119909119910119910 = 119895119895=minus119877119877

                                                                            119877119877

                                                                            119894119894=minus119877119877

                                                                            119877119877

                                                                            ℎ(119894119894 119895119895) 119891119891(119909119909 + 119894119894119910119910 + 119895119895)

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                                                                            Normalised Cross Correlation

                                                                            Input (f)

                                                                            Template (h)

                                                                            Output Correlation image

                                                                            Real max

                                                                            NCC x y =Correlation

                                                                            Length of image patch sdot Length of template

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                                                                            Length of template Vector length

                                                                            ndash Put all pixel values into a vectorndash Compute the length of this vector

                                                                            Describes the intensity of the templatendash Bright template has a large lengthndash Dark template has a small length

                                                                            Template (h)

                                                                            Length of template = 119895119895=minus119877119877

                                                                            119877119877

                                                                            119894119894=minus119877119877

                                                                            119877119877

                                                                            ℎ(119894119894 119895119895) ℎ(119894119894 119895119895)

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                                                                            Length of image patch Vector length based on pixel values in image patch Describes the intensity of the image patch

                                                                            Template (h)

                                                                            Input (f) with patch

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                                                                            Normalised Cross Correlation The length of the image patch and the length of

                                                                            template normalise the NCC If the image is very bright the NCC will be ldquopulled

                                                                            downrdquo

                                                                            NCC x y =Correlation

                                                                            Length of image patch sdot Length of template

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                                                                            Normalised Cross Correlation NCC will be between

                                                                            ndash 0 No similarity between template and image patchndash 1 Template and image patch are identical

                                                                            Input (f)

                                                                            Template (h)

                                                                            Output Correlation image

                                                                            Real max

                                                                            NCC x y =Correlation

                                                                            Length of image patch sdot Length of template

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                                                                            Normalised Cross Correlation

                                                                            A) 010B) 033C) 083D) 062E) 098

                                                                            Der udfoslashres template matching med og normalized crosscorrelation (NCC) beregnes Hvad bliver NNC i den markerede pixel

                                                                            1

                                                                            2 2

                                                                            3

                                                                            2

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                                                                            1
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                                                                            Edges An edge is where there is a

                                                                            high change in gray level values

                                                                            Objects are often separated from the background by edgesGray level profile

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                                                                            Edges The profile as a function f(d) What value is high when there

                                                                            is an edgendash The slope of fndash The slope of the tangent at d

                                                                            f(d)

                                                                            119891119891prime(119889119889)

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                                                                            Finite Difference Definition of slope

                                                                            Approximation

                                                                            Simpler approximationh = 1

                                                                            119891119891prime 119889119889 = limℎrarr0

                                                                            119891119891 119889119889 + ℎ minus 119891119891(119889119889)ℎ

                                                                            119891119891prime 119889119889 asymp119891119891 119889119889 + ℎ minus 119891119891(119889119889)

                                                                            ℎ

                                                                            119891119891prime 119889119889 asymp 119891119891 119889119889 + 1 minus 119891119891(119889119889)

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                                                                            Edges Discrete approximation of frsquo(d) Can be implemented as a filter

                                                                            -1 0 1

                                                                            f(d-2) f(d-1) f(d) f(d+1) f(d+2) f(d+3)

                                                                            f(d)

                                                                            119891119891prime 119889119889 asymp 119891119891 119889119889 + 1 minus 119891119891(119889119889)

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                                                                            Edges in 2D Changes in gray level values

                                                                            ndash Image gradientndash Gradient is the 2D derivative of a 2D function f(xy)ndash Equal to the slope of the imagendash A steep slope is equal to an edge

                                                                            120571120571119891119891 119909119909119910119910 = 119866(119892119892119909119909119892119892119910119910)

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                                                                            Edge filter kernel The Prewitt filter is a typical

                                                                            edge filter Output image has high

                                                                            values where there are edges

                                                                            -1 0 1

                                                                            -1 0 1

                                                                            -1 0 1Vertical Prewitt filter

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                                                                            Prewitt filter

                                                                            Original Prewitt Prewitt

                                                                            Hot colormapSmooth 15x15

                                                                            Smooth 15x15

                                                                            Prewitt

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                                                                            Edge detection Edge filter

                                                                            ndash Prewitt for example Thresholding

                                                                            ndash Separate edges from non-edges

                                                                            Output is binary imagendash Edges are white

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                                                                            Edge filtering

                                                                            A) MeanB) Horizontal SobelC) Vertical PrewittD) Horisontal PrewittE) Median

                                                                            Der udfoslashres en filtrering (correlation) med et filter paring billedet Der bruges ikke coefficient normalization Den filtrerede vaeligrdi i den markerede pixel bliver -119 Hvilket et 3x3 filter blev benyttet

                                                                            0

                                                                            8

                                                                            1 10

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                                                                            02511 - Niveau af dagens emne forelaeligsingA) Meget letB) LetC) PassendeD) SvaeligrtE) Meget svaeligrt

                                                                            23

                                                                            6

                                                                            10

                                                                            A B C D E

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                                                                            02512 - Niveau af dagens emne forelaeligsingA) Meget letB) LetC) PassendeD) SvaeligrtE) Meget svaeligrt

                                                                            0 0

                                                                            1

                                                                            0 0

                                                                            A B C D E

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                                                                            0

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                                                                            02511 - Mit eget udbytte af dagenA) Jeg har laeligrt meget lidtB) Lidt laeligringC) PassendeD) God laeligringE) Jeg har laeligrt meget

                                                                            0 0

                                                                            2

                                                                            6

                                                                            0

                                                                            A B C D E

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                                                                            02512 - Mit eget udbytte af dagenA) Jeg har laeligrt meget lidtB) Lidt laeligringC) PassendeD) God laeligringE) Jeg har laeligrt meget

                                                                            2

                                                                            1

                                                                            3

                                                                            2

                                                                            0

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                                                                            02511 - Sidste uges oslashvelser (pixelwiseoperations)A) Meget letteB) LetteC) PassendeD) SvaeligreE) Meget svaeligre

                                                                            0 0

                                                                            1

                                                                            4

                                                                            1

                                                                            A B C D E

                                                                            Chart1

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                                                                            02512 - Sidste uges oslashvelser (pixelwiseoperations)A) Meget letteB) LetteC) PassendeD) SvaeligreE) Meget svaeligre

                                                                            3

                                                                            0

                                                                            3

                                                                            0 0

                                                                            A B C D E

                                                                            Chart1

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                                                                            0

                                                                            Sheet1

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                                                                            Denne uges brug af clickersA) click click click ndash jeg bliver

                                                                            sindssygB) For meget clickC) PassendeD) Jeg vil gerne have lidt mereE) Jeg kan ikrsquo faring nok

                                                                            0 0

                                                                            5

                                                                            0

                                                                            6

                                                                            A B C D E

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                                                                            What can you do after today Describe the difference between point processing and neighbourhood

                                                                            processing Compute a rank filtered image using the min max median and

                                                                            difference rank filters Compute a mean filtered image Decide if median or average filtering should be used for noise removal Choose the appropriate image border handling based on a given input

                                                                            image Implement and apply template matching Compute the normalised cross correlation and explain why it should be

                                                                            used Apply given image filter kernels to images Use edge filters on images Describe finite difference approximation of image gradients Describe the concept of edge detection

                                                                            DTU Compute

                                                                            2122018Introduction to Medical Image Analysis84 DTU Compute Technical University of Denmark

                                                                            Oslashvelsesrapport over oslashvelse 4 - 02511 Oslashvelser taeligller cirka 30 af karakteren Skal afleveres senest den 7 marts kl 2359 Kan afleveres af 1 eller 2 personer

                                                                            ndash I skal skrive jeres egen oslashvelsesrapportndash Brug mindst et af jeres egne billeder

                                                                            Afleveres som PDF Lad vaeligre med at kopiere opgaveteksten ind i jeres

                                                                            opgave Put Matlab kode i et Appendix og henvis fra teksten Eksempel rapport over oslashvelse findes paring

                                                                            hjemmesiden under eksamen

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                                                                            Exercises

                                                                            • Introduction to Medical Image Analysis
                                                                            • Lecture 4 ndash Neighbourhood Processing
                                                                            • What can you do after today
                                                                            • Point processing
                                                                            • Point processing
                                                                            • Neighbourhood processing
                                                                            • Use of filtering
                                                                            • Salt and pepper noise
                                                                            • Salt and pepper noise
                                                                            • What is so special about noise
                                                                            • Noise ndash go away
                                                                            • What is the median Value
                                                                            • The median value
                                                                            • Noise away ndash the median filter
                                                                            • Noise removal ndash average filter
                                                                            • Noise removal ndash median filter
                                                                            • Image Filtering
                                                                            • Median filter
                                                                            • Rank filters
                                                                            • Median filter
                                                                            • Correlation
                                                                            • Why do we need similarity
                                                                            • Correlation (1D)
                                                                            • Correlation (1D)
                                                                            • Normalisation
                                                                            • Normalisation
                                                                            • Correlation on images
                                                                            • Correlation on images
                                                                            • Correlation on images
                                                                            • Draw your filter
                                                                            • Correlation on images ndash no normalisation
                                                                            • Correlation on images ndash no normalisation 2
                                                                            • Mathematics of 2D Correlation
                                                                            • Mathematics of 2D Correlation
                                                                            • Mathematics of 2D Correlation
                                                                            • Slide Number 40
                                                                            • 2D Kernel Normalisation
                                                                            • Correlation
                                                                            • Smoothing filters
                                                                            • Use of smoothing
                                                                            • Use of smoothing
                                                                            • Mean filter
                                                                            • Border handling
                                                                            • Border handling ndash extend the input
                                                                            • Correlation with zero padding
                                                                            • Border handling ndash extend the input
                                                                            • Template Matching
                                                                            • Template Matching
                                                                            • Template Matching
                                                                            • Template Matching
                                                                            • Problematic Correlation
                                                                            • Normalised Cross Correlation
                                                                            • Length of template
                                                                            • Length of image patch
                                                                            • Normalised Cross Correlation
                                                                            • Normalised Cross Correlation
                                                                            • Normalised Cross Correlation
                                                                            • Edges
                                                                            • Edges
                                                                            • Finite Difference
                                                                            • Edges
                                                                            • Edges in 2D
                                                                            • Edge filter kernel
                                                                            • Prewitt filter
                                                                            • Edge detection
                                                                            • Edge filtering
                                                                            • 02511 - Niveau af dagens emne forelaeligsing
                                                                            • 02512 - Niveau af dagens emne forelaeligsing
                                                                            • 02511 - Mit eget udbytte af dagen
                                                                            • 02512 - Mit eget udbytte af dagen
                                                                            • 02511 - Sidste uges oslashvelser (pixelwise operations)
                                                                            • 02512 - Sidste uges oslashvelser (pixelwise operations)
                                                                            • Denne uges brug af clickers
                                                                            • What can you do after today
                                                                            • Oslashvelsesrapport over oslashvelse 4 - 02511
                                                                            • Exercises
                                                                              A0
                                                                              B0
                                                                              C5
                                                                              D0
                                                                              E6
                                                                              A
                                                                              B
                                                                              C
                                                                              D
                                                                              E
                                                                              A3
                                                                              B0
                                                                              C3
                                                                              D0
                                                                              E0
                                                                              A
                                                                              B
                                                                              C
                                                                              D
                                                                              E
                                                                              A0
                                                                              B0
                                                                              C1
                                                                              D4
                                                                              E1
                                                                              A
                                                                              B
                                                                              C
                                                                              D
                                                                              E
                                                                              A2
                                                                              B1
                                                                              C3
                                                                              D2
                                                                              E0
                                                                              A
                                                                              B
                                                                              C
                                                                              D
                                                                              E
                                                                              A0
                                                                              B0
                                                                              C2
                                                                              D6
                                                                              E0
                                                                              A
                                                                              B
                                                                              C
                                                                              D
                                                                              E
                                                                              A0
                                                                              B0
                                                                              C1
                                                                              D0
                                                                              E0
                                                                              A
                                                                              B
                                                                              C
                                                                              D
                                                                              E
                                                                              A2
                                                                              B3
                                                                              C6
                                                                              D1
                                                                              E0
                                                                              A
                                                                              B
                                                                              C
                                                                              D
                                                                              E
                                                                              A0
                                                                              B8
                                                                              C1
                                                                              D1
                                                                              E0
                                                                              A
                                                                              B
                                                                              C
                                                                              D
                                                                              E
                                                                              A1
                                                                              B2
                                                                              C2
                                                                              D3
                                                                              E2
                                                                              A
                                                                              B
                                                                              C
                                                                              D
                                                                              E
                                                                              A0
                                                                              B13
                                                                              C0
                                                                              D0
                                                                              E0
                                                                              A
                                                                              B
                                                                              C
                                                                              D
                                                                              E
                                                                              A12
                                                                              B0
                                                                              C0
                                                                              D0
                                                                              E0
                                                                              A
                                                                              B
                                                                              C
                                                                              D
                                                                              E
                                                                              A0
                                                                              B0
                                                                              C0
                                                                              D0
                                                                              E13
                                                                              A
                                                                              B
                                                                              C
                                                                              D
                                                                              E
                                                                              A13
                                                                              B0
                                                                              C0
                                                                              D0
                                                                              E0
                                                                              A
                                                                              B
                                                                              C
                                                                              D
                                                                              E
                                                                              A1
                                                                              B0
                                                                              C14
                                                                              D0
                                                                              E0
                                                                              A
                                                                              B
                                                                              C
                                                                              D
                                                                              E

                                                                              Sheet1

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                                                                              Correlation on images ndash no normalisation 2A) 010B) 3 3C) 6 2D) 10 15E) 11 32

                                                                              13

                                                                              0 0 0 0

                                                                              A B C D E

                                                                              -1 -2 -10 0 01 2 1

                                                                              0 2 41 2 2

                                                                              1 6 3

                                                                              1 2 12 5 3

                                                                              2 1 3

                                                                              1 3 1

                                                                              2 2 2

                                                                              0 1 3

                                                                              1 2 0

                                                                              2 1 4

                                                                              1 0 1

                                                                              Chart1

                                                                              13
                                                                              0
                                                                              0
                                                                              0
                                                                              0

                                                                              Sheet1

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                                                                              Mathematics of 2D Correlation

                                                                              h

                                                                              f

                                                                              Correlation operator

                                                                              1 2 11 3 11 2 1

                                                                              0 2 4

                                                                              1 2 2

                                                                              1 6 3

                                                                              1 2 1

                                                                              2 5 3

                                                                              2 1 3

                                                                              1 3 1

                                                                              2 2 2

                                                                              0 1 3

                                                                              1 2 0

                                                                              2 1 4

                                                                              1 0 1

                                                                              119892119892 119909119909119910119910 = 119891119891 119909119909119910119910 ∘ ℎ(119909119909119910119910)

                                                                              DTU Compute

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                                                                              Mathematics of 2D Correlation

                                                                              1 2 11 3 11 2 1

                                                                              0 2 4

                                                                              1 2 2

                                                                              1 6 3

                                                                              1 2 1

                                                                              2 5 3

                                                                              2 1 3

                                                                              1 3 1

                                                                              2 2 2

                                                                              0 1 3

                                                                              1 2 0

                                                                              2 1 4

                                                                              1 0 1

                                                                              h

                                                                              fh(00)

                                                                              f(21)

                                                                              Example g(21)

                                                                              i = -1 j = -1

                                                                              i = 1 j = 0

                                                                              119892119892 119909119909119910119910 = 119895119895=minus119877119877

                                                                              119877119877

                                                                              119894119894=minus119877119877

                                                                              119877119877

                                                                              ℎ(119894119894 119895119895) 119891119891(119909119909 + 119894119894119910119910 + 119895119895)

                                                                              DTU Compute

                                                                              2122018Introduction to Medical Image Analysis39 DTU Compute Technical University of Denmark

                                                                              Mathematics of 2D Correlation

                                                                              1 2 11 3 11 2 1

                                                                              0 2 4

                                                                              1 2 2

                                                                              1 6 3

                                                                              1 2 1

                                                                              2 5 3

                                                                              2 1 3

                                                                              1 3 1

                                                                              2 2 2

                                                                              0 1 3

                                                                              1 2 0

                                                                              2 1 4

                                                                              1 0 1

                                                                              h

                                                                              f

                                                                              119892119892 119909119909119910119910 = 119895119895=minus119877119877

                                                                              119877119877

                                                                              119894119894=minus119877119877

                                                                              119877119877

                                                                              ℎ(119894119894 119895119895) 119891119891(119909119909 + 119894119894119910119910 + 119895119895)

                                                                              119892119892(119909119909119910119910 = 1 2 + 2 0 + 1 1 + 1 1 + 3 4 + 1 2 + 1 0 + 2 1 + 1 0

                                                                              DTU Compute

                                                                              2122018Introduction to Medical Image Analysis40 DTU Compute Technical University of Denmark

                                                                              119892119892 119909119909 119910119910 = 119895119895=minus119877119877

                                                                              119877119877

                                                                              119894119894=minus119877119877

                                                                              119877119877

                                                                              ℎ(119894119894 119895119895) 119891119891(119909119909 + 119894119894119910119910 + 119895119895)

                                                                              119892119892 22 =ℎ minus1minus1 sdot 119891119891 11 + ℎ 0minus1 sdot 119891119891 21 + ℎ 1minus1 sdot 119891119891 31 +ℎ minus10 sdot 119891119891 12 + ℎ 00 sdot 119891119891 22 + ℎ 10 sdot 119891119891 32 +ℎ minus11 sdot 119891119891 13 + ℎ 01 sdot 119891119891 23 + ℎ 11 sdot 119891119891 33

                                                                              DTU Compute

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                                                                              2D Kernel Normalisation

                                                                              1 2 11 3 11 2 1

                                                                              h

                                                                              Normalisation factor

                                                                              1 + 2 + 1 + 1 + 3 + 1 + 1 + 2 + 1 = 13

                                                                              119909119909

                                                                              119910119910

                                                                              ℎ(119909119909119910119910)

                                                                              DTU Compute

                                                                              2122018Introduction to Medical Image Analysis42 DTU Compute Technical University of Denmark

                                                                              CorrelationA) 50122B) 123001C) 11233D) 2550E) 90454

                                                                              0 0 0 0

                                                                              13

                                                                              A B C D E

                                                                              Chart1

                                                                              0
                                                                              0
                                                                              0
                                                                              0
                                                                              13

                                                                              Sheet1

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                                                                              2122018Introduction to Medical Image Analysis44 DTU Compute Technical University of Denmark

                                                                              Smoothing filters

                                                                              Also know as ndash Smoothing kernel Mean filter Low pass filter blurring

                                                                              The simplest filter ndash Spatial low pass filterndash Removes high frequencies

                                                                              Another mask ndash Gaussian filter

                                                                              1 1 1

                                                                              1 1 1

                                                                              1 1 191

                                                                              1 2 1

                                                                              2 4 2

                                                                              1 2 1161

                                                                              Why Gaussian

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                                                                              Use of smoothing

                                                                              3x3 7x7 11x11 15x15

                                                                              DTU Compute

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                                                                              Use of smoothing Large kernels smooth more Removes high frequency information Good at enhancing big structures

                                                                              3x3 15x15

                                                                              DTU Compute

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                                                                              Mean filterA) 166B) 113C) 12D) 51E) 245

                                                                              0 0 0 0

                                                                              A B C D E

                                                                              Chart1

                                                                              12
                                                                              0
                                                                              0
                                                                              0
                                                                              0

                                                                              Sheet1

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                                                                              Border handling

                                                                              0 2 41 2 2

                                                                              1 6 3

                                                                              1 2 12 5 3

                                                                              2 1 3

                                                                              1 3 1

                                                                              2 2 2

                                                                              0 1 3

                                                                              1 2 0

                                                                              2 1 4

                                                                              1 0 1

                                                                              Input Output

                                                                              No values at the border

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                                                                              Border handling ndash extend the input

                                                                              0 2 41 2 2

                                                                              1 6 3

                                                                              1 2 12 5 3

                                                                              2 1 3

                                                                              1 3 1

                                                                              2 2 2

                                                                              0 1 3

                                                                              1 2 0

                                                                              2 1 4

                                                                              1 0 1

                                                                              Input

                                                                              0 0 0 0 000000

                                                                              bull Zero padding ndash what happens

                                                                              bull Zero is black ndash creates dark border around the image

                                                                              DTU Compute

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                                                                              Correlation with zero paddingA) 5 8B) 12 16C) 13 3D) 15 21E) 17 12

                                                                              1 2 11 3 11 2 1

                                                                              0 2 41 2 2

                                                                              1 6 3

                                                                              1 2 12 5 3

                                                                              2 1 3

                                                                              1 3 1

                                                                              2 2 2

                                                                              0 1 3

                                                                              1 2 0

                                                                              2 1 4

                                                                              1 0 1

                                                                              0

                                                                              13

                                                                              0 0 0

                                                                              A B C D E

                                                                              Chart1

                                                                              0
                                                                              13
                                                                              0
                                                                              0
                                                                              0

                                                                              Sheet1

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                                                                              Border handling ndash extend the input

                                                                              0 2 41 2 2

                                                                              1 6 3

                                                                              1 2 12 5 3

                                                                              2 1 3

                                                                              1 3 1

                                                                              2 2 2

                                                                              0 1 3

                                                                              1 2 0

                                                                              2 1 4

                                                                              1 0 1

                                                                              Input

                                                                              1 2 0 1 311211

                                                                              bull Reflection

                                                                              bull Normally better than zero padding

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                                                                              Template Matching Template

                                                                              ndash Skabelon paring dansk Locates objects in images

                                                                              Input

                                                                              Template

                                                                              Output Correlation image

                                                                              DTU Compute

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                                                                              Template Matching The correlation between the template and the input

                                                                              image is computed for each pixel

                                                                              Input

                                                                              Template

                                                                              Output Correlation image

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                                                                              Template Matching The pixel with the highest value is found in the

                                                                              output imagendash Here is the highest correlation

                                                                              Input

                                                                              Template

                                                                              Output Correlation image

                                                                              DTU Compute

                                                                              2122018Introduction to Medical Image Analysis57 DTU Compute Technical University of Denmark

                                                                              Template Matching This corresponds to the found pattern in the input

                                                                              image

                                                                              Input

                                                                              Template

                                                                              Output Correlation image

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                                                                              Problematic Correlation Correlation matching has problem with light areas ndash

                                                                              why

                                                                              Input (f)

                                                                              Template (h)

                                                                              Output Correlation imageFake max

                                                                              Real max

                                                                              Very High119892119892 119909119909119910119910 = 119895119895=minus119877119877

                                                                              119877119877

                                                                              119894119894=minus119877119877

                                                                              119877119877

                                                                              ℎ(119894119894 119895119895) 119891119891(119909119909 + 119894119894119910119910 + 119895119895)

                                                                              DTU Compute

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                                                                              Normalised Cross Correlation

                                                                              Input (f)

                                                                              Template (h)

                                                                              Output Correlation image

                                                                              Real max

                                                                              NCC x y =Correlation

                                                                              Length of image patch sdot Length of template

                                                                              DTU Compute

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                                                                              Length of template Vector length

                                                                              ndash Put all pixel values into a vectorndash Compute the length of this vector

                                                                              Describes the intensity of the templatendash Bright template has a large lengthndash Dark template has a small length

                                                                              Template (h)

                                                                              Length of template = 119895119895=minus119877119877

                                                                              119877119877

                                                                              119894119894=minus119877119877

                                                                              119877119877

                                                                              ℎ(119894119894 119895119895) ℎ(119894119894 119895119895)

                                                                              DTU Compute

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                                                                              Length of image patch Vector length based on pixel values in image patch Describes the intensity of the image patch

                                                                              Template (h)

                                                                              Input (f) with patch

                                                                              DTU Compute

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                                                                              Normalised Cross Correlation The length of the image patch and the length of

                                                                              template normalise the NCC If the image is very bright the NCC will be ldquopulled

                                                                              downrdquo

                                                                              NCC x y =Correlation

                                                                              Length of image patch sdot Length of template

                                                                              DTU Compute

                                                                              2122018Introduction to Medical Image Analysis63 DTU Compute Technical University of Denmark

                                                                              Normalised Cross Correlation NCC will be between

                                                                              ndash 0 No similarity between template and image patchndash 1 Template and image patch are identical

                                                                              Input (f)

                                                                              Template (h)

                                                                              Output Correlation image

                                                                              Real max

                                                                              NCC x y =Correlation

                                                                              Length of image patch sdot Length of template

                                                                              DTU Compute

                                                                              2122018Introduction to Medical Image Analysis64 DTU Compute Technical University of Denmark

                                                                              Normalised Cross Correlation

                                                                              A) 010B) 033C) 083D) 062E) 098

                                                                              Der udfoslashres template matching med og normalized crosscorrelation (NCC) beregnes Hvad bliver NNC i den markerede pixel

                                                                              1

                                                                              2 2

                                                                              3

                                                                              2

                                                                              A B C D E

                                                                              Chart1

                                                                              1
                                                                              2
                                                                              2
                                                                              3
                                                                              2

                                                                              Sheet1

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                                                                              Edges An edge is where there is a

                                                                              high change in gray level values

                                                                              Objects are often separated from the background by edgesGray level profile

                                                                              DTU Compute

                                                                              2122018Introduction to Medical Image Analysis67 DTU Compute Technical University of Denmark

                                                                              Edges The profile as a function f(d) What value is high when there

                                                                              is an edgendash The slope of fndash The slope of the tangent at d

                                                                              f(d)

                                                                              119891119891prime(119889119889)

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                                                                              Finite Difference Definition of slope

                                                                              Approximation

                                                                              Simpler approximationh = 1

                                                                              119891119891prime 119889119889 = limℎrarr0

                                                                              119891119891 119889119889 + ℎ minus 119891119891(119889119889)ℎ

                                                                              119891119891prime 119889119889 asymp119891119891 119889119889 + ℎ minus 119891119891(119889119889)

                                                                              ℎ

                                                                              119891119891prime 119889119889 asymp 119891119891 119889119889 + 1 minus 119891119891(119889119889)

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                                                                              Edges Discrete approximation of frsquo(d) Can be implemented as a filter

                                                                              -1 0 1

                                                                              f(d-2) f(d-1) f(d) f(d+1) f(d+2) f(d+3)

                                                                              f(d)

                                                                              119891119891prime 119889119889 asymp 119891119891 119889119889 + 1 minus 119891119891(119889119889)

                                                                              DTU Compute

                                                                              2122018Introduction to Medical Image Analysis70 DTU Compute Technical University of Denmark

                                                                              Edges in 2D Changes in gray level values

                                                                              ndash Image gradientndash Gradient is the 2D derivative of a 2D function f(xy)ndash Equal to the slope of the imagendash A steep slope is equal to an edge

                                                                              120571120571119891119891 119909119909119910119910 = 119866(119892119892119909119909119892119892119910119910)

                                                                              DTU Compute

                                                                              2122018Introduction to Medical Image Analysis71 DTU Compute Technical University of Denmark

                                                                              Edge filter kernel The Prewitt filter is a typical

                                                                              edge filter Output image has high

                                                                              values where there are edges

                                                                              -1 0 1

                                                                              -1 0 1

                                                                              -1 0 1Vertical Prewitt filter

                                                                              DTU Compute

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                                                                              Prewitt filter

                                                                              Original Prewitt Prewitt

                                                                              Hot colormapSmooth 15x15

                                                                              Smooth 15x15

                                                                              Prewitt

                                                                              DTU Compute

                                                                              2122018Introduction to Medical Image Analysis73 DTU Compute Technical University of Denmark

                                                                              Edge detection Edge filter

                                                                              ndash Prewitt for example Thresholding

                                                                              ndash Separate edges from non-edges

                                                                              Output is binary imagendash Edges are white

                                                                              DTU Compute

                                                                              2122018Introduction to Medical Image Analysis74 DTU Compute Technical University of Denmark

                                                                              Edge filtering

                                                                              A) MeanB) Horizontal SobelC) Vertical PrewittD) Horisontal PrewittE) Median

                                                                              Der udfoslashres en filtrering (correlation) med et filter paring billedet Der bruges ikke coefficient normalization Den filtrerede vaeligrdi i den markerede pixel bliver -119 Hvilket et 3x3 filter blev benyttet

                                                                              0

                                                                              8

                                                                              1 10

                                                                              A B C D E

                                                                              Chart1

                                                                              0
                                                                              8
                                                                              1
                                                                              1
                                                                              0

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                                                                              02511 - Niveau af dagens emne forelaeligsingA) Meget letB) LetC) PassendeD) SvaeligrtE) Meget svaeligrt

                                                                              23

                                                                              6

                                                                              10

                                                                              A B C D E

                                                                              Chart1

                                                                              2
                                                                              3
                                                                              6
                                                                              1
                                                                              0

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                                                                              02512 - Niveau af dagens emne forelaeligsingA) Meget letB) LetC) PassendeD) SvaeligrtE) Meget svaeligrt

                                                                              0 0

                                                                              1

                                                                              0 0

                                                                              A B C D E

                                                                              Chart1

                                                                              0
                                                                              0
                                                                              1
                                                                              0
                                                                              0

                                                                              Sheet1

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                                                                              02511 - Mit eget udbytte af dagenA) Jeg har laeligrt meget lidtB) Lidt laeligringC) PassendeD) God laeligringE) Jeg har laeligrt meget

                                                                              0 0

                                                                              2

                                                                              6

                                                                              0

                                                                              A B C D E

                                                                              Chart1

                                                                              0
                                                                              0
                                                                              2
                                                                              6
                                                                              0

                                                                              Sheet1

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                                                                              02512 - Mit eget udbytte af dagenA) Jeg har laeligrt meget lidtB) Lidt laeligringC) PassendeD) God laeligringE) Jeg har laeligrt meget

                                                                              2

                                                                              1

                                                                              3

                                                                              2

                                                                              0

                                                                              A B C D E

                                                                              Chart1

                                                                              2
                                                                              1
                                                                              3
                                                                              2
                                                                              0

                                                                              Sheet1

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                                                                              02511 - Sidste uges oslashvelser (pixelwiseoperations)A) Meget letteB) LetteC) PassendeD) SvaeligreE) Meget svaeligre

                                                                              0 0

                                                                              1

                                                                              4

                                                                              1

                                                                              A B C D E

                                                                              Chart1

                                                                              0
                                                                              0
                                                                              1
                                                                              4
                                                                              1

                                                                              Sheet1

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                                                                              02512 - Sidste uges oslashvelser (pixelwiseoperations)A) Meget letteB) LetteC) PassendeD) SvaeligreE) Meget svaeligre

                                                                              3

                                                                              0

                                                                              3

                                                                              0 0

                                                                              A B C D E

                                                                              Chart1

                                                                              3
                                                                              0
                                                                              3
                                                                              0
                                                                              0

                                                                              Sheet1

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                                                                              Denne uges brug af clickersA) click click click ndash jeg bliver

                                                                              sindssygB) For meget clickC) PassendeD) Jeg vil gerne have lidt mereE) Jeg kan ikrsquo faring nok

                                                                              0 0

                                                                              5

                                                                              0

                                                                              6

                                                                              A B C D E

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                                                                              What can you do after today Describe the difference between point processing and neighbourhood

                                                                              processing Compute a rank filtered image using the min max median and

                                                                              difference rank filters Compute a mean filtered image Decide if median or average filtering should be used for noise removal Choose the appropriate image border handling based on a given input

                                                                              image Implement and apply template matching Compute the normalised cross correlation and explain why it should be

                                                                              used Apply given image filter kernels to images Use edge filters on images Describe finite difference approximation of image gradients Describe the concept of edge detection

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                                                                              Oslashvelsesrapport over oslashvelse 4 - 02511 Oslashvelser taeligller cirka 30 af karakteren Skal afleveres senest den 7 marts kl 2359 Kan afleveres af 1 eller 2 personer

                                                                              ndash I skal skrive jeres egen oslashvelsesrapportndash Brug mindst et af jeres egne billeder

                                                                              Afleveres som PDF Lad vaeligre med at kopiere opgaveteksten ind i jeres

                                                                              opgave Put Matlab kode i et Appendix og henvis fra teksten Eksempel rapport over oslashvelse findes paring

                                                                              hjemmesiden under eksamen

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                                                                              Exercises

                                                                              • Introduction to Medical Image Analysis
                                                                              • Lecture 4 ndash Neighbourhood Processing
                                                                              • What can you do after today
                                                                              • Point processing
                                                                              • Point processing
                                                                              • Neighbourhood processing
                                                                              • Use of filtering
                                                                              • Salt and pepper noise
                                                                              • Salt and pepper noise
                                                                              • What is so special about noise
                                                                              • Noise ndash go away
                                                                              • What is the median Value
                                                                              • The median value
                                                                              • Noise away ndash the median filter
                                                                              • Noise removal ndash average filter
                                                                              • Noise removal ndash median filter
                                                                              • Image Filtering
                                                                              • Median filter
                                                                              • Rank filters
                                                                              • Median filter
                                                                              • Correlation
                                                                              • Why do we need similarity
                                                                              • Correlation (1D)
                                                                              • Correlation (1D)
                                                                              • Normalisation
                                                                              • Normalisation
                                                                              • Correlation on images
                                                                              • Correlation on images
                                                                              • Correlation on images
                                                                              • Draw your filter
                                                                              • Correlation on images ndash no normalisation
                                                                              • Correlation on images ndash no normalisation 2
                                                                              • Mathematics of 2D Correlation
                                                                              • Mathematics of 2D Correlation
                                                                              • Mathematics of 2D Correlation
                                                                              • Slide Number 40
                                                                              • 2D Kernel Normalisation
                                                                              • Correlation
                                                                              • Smoothing filters
                                                                              • Use of smoothing
                                                                              • Use of smoothing
                                                                              • Mean filter
                                                                              • Border handling
                                                                              • Border handling ndash extend the input
                                                                              • Correlation with zero padding
                                                                              • Border handling ndash extend the input
                                                                              • Template Matching
                                                                              • Template Matching
                                                                              • Template Matching
                                                                              • Template Matching
                                                                              • Problematic Correlation
                                                                              • Normalised Cross Correlation
                                                                              • Length of template
                                                                              • Length of image patch
                                                                              • Normalised Cross Correlation
                                                                              • Normalised Cross Correlation
                                                                              • Normalised Cross Correlation
                                                                              • Edges
                                                                              • Edges
                                                                              • Finite Difference
                                                                              • Edges
                                                                              • Edges in 2D
                                                                              • Edge filter kernel
                                                                              • Prewitt filter
                                                                              • Edge detection
                                                                              • Edge filtering
                                                                              • 02511 - Niveau af dagens emne forelaeligsing
                                                                              • 02512 - Niveau af dagens emne forelaeligsing
                                                                              • 02511 - Mit eget udbytte af dagen
                                                                              • 02512 - Mit eget udbytte af dagen
                                                                              • 02511 - Sidste uges oslashvelser (pixelwise operations)
                                                                              • 02512 - Sidste uges oslashvelser (pixelwise operations)
                                                                              • Denne uges brug af clickers
                                                                              • What can you do after today
                                                                              • Oslashvelsesrapport over oslashvelse 4 - 02511
                                                                              • Exercises
                                                                                A0
                                                                                B0
                                                                                C5
                                                                                D0
                                                                                E6
                                                                                A
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                                                                                D
                                                                                E
                                                                                A3
                                                                                B0
                                                                                C3
                                                                                D0
                                                                                E0
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                                                                                B
                                                                                C
                                                                                D
                                                                                E
                                                                                A0
                                                                                B0
                                                                                C1
                                                                                D4
                                                                                E1
                                                                                A
                                                                                B
                                                                                C
                                                                                D
                                                                                E
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                                                                                B1
                                                                                C3
                                                                                D2
                                                                                E0
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                                                                                E
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                                                                                B0
                                                                                C2
                                                                                D6
                                                                                E0
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                                                                                C
                                                                                D
                                                                                E
                                                                                A0
                                                                                B0
                                                                                C1
                                                                                D0
                                                                                E0
                                                                                A
                                                                                B
                                                                                C
                                                                                D
                                                                                E
                                                                                A2
                                                                                B3
                                                                                C6
                                                                                D1
                                                                                E0
                                                                                A
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                                                                                E
                                                                                A0
                                                                                B8
                                                                                C1
                                                                                D1
                                                                                E0
                                                                                A
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                                                                                C
                                                                                D
                                                                                E
                                                                                A1
                                                                                B2
                                                                                C2
                                                                                D3
                                                                                E2
                                                                                A
                                                                                B
                                                                                C
                                                                                D
                                                                                E
                                                                                A0
                                                                                B13
                                                                                C0
                                                                                D0
                                                                                E0
                                                                                A
                                                                                B
                                                                                C
                                                                                D
                                                                                E
                                                                                A12
                                                                                B0
                                                                                C0
                                                                                D0
                                                                                E0
                                                                                A
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                                                                                C
                                                                                D
                                                                                E
                                                                                A0
                                                                                B0
                                                                                C0
                                                                                D0
                                                                                E13
                                                                                A
                                                                                B
                                                                                C
                                                                                D
                                                                                E
                                                                                A13
                                                                                B0
                                                                                C0
                                                                                D0
                                                                                E0
                                                                                A
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                                                                                A1
                                                                                B0
                                                                                C14
                                                                                D0
                                                                                E0

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                                                                                Correlation on images ndash no normalisation 2A) 010B) 3 3C) 6 2D) 10 15E) 11 32

                                                                                13

                                                                                0 0 0 0

                                                                                A B C D E

                                                                                -1 -2 -10 0 01 2 1

                                                                                0 2 41 2 2

                                                                                1 6 3

                                                                                1 2 12 5 3

                                                                                2 1 3

                                                                                1 3 1

                                                                                2 2 2

                                                                                0 1 3

                                                                                1 2 0

                                                                                2 1 4

                                                                                1 0 1

                                                                                Chart1

                                                                                13
                                                                                0
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                                                                                0
                                                                                0

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                                                                                Mathematics of 2D Correlation

                                                                                h

                                                                                f

                                                                                Correlation operator

                                                                                1 2 11 3 11 2 1

                                                                                0 2 4

                                                                                1 2 2

                                                                                1 6 3

                                                                                1 2 1

                                                                                2 5 3

                                                                                2 1 3

                                                                                1 3 1

                                                                                2 2 2

                                                                                0 1 3

                                                                                1 2 0

                                                                                2 1 4

                                                                                1 0 1

                                                                                119892119892 119909119909119910119910 = 119891119891 119909119909119910119910 ∘ ℎ(119909119909119910119910)

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                                                                                Mathematics of 2D Correlation

                                                                                1 2 11 3 11 2 1

                                                                                0 2 4

                                                                                1 2 2

                                                                                1 6 3

                                                                                1 2 1

                                                                                2 5 3

                                                                                2 1 3

                                                                                1 3 1

                                                                                2 2 2

                                                                                0 1 3

                                                                                1 2 0

                                                                                2 1 4

                                                                                1 0 1

                                                                                h

                                                                                fh(00)

                                                                                f(21)

                                                                                Example g(21)

                                                                                i = -1 j = -1

                                                                                i = 1 j = 0

                                                                                119892119892 119909119909119910119910 = 119895119895=minus119877119877

                                                                                119877119877

                                                                                119894119894=minus119877119877

                                                                                119877119877

                                                                                ℎ(119894119894 119895119895) 119891119891(119909119909 + 119894119894119910119910 + 119895119895)

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                                                                                Mathematics of 2D Correlation

                                                                                1 2 11 3 11 2 1

                                                                                0 2 4

                                                                                1 2 2

                                                                                1 6 3

                                                                                1 2 1

                                                                                2 5 3

                                                                                2 1 3

                                                                                1 3 1

                                                                                2 2 2

                                                                                0 1 3

                                                                                1 2 0

                                                                                2 1 4

                                                                                1 0 1

                                                                                h

                                                                                f

                                                                                119892119892 119909119909119910119910 = 119895119895=minus119877119877

                                                                                119877119877

                                                                                119894119894=minus119877119877

                                                                                119877119877

                                                                                ℎ(119894119894 119895119895) 119891119891(119909119909 + 119894119894119910119910 + 119895119895)

                                                                                119892119892(119909119909119910119910 = 1 2 + 2 0 + 1 1 + 1 1 + 3 4 + 1 2 + 1 0 + 2 1 + 1 0

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                                                                                119892119892 119909119909 119910119910 = 119895119895=minus119877119877

                                                                                119877119877

                                                                                119894119894=minus119877119877

                                                                                119877119877

                                                                                ℎ(119894119894 119895119895) 119891119891(119909119909 + 119894119894119910119910 + 119895119895)

                                                                                119892119892 22 =ℎ minus1minus1 sdot 119891119891 11 + ℎ 0minus1 sdot 119891119891 21 + ℎ 1minus1 sdot 119891119891 31 +ℎ minus10 sdot 119891119891 12 + ℎ 00 sdot 119891119891 22 + ℎ 10 sdot 119891119891 32 +ℎ minus11 sdot 119891119891 13 + ℎ 01 sdot 119891119891 23 + ℎ 11 sdot 119891119891 33

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                                                                                2D Kernel Normalisation

                                                                                1 2 11 3 11 2 1

                                                                                h

                                                                                Normalisation factor

                                                                                1 + 2 + 1 + 1 + 3 + 1 + 1 + 2 + 1 = 13

                                                                                119909119909

                                                                                119910119910

                                                                                ℎ(119909119909119910119910)

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                                                                                CorrelationA) 50122B) 123001C) 11233D) 2550E) 90454

                                                                                0 0 0 0

                                                                                13

                                                                                A B C D E

                                                                                Chart1

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                                                                                0
                                                                                13

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                                                                                Smoothing filters

                                                                                Also know as ndash Smoothing kernel Mean filter Low pass filter blurring

                                                                                The simplest filter ndash Spatial low pass filterndash Removes high frequencies

                                                                                Another mask ndash Gaussian filter

                                                                                1 1 1

                                                                                1 1 1

                                                                                1 1 191

                                                                                1 2 1

                                                                                2 4 2

                                                                                1 2 1161

                                                                                Why Gaussian

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                                                                                Use of smoothing

                                                                                3x3 7x7 11x11 15x15

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                                                                                Use of smoothing Large kernels smooth more Removes high frequency information Good at enhancing big structures

                                                                                3x3 15x15

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                                                                                Mean filterA) 166B) 113C) 12D) 51E) 245

                                                                                0 0 0 0

                                                                                A B C D E

                                                                                Chart1

                                                                                12
                                                                                0
                                                                                0
                                                                                0
                                                                                0

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                                                                                Border handling

                                                                                0 2 41 2 2

                                                                                1 6 3

                                                                                1 2 12 5 3

                                                                                2 1 3

                                                                                1 3 1

                                                                                2 2 2

                                                                                0 1 3

                                                                                1 2 0

                                                                                2 1 4

                                                                                1 0 1

                                                                                Input Output

                                                                                No values at the border

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                                                                                Border handling ndash extend the input

                                                                                0 2 41 2 2

                                                                                1 6 3

                                                                                1 2 12 5 3

                                                                                2 1 3

                                                                                1 3 1

                                                                                2 2 2

                                                                                0 1 3

                                                                                1 2 0

                                                                                2 1 4

                                                                                1 0 1

                                                                                Input

                                                                                0 0 0 0 000000

                                                                                bull Zero padding ndash what happens

                                                                                bull Zero is black ndash creates dark border around the image

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                                                                                Correlation with zero paddingA) 5 8B) 12 16C) 13 3D) 15 21E) 17 12

                                                                                1 2 11 3 11 2 1

                                                                                0 2 41 2 2

                                                                                1 6 3

                                                                                1 2 12 5 3

                                                                                2 1 3

                                                                                1 3 1

                                                                                2 2 2

                                                                                0 1 3

                                                                                1 2 0

                                                                                2 1 4

                                                                                1 0 1

                                                                                0

                                                                                13

                                                                                0 0 0

                                                                                A B C D E

                                                                                Chart1

                                                                                0
                                                                                13
                                                                                0
                                                                                0
                                                                                0

                                                                                Sheet1

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                                                                                Border handling ndash extend the input

                                                                                0 2 41 2 2

                                                                                1 6 3

                                                                                1 2 12 5 3

                                                                                2 1 3

                                                                                1 3 1

                                                                                2 2 2

                                                                                0 1 3

                                                                                1 2 0

                                                                                2 1 4

                                                                                1 0 1

                                                                                Input

                                                                                1 2 0 1 311211

                                                                                bull Reflection

                                                                                bull Normally better than zero padding

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                                                                                Template Matching Template

                                                                                ndash Skabelon paring dansk Locates objects in images

                                                                                Input

                                                                                Template

                                                                                Output Correlation image

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                                                                                Template Matching The correlation between the template and the input

                                                                                image is computed for each pixel

                                                                                Input

                                                                                Template

                                                                                Output Correlation image

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                                                                                Template Matching The pixel with the highest value is found in the

                                                                                output imagendash Here is the highest correlation

                                                                                Input

                                                                                Template

                                                                                Output Correlation image

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                                                                                Template Matching This corresponds to the found pattern in the input

                                                                                image

                                                                                Input

                                                                                Template

                                                                                Output Correlation image

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                                                                                Problematic Correlation Correlation matching has problem with light areas ndash

                                                                                why

                                                                                Input (f)

                                                                                Template (h)

                                                                                Output Correlation imageFake max

                                                                                Real max

                                                                                Very High119892119892 119909119909119910119910 = 119895119895=minus119877119877

                                                                                119877119877

                                                                                119894119894=minus119877119877

                                                                                119877119877

                                                                                ℎ(119894119894 119895119895) 119891119891(119909119909 + 119894119894119910119910 + 119895119895)

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                                                                                Normalised Cross Correlation

                                                                                Input (f)

                                                                                Template (h)

                                                                                Output Correlation image

                                                                                Real max

                                                                                NCC x y =Correlation

                                                                                Length of image patch sdot Length of template

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                                                                                Length of template Vector length

                                                                                ndash Put all pixel values into a vectorndash Compute the length of this vector

                                                                                Describes the intensity of the templatendash Bright template has a large lengthndash Dark template has a small length

                                                                                Template (h)

                                                                                Length of template = 119895119895=minus119877119877

                                                                                119877119877

                                                                                119894119894=minus119877119877

                                                                                119877119877

                                                                                ℎ(119894119894 119895119895) ℎ(119894119894 119895119895)

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                                                                                Length of image patch Vector length based on pixel values in image patch Describes the intensity of the image patch

                                                                                Template (h)

                                                                                Input (f) with patch

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                                                                                Normalised Cross Correlation The length of the image patch and the length of

                                                                                template normalise the NCC If the image is very bright the NCC will be ldquopulled

                                                                                downrdquo

                                                                                NCC x y =Correlation

                                                                                Length of image patch sdot Length of template

                                                                                DTU Compute

                                                                                2122018Introduction to Medical Image Analysis63 DTU Compute Technical University of Denmark

                                                                                Normalised Cross Correlation NCC will be between

                                                                                ndash 0 No similarity between template and image patchndash 1 Template and image patch are identical

                                                                                Input (f)

                                                                                Template (h)

                                                                                Output Correlation image

                                                                                Real max

                                                                                NCC x y =Correlation

                                                                                Length of image patch sdot Length of template

                                                                                DTU Compute

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                                                                                Normalised Cross Correlation

                                                                                A) 010B) 033C) 083D) 062E) 098

                                                                                Der udfoslashres template matching med og normalized crosscorrelation (NCC) beregnes Hvad bliver NNC i den markerede pixel

                                                                                1

                                                                                2 2

                                                                                3

                                                                                2

                                                                                A B C D E

                                                                                Chart1

                                                                                1
                                                                                2
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                                                                                Edges An edge is where there is a

                                                                                high change in gray level values

                                                                                Objects are often separated from the background by edgesGray level profile

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                                                                                Edges The profile as a function f(d) What value is high when there

                                                                                is an edgendash The slope of fndash The slope of the tangent at d

                                                                                f(d)

                                                                                119891119891prime(119889119889)

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                                                                                Finite Difference Definition of slope

                                                                                Approximation

                                                                                Simpler approximationh = 1

                                                                                119891119891prime 119889119889 = limℎrarr0

                                                                                119891119891 119889119889 + ℎ minus 119891119891(119889119889)ℎ

                                                                                119891119891prime 119889119889 asymp119891119891 119889119889 + ℎ minus 119891119891(119889119889)

                                                                                ℎ

                                                                                119891119891prime 119889119889 asymp 119891119891 119889119889 + 1 minus 119891119891(119889119889)

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                                                                                Edges Discrete approximation of frsquo(d) Can be implemented as a filter

                                                                                -1 0 1

                                                                                f(d-2) f(d-1) f(d) f(d+1) f(d+2) f(d+3)

                                                                                f(d)

                                                                                119891119891prime 119889119889 asymp 119891119891 119889119889 + 1 minus 119891119891(119889119889)

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                                                                                Edges in 2D Changes in gray level values

                                                                                ndash Image gradientndash Gradient is the 2D derivative of a 2D function f(xy)ndash Equal to the slope of the imagendash A steep slope is equal to an edge

                                                                                120571120571119891119891 119909119909119910119910 = 119866(119892119892119909119909119892119892119910119910)

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                                                                                Edge filter kernel The Prewitt filter is a typical

                                                                                edge filter Output image has high

                                                                                values where there are edges

                                                                                -1 0 1

                                                                                -1 0 1

                                                                                -1 0 1Vertical Prewitt filter

                                                                                DTU Compute

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                                                                                Prewitt filter

                                                                                Original Prewitt Prewitt

                                                                                Hot colormapSmooth 15x15

                                                                                Smooth 15x15

                                                                                Prewitt

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                                                                                Edge detection Edge filter

                                                                                ndash Prewitt for example Thresholding

                                                                                ndash Separate edges from non-edges

                                                                                Output is binary imagendash Edges are white

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                                                                                Edge filtering

                                                                                A) MeanB) Horizontal SobelC) Vertical PrewittD) Horisontal PrewittE) Median

                                                                                Der udfoslashres en filtrering (correlation) med et filter paring billedet Der bruges ikke coefficient normalization Den filtrerede vaeligrdi i den markerede pixel bliver -119 Hvilket et 3x3 filter blev benyttet

                                                                                0

                                                                                8

                                                                                1 10

                                                                                A B C D E

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                                                                                02511 - Niveau af dagens emne forelaeligsingA) Meget letB) LetC) PassendeD) SvaeligrtE) Meget svaeligrt

                                                                                23

                                                                                6

                                                                                10

                                                                                A B C D E

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                                                                                02512 - Niveau af dagens emne forelaeligsingA) Meget letB) LetC) PassendeD) SvaeligrtE) Meget svaeligrt

                                                                                0 0

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                                                                                02511 - Mit eget udbytte af dagenA) Jeg har laeligrt meget lidtB) Lidt laeligringC) PassendeD) God laeligringE) Jeg har laeligrt meget

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                                                                                02512 - Mit eget udbytte af dagenA) Jeg har laeligrt meget lidtB) Lidt laeligringC) PassendeD) God laeligringE) Jeg har laeligrt meget

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                                                                                02511 - Sidste uges oslashvelser (pixelwiseoperations)A) Meget letteB) LetteC) PassendeD) SvaeligreE) Meget svaeligre

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                                                                                02512 - Sidste uges oslashvelser (pixelwiseoperations)A) Meget letteB) LetteC) PassendeD) SvaeligreE) Meget svaeligre

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                                                                                Denne uges brug af clickersA) click click click ndash jeg bliver

                                                                                sindssygB) For meget clickC) PassendeD) Jeg vil gerne have lidt mereE) Jeg kan ikrsquo faring nok

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                                                                                What can you do after today Describe the difference between point processing and neighbourhood

                                                                                processing Compute a rank filtered image using the min max median and

                                                                                difference rank filters Compute a mean filtered image Decide if median or average filtering should be used for noise removal Choose the appropriate image border handling based on a given input

                                                                                image Implement and apply template matching Compute the normalised cross correlation and explain why it should be

                                                                                used Apply given image filter kernels to images Use edge filters on images Describe finite difference approximation of image gradients Describe the concept of edge detection

                                                                                DTU Compute

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                                                                                Oslashvelsesrapport over oslashvelse 4 - 02511 Oslashvelser taeligller cirka 30 af karakteren Skal afleveres senest den 7 marts kl 2359 Kan afleveres af 1 eller 2 personer

                                                                                ndash I skal skrive jeres egen oslashvelsesrapportndash Brug mindst et af jeres egne billeder

                                                                                Afleveres som PDF Lad vaeligre med at kopiere opgaveteksten ind i jeres

                                                                                opgave Put Matlab kode i et Appendix og henvis fra teksten Eksempel rapport over oslashvelse findes paring

                                                                                hjemmesiden under eksamen

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                                                                                Exercises

                                                                                • Introduction to Medical Image Analysis
                                                                                • Lecture 4 ndash Neighbourhood Processing
                                                                                • What can you do after today
                                                                                • Point processing
                                                                                • Point processing
                                                                                • Neighbourhood processing
                                                                                • Use of filtering
                                                                                • Salt and pepper noise
                                                                                • Salt and pepper noise
                                                                                • What is so special about noise
                                                                                • Noise ndash go away
                                                                                • What is the median Value
                                                                                • The median value
                                                                                • Noise away ndash the median filter
                                                                                • Noise removal ndash average filter
                                                                                • Noise removal ndash median filter
                                                                                • Image Filtering
                                                                                • Median filter
                                                                                • Rank filters
                                                                                • Median filter
                                                                                • Correlation
                                                                                • Why do we need similarity
                                                                                • Correlation (1D)
                                                                                • Correlation (1D)
                                                                                • Normalisation
                                                                                • Normalisation
                                                                                • Correlation on images
                                                                                • Correlation on images
                                                                                • Correlation on images
                                                                                • Draw your filter
                                                                                • Correlation on images ndash no normalisation
                                                                                • Correlation on images ndash no normalisation 2
                                                                                • Mathematics of 2D Correlation
                                                                                • Mathematics of 2D Correlation
                                                                                • Mathematics of 2D Correlation
                                                                                • Slide Number 40
                                                                                • 2D Kernel Normalisation
                                                                                • Correlation
                                                                                • Smoothing filters
                                                                                • Use of smoothing
                                                                                • Use of smoothing
                                                                                • Mean filter
                                                                                • Border handling
                                                                                • Border handling ndash extend the input
                                                                                • Correlation with zero padding
                                                                                • Border handling ndash extend the input
                                                                                • Template Matching
                                                                                • Template Matching
                                                                                • Template Matching
                                                                                • Template Matching
                                                                                • Problematic Correlation
                                                                                • Normalised Cross Correlation
                                                                                • Length of template
                                                                                • Length of image patch
                                                                                • Normalised Cross Correlation
                                                                                • Normalised Cross Correlation
                                                                                • Normalised Cross Correlation
                                                                                • Edges
                                                                                • Edges
                                                                                • Finite Difference
                                                                                • Edges
                                                                                • Edges in 2D
                                                                                • Edge filter kernel
                                                                                • Prewitt filter
                                                                                • Edge detection
                                                                                • Edge filtering
                                                                                • 02511 - Niveau af dagens emne forelaeligsing
                                                                                • 02512 - Niveau af dagens emne forelaeligsing
                                                                                • 02511 - Mit eget udbytte af dagen
                                                                                • 02512 - Mit eget udbytte af dagen
                                                                                • 02511 - Sidste uges oslashvelser (pixelwise operations)
                                                                                • 02512 - Sidste uges oslashvelser (pixelwise operations)
                                                                                • Denne uges brug af clickers
                                                                                • What can you do after today
                                                                                • Oslashvelsesrapport over oslashvelse 4 - 02511
                                                                                • Exercises
                                                                                  A0
                                                                                  B0
                                                                                  C5
                                                                                  D0
                                                                                  E6
                                                                                  A
                                                                                  B
                                                                                  C
                                                                                  D
                                                                                  E
                                                                                  A3
                                                                                  B0
                                                                                  C3
                                                                                  D0
                                                                                  E0
                                                                                  A
                                                                                  B
                                                                                  C
                                                                                  D
                                                                                  E
                                                                                  A0
                                                                                  B0
                                                                                  C1
                                                                                  D4
                                                                                  E1
                                                                                  A
                                                                                  B
                                                                                  C
                                                                                  D
                                                                                  E
                                                                                  A2
                                                                                  B1
                                                                                  C3
                                                                                  D2
                                                                                  E0
                                                                                  A
                                                                                  B
                                                                                  C
                                                                                  D
                                                                                  E
                                                                                  A0
                                                                                  B0
                                                                                  C2
                                                                                  D6
                                                                                  E0
                                                                                  A
                                                                                  B
                                                                                  C
                                                                                  D
                                                                                  E
                                                                                  A0
                                                                                  B0
                                                                                  C1
                                                                                  D0
                                                                                  E0
                                                                                  A
                                                                                  B
                                                                                  C
                                                                                  D
                                                                                  E
                                                                                  A2
                                                                                  B3
                                                                                  C6
                                                                                  D1
                                                                                  E0
                                                                                  A
                                                                                  B
                                                                                  C
                                                                                  D
                                                                                  E
                                                                                  A0
                                                                                  B8
                                                                                  C1
                                                                                  D1
                                                                                  E0
                                                                                  A
                                                                                  B
                                                                                  C
                                                                                  D
                                                                                  E
                                                                                  A1
                                                                                  B2
                                                                                  C2
                                                                                  D3
                                                                                  E2
                                                                                  A
                                                                                  B
                                                                                  C
                                                                                  D
                                                                                  E
                                                                                  A0
                                                                                  B13
                                                                                  C0
                                                                                  D0
                                                                                  E0
                                                                                  A
                                                                                  B
                                                                                  C
                                                                                  D
                                                                                  E
                                                                                  A12
                                                                                  B0
                                                                                  C0
                                                                                  D0
                                                                                  E0
                                                                                  A
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                                                                                  C
                                                                                  D
                                                                                  E
                                                                                  A0
                                                                                  B0
                                                                                  C0
                                                                                  D0
                                                                                  E13
                                                                                  A
                                                                                  B
                                                                                  C
                                                                                  D
                                                                                  E
                                                                                  A13
                                                                                  B0
                                                                                  C0
                                                                                  D0
                                                                                  E0
                                                                                  A
                                                                                  B
                                                                                  C
                                                                                  D
                                                                                  E

                                                                                  Chart1

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                                                                                  Mathematics of 2D Correlation

                                                                                  h

                                                                                  f

                                                                                  Correlation operator

                                                                                  1 2 11 3 11 2 1

                                                                                  0 2 4

                                                                                  1 2 2

                                                                                  1 6 3

                                                                                  1 2 1

                                                                                  2 5 3

                                                                                  2 1 3

                                                                                  1 3 1

                                                                                  2 2 2

                                                                                  0 1 3

                                                                                  1 2 0

                                                                                  2 1 4

                                                                                  1 0 1

                                                                                  119892119892 119909119909119910119910 = 119891119891 119909119909119910119910 ∘ ℎ(119909119909119910119910)

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                                                                                  Mathematics of 2D Correlation

                                                                                  1 2 11 3 11 2 1

                                                                                  0 2 4

                                                                                  1 2 2

                                                                                  1 6 3

                                                                                  1 2 1

                                                                                  2 5 3

                                                                                  2 1 3

                                                                                  1 3 1

                                                                                  2 2 2

                                                                                  0 1 3

                                                                                  1 2 0

                                                                                  2 1 4

                                                                                  1 0 1

                                                                                  h

                                                                                  fh(00)

                                                                                  f(21)

                                                                                  Example g(21)

                                                                                  i = -1 j = -1

                                                                                  i = 1 j = 0

                                                                                  119892119892 119909119909119910119910 = 119895119895=minus119877119877

                                                                                  119877119877

                                                                                  119894119894=minus119877119877

                                                                                  119877119877

                                                                                  ℎ(119894119894 119895119895) 119891119891(119909119909 + 119894119894119910119910 + 119895119895)

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                                                                                  Mathematics of 2D Correlation

                                                                                  1 2 11 3 11 2 1

                                                                                  0 2 4

                                                                                  1 2 2

                                                                                  1 6 3

                                                                                  1 2 1

                                                                                  2 5 3

                                                                                  2 1 3

                                                                                  1 3 1

                                                                                  2 2 2

                                                                                  0 1 3

                                                                                  1 2 0

                                                                                  2 1 4

                                                                                  1 0 1

                                                                                  h

                                                                                  f

                                                                                  119892119892 119909119909119910119910 = 119895119895=minus119877119877

                                                                                  119877119877

                                                                                  119894119894=minus119877119877

                                                                                  119877119877

                                                                                  ℎ(119894119894 119895119895) 119891119891(119909119909 + 119894119894119910119910 + 119895119895)

                                                                                  119892119892(119909119909119910119910 = 1 2 + 2 0 + 1 1 + 1 1 + 3 4 + 1 2 + 1 0 + 2 1 + 1 0

                                                                                  DTU Compute

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                                                                                  119892119892 119909119909 119910119910 = 119895119895=minus119877119877

                                                                                  119877119877

                                                                                  119894119894=minus119877119877

                                                                                  119877119877

                                                                                  ℎ(119894119894 119895119895) 119891119891(119909119909 + 119894119894119910119910 + 119895119895)

                                                                                  119892119892 22 =ℎ minus1minus1 sdot 119891119891 11 + ℎ 0minus1 sdot 119891119891 21 + ℎ 1minus1 sdot 119891119891 31 +ℎ minus10 sdot 119891119891 12 + ℎ 00 sdot 119891119891 22 + ℎ 10 sdot 119891119891 32 +ℎ minus11 sdot 119891119891 13 + ℎ 01 sdot 119891119891 23 + ℎ 11 sdot 119891119891 33

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                                                                                  2D Kernel Normalisation

                                                                                  1 2 11 3 11 2 1

                                                                                  h

                                                                                  Normalisation factor

                                                                                  1 + 2 + 1 + 1 + 3 + 1 + 1 + 2 + 1 = 13

                                                                                  119909119909

                                                                                  119910119910

                                                                                  ℎ(119909119909119910119910)

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                                                                                  CorrelationA) 50122B) 123001C) 11233D) 2550E) 90454

                                                                                  0 0 0 0

                                                                                  13

                                                                                  A B C D E

                                                                                  Chart1

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                                                                                  0
                                                                                  0
                                                                                  13

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                                                                                  Smoothing filters

                                                                                  Also know as ndash Smoothing kernel Mean filter Low pass filter blurring

                                                                                  The simplest filter ndash Spatial low pass filterndash Removes high frequencies

                                                                                  Another mask ndash Gaussian filter

                                                                                  1 1 1

                                                                                  1 1 1

                                                                                  1 1 191

                                                                                  1 2 1

                                                                                  2 4 2

                                                                                  1 2 1161

                                                                                  Why Gaussian

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                                                                                  Use of smoothing

                                                                                  3x3 7x7 11x11 15x15

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                                                                                  Use of smoothing Large kernels smooth more Removes high frequency information Good at enhancing big structures

                                                                                  3x3 15x15

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                                                                                  Mean filterA) 166B) 113C) 12D) 51E) 245

                                                                                  0 0 0 0

                                                                                  A B C D E

                                                                                  Chart1

                                                                                  12
                                                                                  0
                                                                                  0
                                                                                  0
                                                                                  0

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                                                                                  Border handling

                                                                                  0 2 41 2 2

                                                                                  1 6 3

                                                                                  1 2 12 5 3

                                                                                  2 1 3

                                                                                  1 3 1

                                                                                  2 2 2

                                                                                  0 1 3

                                                                                  1 2 0

                                                                                  2 1 4

                                                                                  1 0 1

                                                                                  Input Output

                                                                                  No values at the border

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                                                                                  Border handling ndash extend the input

                                                                                  0 2 41 2 2

                                                                                  1 6 3

                                                                                  1 2 12 5 3

                                                                                  2 1 3

                                                                                  1 3 1

                                                                                  2 2 2

                                                                                  0 1 3

                                                                                  1 2 0

                                                                                  2 1 4

                                                                                  1 0 1

                                                                                  Input

                                                                                  0 0 0 0 000000

                                                                                  bull Zero padding ndash what happens

                                                                                  bull Zero is black ndash creates dark border around the image

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                                                                                  Correlation with zero paddingA) 5 8B) 12 16C) 13 3D) 15 21E) 17 12

                                                                                  1 2 11 3 11 2 1

                                                                                  0 2 41 2 2

                                                                                  1 6 3

                                                                                  1 2 12 5 3

                                                                                  2 1 3

                                                                                  1 3 1

                                                                                  2 2 2

                                                                                  0 1 3

                                                                                  1 2 0

                                                                                  2 1 4

                                                                                  1 0 1

                                                                                  0

                                                                                  13

                                                                                  0 0 0

                                                                                  A B C D E

                                                                                  Chart1

                                                                                  0
                                                                                  13
                                                                                  0
                                                                                  0
                                                                                  0

                                                                                  Sheet1

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                                                                                  Border handling ndash extend the input

                                                                                  0 2 41 2 2

                                                                                  1 6 3

                                                                                  1 2 12 5 3

                                                                                  2 1 3

                                                                                  1 3 1

                                                                                  2 2 2

                                                                                  0 1 3

                                                                                  1 2 0

                                                                                  2 1 4

                                                                                  1 0 1

                                                                                  Input

                                                                                  1 2 0 1 311211

                                                                                  bull Reflection

                                                                                  bull Normally better than zero padding

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                                                                                  Template Matching Template

                                                                                  ndash Skabelon paring dansk Locates objects in images

                                                                                  Input

                                                                                  Template

                                                                                  Output Correlation image

                                                                                  DTU Compute

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                                                                                  Template Matching The correlation between the template and the input

                                                                                  image is computed for each pixel

                                                                                  Input

                                                                                  Template

                                                                                  Output Correlation image

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                                                                                  Template Matching The pixel with the highest value is found in the

                                                                                  output imagendash Here is the highest correlation

                                                                                  Input

                                                                                  Template

                                                                                  Output Correlation image

                                                                                  DTU Compute

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                                                                                  Template Matching This corresponds to the found pattern in the input

                                                                                  image

                                                                                  Input

                                                                                  Template

                                                                                  Output Correlation image

                                                                                  DTU Compute

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                                                                                  Problematic Correlation Correlation matching has problem with light areas ndash

                                                                                  why

                                                                                  Input (f)

                                                                                  Template (h)

                                                                                  Output Correlation imageFake max

                                                                                  Real max

                                                                                  Very High119892119892 119909119909119910119910 = 119895119895=minus119877119877

                                                                                  119877119877

                                                                                  119894119894=minus119877119877

                                                                                  119877119877

                                                                                  ℎ(119894119894 119895119895) 119891119891(119909119909 + 119894119894119910119910 + 119895119895)

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                                                                                  Normalised Cross Correlation

                                                                                  Input (f)

                                                                                  Template (h)

                                                                                  Output Correlation image

                                                                                  Real max

                                                                                  NCC x y =Correlation

                                                                                  Length of image patch sdot Length of template

                                                                                  DTU Compute

                                                                                  2122018Introduction to Medical Image Analysis60 DTU Compute Technical University of Denmark

                                                                                  Length of template Vector length

                                                                                  ndash Put all pixel values into a vectorndash Compute the length of this vector

                                                                                  Describes the intensity of the templatendash Bright template has a large lengthndash Dark template has a small length

                                                                                  Template (h)

                                                                                  Length of template = 119895119895=minus119877119877

                                                                                  119877119877

                                                                                  119894119894=minus119877119877

                                                                                  119877119877

                                                                                  ℎ(119894119894 119895119895) ℎ(119894119894 119895119895)

                                                                                  DTU Compute

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                                                                                  Length of image patch Vector length based on pixel values in image patch Describes the intensity of the image patch

                                                                                  Template (h)

                                                                                  Input (f) with patch

                                                                                  DTU Compute

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                                                                                  Normalised Cross Correlation The length of the image patch and the length of

                                                                                  template normalise the NCC If the image is very bright the NCC will be ldquopulled

                                                                                  downrdquo

                                                                                  NCC x y =Correlation

                                                                                  Length of image patch sdot Length of template

                                                                                  DTU Compute

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                                                                                  Normalised Cross Correlation NCC will be between

                                                                                  ndash 0 No similarity between template and image patchndash 1 Template and image patch are identical

                                                                                  Input (f)

                                                                                  Template (h)

                                                                                  Output Correlation image

                                                                                  Real max

                                                                                  NCC x y =Correlation

                                                                                  Length of image patch sdot Length of template

                                                                                  DTU Compute

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                                                                                  Normalised Cross Correlation

                                                                                  A) 010B) 033C) 083D) 062E) 098

                                                                                  Der udfoslashres template matching med og normalized crosscorrelation (NCC) beregnes Hvad bliver NNC i den markerede pixel

                                                                                  1

                                                                                  2 2

                                                                                  3

                                                                                  2

                                                                                  A B C D E

                                                                                  Chart1

                                                                                  1
                                                                                  2
                                                                                  2
                                                                                  3
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                                                                                  Edges An edge is where there is a

                                                                                  high change in gray level values

                                                                                  Objects are often separated from the background by edgesGray level profile

                                                                                  DTU Compute

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                                                                                  Edges The profile as a function f(d) What value is high when there

                                                                                  is an edgendash The slope of fndash The slope of the tangent at d

                                                                                  f(d)

                                                                                  119891119891prime(119889119889)

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                                                                                  Finite Difference Definition of slope

                                                                                  Approximation

                                                                                  Simpler approximationh = 1

                                                                                  119891119891prime 119889119889 = limℎrarr0

                                                                                  119891119891 119889119889 + ℎ minus 119891119891(119889119889)ℎ

                                                                                  119891119891prime 119889119889 asymp119891119891 119889119889 + ℎ minus 119891119891(119889119889)

                                                                                  ℎ

                                                                                  119891119891prime 119889119889 asymp 119891119891 119889119889 + 1 minus 119891119891(119889119889)

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                                                                                  Edges Discrete approximation of frsquo(d) Can be implemented as a filter

                                                                                  -1 0 1

                                                                                  f(d-2) f(d-1) f(d) f(d+1) f(d+2) f(d+3)

                                                                                  f(d)

                                                                                  119891119891prime 119889119889 asymp 119891119891 119889119889 + 1 minus 119891119891(119889119889)

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                                                                                  Edges in 2D Changes in gray level values

                                                                                  ndash Image gradientndash Gradient is the 2D derivative of a 2D function f(xy)ndash Equal to the slope of the imagendash A steep slope is equal to an edge

                                                                                  120571120571119891119891 119909119909119910119910 = 119866(119892119892119909119909119892119892119910119910)

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                                                                                  Edge filter kernel The Prewitt filter is a typical

                                                                                  edge filter Output image has high

                                                                                  values where there are edges

                                                                                  -1 0 1

                                                                                  -1 0 1

                                                                                  -1 0 1Vertical Prewitt filter

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                                                                                  Prewitt filter

                                                                                  Original Prewitt Prewitt

                                                                                  Hot colormapSmooth 15x15

                                                                                  Smooth 15x15

                                                                                  Prewitt

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                                                                                  Edge detection Edge filter

                                                                                  ndash Prewitt for example Thresholding

                                                                                  ndash Separate edges from non-edges

                                                                                  Output is binary imagendash Edges are white

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                                                                                  Edge filtering

                                                                                  A) MeanB) Horizontal SobelC) Vertical PrewittD) Horisontal PrewittE) Median

                                                                                  Der udfoslashres en filtrering (correlation) med et filter paring billedet Der bruges ikke coefficient normalization Den filtrerede vaeligrdi i den markerede pixel bliver -119 Hvilket et 3x3 filter blev benyttet

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                                                                                  02511 - Niveau af dagens emne forelaeligsingA) Meget letB) LetC) PassendeD) SvaeligrtE) Meget svaeligrt

                                                                                  23

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                                                                                  02512 - Niveau af dagens emne forelaeligsingA) Meget letB) LetC) PassendeD) SvaeligrtE) Meget svaeligrt

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                                                                                  02511 - Mit eget udbytte af dagenA) Jeg har laeligrt meget lidtB) Lidt laeligringC) PassendeD) God laeligringE) Jeg har laeligrt meget

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                                                                                  02512 - Mit eget udbytte af dagenA) Jeg har laeligrt meget lidtB) Lidt laeligringC) PassendeD) God laeligringE) Jeg har laeligrt meget

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                                                                                  02511 - Sidste uges oslashvelser (pixelwiseoperations)A) Meget letteB) LetteC) PassendeD) SvaeligreE) Meget svaeligre

                                                                                  0 0

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                                                                                  02512 - Sidste uges oslashvelser (pixelwiseoperations)A) Meget letteB) LetteC) PassendeD) SvaeligreE) Meget svaeligre

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                                                                                  Denne uges brug af clickersA) click click click ndash jeg bliver

                                                                                  sindssygB) For meget clickC) PassendeD) Jeg vil gerne have lidt mereE) Jeg kan ikrsquo faring nok

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                                                                                  What can you do after today Describe the difference between point processing and neighbourhood

                                                                                  processing Compute a rank filtered image using the min max median and

                                                                                  difference rank filters Compute a mean filtered image Decide if median or average filtering should be used for noise removal Choose the appropriate image border handling based on a given input

                                                                                  image Implement and apply template matching Compute the normalised cross correlation and explain why it should be

                                                                                  used Apply given image filter kernels to images Use edge filters on images Describe finite difference approximation of image gradients Describe the concept of edge detection

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                                                                                  Oslashvelsesrapport over oslashvelse 4 - 02511 Oslashvelser taeligller cirka 30 af karakteren Skal afleveres senest den 7 marts kl 2359 Kan afleveres af 1 eller 2 personer

                                                                                  ndash I skal skrive jeres egen oslashvelsesrapportndash Brug mindst et af jeres egne billeder

                                                                                  Afleveres som PDF Lad vaeligre med at kopiere opgaveteksten ind i jeres

                                                                                  opgave Put Matlab kode i et Appendix og henvis fra teksten Eksempel rapport over oslashvelse findes paring

                                                                                  hjemmesiden under eksamen

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                                                                                  Exercises

                                                                                  • Introduction to Medical Image Analysis
                                                                                  • Lecture 4 ndash Neighbourhood Processing
                                                                                  • What can you do after today
                                                                                  • Point processing
                                                                                  • Point processing
                                                                                  • Neighbourhood processing
                                                                                  • Use of filtering
                                                                                  • Salt and pepper noise
                                                                                  • Salt and pepper noise
                                                                                  • What is so special about noise
                                                                                  • Noise ndash go away
                                                                                  • What is the median Value
                                                                                  • The median value
                                                                                  • Noise away ndash the median filter
                                                                                  • Noise removal ndash average filter
                                                                                  • Noise removal ndash median filter
                                                                                  • Image Filtering
                                                                                  • Median filter
                                                                                  • Rank filters
                                                                                  • Median filter
                                                                                  • Correlation
                                                                                  • Why do we need similarity
                                                                                  • Correlation (1D)
                                                                                  • Correlation (1D)
                                                                                  • Normalisation
                                                                                  • Normalisation
                                                                                  • Correlation on images
                                                                                  • Correlation on images
                                                                                  • Correlation on images
                                                                                  • Draw your filter
                                                                                  • Correlation on images ndash no normalisation
                                                                                  • Correlation on images ndash no normalisation 2
                                                                                  • Mathematics of 2D Correlation
                                                                                  • Mathematics of 2D Correlation
                                                                                  • Mathematics of 2D Correlation
                                                                                  • Slide Number 40
                                                                                  • 2D Kernel Normalisation
                                                                                  • Correlation
                                                                                  • Smoothing filters
                                                                                  • Use of smoothing
                                                                                  • Use of smoothing
                                                                                  • Mean filter
                                                                                  • Border handling
                                                                                  • Border handling ndash extend the input
                                                                                  • Correlation with zero padding
                                                                                  • Border handling ndash extend the input
                                                                                  • Template Matching
                                                                                  • Template Matching
                                                                                  • Template Matching
                                                                                  • Template Matching
                                                                                  • Problematic Correlation
                                                                                  • Normalised Cross Correlation
                                                                                  • Length of template
                                                                                  • Length of image patch
                                                                                  • Normalised Cross Correlation
                                                                                  • Normalised Cross Correlation
                                                                                  • Normalised Cross Correlation
                                                                                  • Edges
                                                                                  • Edges
                                                                                  • Finite Difference
                                                                                  • Edges
                                                                                  • Edges in 2D
                                                                                  • Edge filter kernel
                                                                                  • Prewitt filter
                                                                                  • Edge detection
                                                                                  • Edge filtering
                                                                                  • 02511 - Niveau af dagens emne forelaeligsing
                                                                                  • 02512 - Niveau af dagens emne forelaeligsing
                                                                                  • 02511 - Mit eget udbytte af dagen
                                                                                  • 02512 - Mit eget udbytte af dagen
                                                                                  • 02511 - Sidste uges oslashvelser (pixelwise operations)
                                                                                  • 02512 - Sidste uges oslashvelser (pixelwise operations)
                                                                                  • Denne uges brug af clickers
                                                                                  • What can you do after today
                                                                                  • Oslashvelsesrapport over oslashvelse 4 - 02511
                                                                                  • Exercises
                                                                                    A0
                                                                                    B0
                                                                                    C5
                                                                                    D0
                                                                                    E6
                                                                                    A
                                                                                    B
                                                                                    C
                                                                                    D
                                                                                    E
                                                                                    A3
                                                                                    B0
                                                                                    C3
                                                                                    D0
                                                                                    E0
                                                                                    A
                                                                                    B
                                                                                    C
                                                                                    D
                                                                                    E
                                                                                    A0
                                                                                    B0
                                                                                    C1
                                                                                    D4
                                                                                    E1
                                                                                    A
                                                                                    B
                                                                                    C
                                                                                    D
                                                                                    E
                                                                                    A2
                                                                                    B1
                                                                                    C3
                                                                                    D2
                                                                                    E0
                                                                                    A
                                                                                    B
                                                                                    C
                                                                                    D
                                                                                    E
                                                                                    A0
                                                                                    B0
                                                                                    C2
                                                                                    D6
                                                                                    E0
                                                                                    A
                                                                                    B
                                                                                    C
                                                                                    D
                                                                                    E
                                                                                    A0
                                                                                    B0
                                                                                    C1
                                                                                    D0
                                                                                    E0
                                                                                    A
                                                                                    B
                                                                                    C
                                                                                    D
                                                                                    E
                                                                                    A2
                                                                                    B3
                                                                                    C6
                                                                                    D1
                                                                                    E0
                                                                                    A
                                                                                    B
                                                                                    C
                                                                                    D
                                                                                    E
                                                                                    A0
                                                                                    B8
                                                                                    C1
                                                                                    D1
                                                                                    E0
                                                                                    A
                                                                                    B
                                                                                    C
                                                                                    D
                                                                                    E
                                                                                    A1
                                                                                    B2
                                                                                    C2
                                                                                    D3
                                                                                    E2
                                                                                    A
                                                                                    B
                                                                                    C
                                                                                    D
                                                                                    E
                                                                                    A0
                                                                                    B13
                                                                                    C0
                                                                                    D0
                                                                                    E0
                                                                                    A
                                                                                    B
                                                                                    C
                                                                                    D
                                                                                    E
                                                                                    A12
                                                                                    B0
                                                                                    C0
                                                                                    D0
                                                                                    E0
                                                                                    A
                                                                                    B
                                                                                    C
                                                                                    D
                                                                                    E
                                                                                    A0
                                                                                    B0
                                                                                    C0
                                                                                    D0
                                                                                    E13
                                                                                    A
                                                                                    B
                                                                                    C
                                                                                    D
                                                                                    E
                                                                                    A13
                                                                                    B0
                                                                                    C0
                                                                                    D0
                                                                                    E0
                                                                                    A
                                                                                    B
                                                                                    C
                                                                                    D
                                                                                    E

                                                                                    Sheet1

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                                                                                    Mathematics of 2D Correlation

                                                                                    h

                                                                                    f

                                                                                    Correlation operator

                                                                                    1 2 11 3 11 2 1

                                                                                    0 2 4

                                                                                    1 2 2

                                                                                    1 6 3

                                                                                    1 2 1

                                                                                    2 5 3

                                                                                    2 1 3

                                                                                    1 3 1

                                                                                    2 2 2

                                                                                    0 1 3

                                                                                    1 2 0

                                                                                    2 1 4

                                                                                    1 0 1

                                                                                    119892119892 119909119909119910119910 = 119891119891 119909119909119910119910 ∘ ℎ(119909119909119910119910)

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                                                                                    Mathematics of 2D Correlation

                                                                                    1 2 11 3 11 2 1

                                                                                    0 2 4

                                                                                    1 2 2

                                                                                    1 6 3

                                                                                    1 2 1

                                                                                    2 5 3

                                                                                    2 1 3

                                                                                    1 3 1

                                                                                    2 2 2

                                                                                    0 1 3

                                                                                    1 2 0

                                                                                    2 1 4

                                                                                    1 0 1

                                                                                    h

                                                                                    fh(00)

                                                                                    f(21)

                                                                                    Example g(21)

                                                                                    i = -1 j = -1

                                                                                    i = 1 j = 0

                                                                                    119892119892 119909119909119910119910 = 119895119895=minus119877119877

                                                                                    119877119877

                                                                                    119894119894=minus119877119877

                                                                                    119877119877

                                                                                    ℎ(119894119894 119895119895) 119891119891(119909119909 + 119894119894119910119910 + 119895119895)

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                                                                                    2122018Introduction to Medical Image Analysis39 DTU Compute Technical University of Denmark

                                                                                    Mathematics of 2D Correlation

                                                                                    1 2 11 3 11 2 1

                                                                                    0 2 4

                                                                                    1 2 2

                                                                                    1 6 3

                                                                                    1 2 1

                                                                                    2 5 3

                                                                                    2 1 3

                                                                                    1 3 1

                                                                                    2 2 2

                                                                                    0 1 3

                                                                                    1 2 0

                                                                                    2 1 4

                                                                                    1 0 1

                                                                                    h

                                                                                    f

                                                                                    119892119892 119909119909119910119910 = 119895119895=minus119877119877

                                                                                    119877119877

                                                                                    119894119894=minus119877119877

                                                                                    119877119877

                                                                                    ℎ(119894119894 119895119895) 119891119891(119909119909 + 119894119894119910119910 + 119895119895)

                                                                                    119892119892(119909119909119910119910 = 1 2 + 2 0 + 1 1 + 1 1 + 3 4 + 1 2 + 1 0 + 2 1 + 1 0

                                                                                    DTU Compute

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                                                                                    119892119892 119909119909 119910119910 = 119895119895=minus119877119877

                                                                                    119877119877

                                                                                    119894119894=minus119877119877

                                                                                    119877119877

                                                                                    ℎ(119894119894 119895119895) 119891119891(119909119909 + 119894119894119910119910 + 119895119895)

                                                                                    119892119892 22 =ℎ minus1minus1 sdot 119891119891 11 + ℎ 0minus1 sdot 119891119891 21 + ℎ 1minus1 sdot 119891119891 31 +ℎ minus10 sdot 119891119891 12 + ℎ 00 sdot 119891119891 22 + ℎ 10 sdot 119891119891 32 +ℎ minus11 sdot 119891119891 13 + ℎ 01 sdot 119891119891 23 + ℎ 11 sdot 119891119891 33

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                                                                                    2D Kernel Normalisation

                                                                                    1 2 11 3 11 2 1

                                                                                    h

                                                                                    Normalisation factor

                                                                                    1 + 2 + 1 + 1 + 3 + 1 + 1 + 2 + 1 = 13

                                                                                    119909119909

                                                                                    119910119910

                                                                                    ℎ(119909119909119910119910)

                                                                                    DTU Compute

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                                                                                    CorrelationA) 50122B) 123001C) 11233D) 2550E) 90454

                                                                                    0 0 0 0

                                                                                    13

                                                                                    A B C D E

                                                                                    Chart1

                                                                                    0
                                                                                    0
                                                                                    0
                                                                                    0
                                                                                    13

                                                                                    Sheet1

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                                                                                    Smoothing filters

                                                                                    Also know as ndash Smoothing kernel Mean filter Low pass filter blurring

                                                                                    The simplest filter ndash Spatial low pass filterndash Removes high frequencies

                                                                                    Another mask ndash Gaussian filter

                                                                                    1 1 1

                                                                                    1 1 1

                                                                                    1 1 191

                                                                                    1 2 1

                                                                                    2 4 2

                                                                                    1 2 1161

                                                                                    Why Gaussian

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                                                                                    Use of smoothing

                                                                                    3x3 7x7 11x11 15x15

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                                                                                    Use of smoothing Large kernels smooth more Removes high frequency information Good at enhancing big structures

                                                                                    3x3 15x15

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                                                                                    Mean filterA) 166B) 113C) 12D) 51E) 245

                                                                                    0 0 0 0

                                                                                    A B C D E

                                                                                    Chart1

                                                                                    12
                                                                                    0
                                                                                    0
                                                                                    0
                                                                                    0

                                                                                    Sheet1

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                                                                                    Border handling

                                                                                    0 2 41 2 2

                                                                                    1 6 3

                                                                                    1 2 12 5 3

                                                                                    2 1 3

                                                                                    1 3 1

                                                                                    2 2 2

                                                                                    0 1 3

                                                                                    1 2 0

                                                                                    2 1 4

                                                                                    1 0 1

                                                                                    Input Output

                                                                                    No values at the border

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                                                                                    Border handling ndash extend the input

                                                                                    0 2 41 2 2

                                                                                    1 6 3

                                                                                    1 2 12 5 3

                                                                                    2 1 3

                                                                                    1 3 1

                                                                                    2 2 2

                                                                                    0 1 3

                                                                                    1 2 0

                                                                                    2 1 4

                                                                                    1 0 1

                                                                                    Input

                                                                                    0 0 0 0 000000

                                                                                    bull Zero padding ndash what happens

                                                                                    bull Zero is black ndash creates dark border around the image

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                                                                                    Correlation with zero paddingA) 5 8B) 12 16C) 13 3D) 15 21E) 17 12

                                                                                    1 2 11 3 11 2 1

                                                                                    0 2 41 2 2

                                                                                    1 6 3

                                                                                    1 2 12 5 3

                                                                                    2 1 3

                                                                                    1 3 1

                                                                                    2 2 2

                                                                                    0 1 3

                                                                                    1 2 0

                                                                                    2 1 4

                                                                                    1 0 1

                                                                                    0

                                                                                    13

                                                                                    0 0 0

                                                                                    A B C D E

                                                                                    Chart1

                                                                                    0
                                                                                    13
                                                                                    0
                                                                                    0
                                                                                    0

                                                                                    Sheet1

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                                                                                    Border handling ndash extend the input

                                                                                    0 2 41 2 2

                                                                                    1 6 3

                                                                                    1 2 12 5 3

                                                                                    2 1 3

                                                                                    1 3 1

                                                                                    2 2 2

                                                                                    0 1 3

                                                                                    1 2 0

                                                                                    2 1 4

                                                                                    1 0 1

                                                                                    Input

                                                                                    1 2 0 1 311211

                                                                                    bull Reflection

                                                                                    bull Normally better than zero padding

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                                                                                    Template Matching Template

                                                                                    ndash Skabelon paring dansk Locates objects in images

                                                                                    Input

                                                                                    Template

                                                                                    Output Correlation image

                                                                                    DTU Compute

                                                                                    2122018Introduction to Medical Image Analysis55 DTU Compute Technical University of Denmark

                                                                                    Template Matching The correlation between the template and the input

                                                                                    image is computed for each pixel

                                                                                    Input

                                                                                    Template

                                                                                    Output Correlation image

                                                                                    DTU Compute

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                                                                                    Template Matching The pixel with the highest value is found in the

                                                                                    output imagendash Here is the highest correlation

                                                                                    Input

                                                                                    Template

                                                                                    Output Correlation image

                                                                                    DTU Compute

                                                                                    2122018Introduction to Medical Image Analysis57 DTU Compute Technical University of Denmark

                                                                                    Template Matching This corresponds to the found pattern in the input

                                                                                    image

                                                                                    Input

                                                                                    Template

                                                                                    Output Correlation image

                                                                                    DTU Compute

                                                                                    2122018Introduction to Medical Image Analysis58 DTU Compute Technical University of Denmark

                                                                                    Problematic Correlation Correlation matching has problem with light areas ndash

                                                                                    why

                                                                                    Input (f)

                                                                                    Template (h)

                                                                                    Output Correlation imageFake max

                                                                                    Real max

                                                                                    Very High119892119892 119909119909119910119910 = 119895119895=minus119877119877

                                                                                    119877119877

                                                                                    119894119894=minus119877119877

                                                                                    119877119877

                                                                                    ℎ(119894119894 119895119895) 119891119891(119909119909 + 119894119894119910119910 + 119895119895)

                                                                                    DTU Compute

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                                                                                    Normalised Cross Correlation

                                                                                    Input (f)

                                                                                    Template (h)

                                                                                    Output Correlation image

                                                                                    Real max

                                                                                    NCC x y =Correlation

                                                                                    Length of image patch sdot Length of template

                                                                                    DTU Compute

                                                                                    2122018Introduction to Medical Image Analysis60 DTU Compute Technical University of Denmark

                                                                                    Length of template Vector length

                                                                                    ndash Put all pixel values into a vectorndash Compute the length of this vector

                                                                                    Describes the intensity of the templatendash Bright template has a large lengthndash Dark template has a small length

                                                                                    Template (h)

                                                                                    Length of template = 119895119895=minus119877119877

                                                                                    119877119877

                                                                                    119894119894=minus119877119877

                                                                                    119877119877

                                                                                    ℎ(119894119894 119895119895) ℎ(119894119894 119895119895)

                                                                                    DTU Compute

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                                                                                    Length of image patch Vector length based on pixel values in image patch Describes the intensity of the image patch

                                                                                    Template (h)

                                                                                    Input (f) with patch

                                                                                    DTU Compute

                                                                                    2122018Introduction to Medical Image Analysis62 DTU Compute Technical University of Denmark

                                                                                    Normalised Cross Correlation The length of the image patch and the length of

                                                                                    template normalise the NCC If the image is very bright the NCC will be ldquopulled

                                                                                    downrdquo

                                                                                    NCC x y =Correlation

                                                                                    Length of image patch sdot Length of template

                                                                                    DTU Compute

                                                                                    2122018Introduction to Medical Image Analysis63 DTU Compute Technical University of Denmark

                                                                                    Normalised Cross Correlation NCC will be between

                                                                                    ndash 0 No similarity between template and image patchndash 1 Template and image patch are identical

                                                                                    Input (f)

                                                                                    Template (h)

                                                                                    Output Correlation image

                                                                                    Real max

                                                                                    NCC x y =Correlation

                                                                                    Length of image patch sdot Length of template

                                                                                    DTU Compute

                                                                                    2122018Introduction to Medical Image Analysis64 DTU Compute Technical University of Denmark

                                                                                    Normalised Cross Correlation

                                                                                    A) 010B) 033C) 083D) 062E) 098

                                                                                    Der udfoslashres template matching med og normalized crosscorrelation (NCC) beregnes Hvad bliver NNC i den markerede pixel

                                                                                    1

                                                                                    2 2

                                                                                    3

                                                                                    2

                                                                                    A B C D E

                                                                                    Chart1

                                                                                    1
                                                                                    2
                                                                                    2
                                                                                    3
                                                                                    2

                                                                                    Sheet1

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                                                                                    Edges An edge is where there is a

                                                                                    high change in gray level values

                                                                                    Objects are often separated from the background by edgesGray level profile

                                                                                    DTU Compute

                                                                                    2122018Introduction to Medical Image Analysis67 DTU Compute Technical University of Denmark

                                                                                    Edges The profile as a function f(d) What value is high when there

                                                                                    is an edgendash The slope of fndash The slope of the tangent at d

                                                                                    f(d)

                                                                                    119891119891prime(119889119889)

                                                                                    DTU Compute

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                                                                                    Finite Difference Definition of slope

                                                                                    Approximation

                                                                                    Simpler approximationh = 1

                                                                                    119891119891prime 119889119889 = limℎrarr0

                                                                                    119891119891 119889119889 + ℎ minus 119891119891(119889119889)ℎ

                                                                                    119891119891prime 119889119889 asymp119891119891 119889119889 + ℎ minus 119891119891(119889119889)

                                                                                    ℎ

                                                                                    119891119891prime 119889119889 asymp 119891119891 119889119889 + 1 minus 119891119891(119889119889)

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                                                                                    Edges Discrete approximation of frsquo(d) Can be implemented as a filter

                                                                                    -1 0 1

                                                                                    f(d-2) f(d-1) f(d) f(d+1) f(d+2) f(d+3)

                                                                                    f(d)

                                                                                    119891119891prime 119889119889 asymp 119891119891 119889119889 + 1 minus 119891119891(119889119889)

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                                                                                    Edges in 2D Changes in gray level values

                                                                                    ndash Image gradientndash Gradient is the 2D derivative of a 2D function f(xy)ndash Equal to the slope of the imagendash A steep slope is equal to an edge

                                                                                    120571120571119891119891 119909119909119910119910 = 119866(119892119892119909119909119892119892119910119910)

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                                                                                    Edge filter kernel The Prewitt filter is a typical

                                                                                    edge filter Output image has high

                                                                                    values where there are edges

                                                                                    -1 0 1

                                                                                    -1 0 1

                                                                                    -1 0 1Vertical Prewitt filter

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                                                                                    Prewitt filter

                                                                                    Original Prewitt Prewitt

                                                                                    Hot colormapSmooth 15x15

                                                                                    Smooth 15x15

                                                                                    Prewitt

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                                                                                    Edge detection Edge filter

                                                                                    ndash Prewitt for example Thresholding

                                                                                    ndash Separate edges from non-edges

                                                                                    Output is binary imagendash Edges are white

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                                                                                    Edge filtering

                                                                                    A) MeanB) Horizontal SobelC) Vertical PrewittD) Horisontal PrewittE) Median

                                                                                    Der udfoslashres en filtrering (correlation) med et filter paring billedet Der bruges ikke coefficient normalization Den filtrerede vaeligrdi i den markerede pixel bliver -119 Hvilket et 3x3 filter blev benyttet

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                                                                                    02511 - Niveau af dagens emne forelaeligsingA) Meget letB) LetC) PassendeD) SvaeligrtE) Meget svaeligrt

                                                                                    23

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                                                                                    02512 - Niveau af dagens emne forelaeligsingA) Meget letB) LetC) PassendeD) SvaeligrtE) Meget svaeligrt

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                                                                                    02511 - Mit eget udbytte af dagenA) Jeg har laeligrt meget lidtB) Lidt laeligringC) PassendeD) God laeligringE) Jeg har laeligrt meget

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                                                                                    02512 - Mit eget udbytte af dagenA) Jeg har laeligrt meget lidtB) Lidt laeligringC) PassendeD) God laeligringE) Jeg har laeligrt meget

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                                                                                    02511 - Sidste uges oslashvelser (pixelwiseoperations)A) Meget letteB) LetteC) PassendeD) SvaeligreE) Meget svaeligre

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                                                                                    02512 - Sidste uges oslashvelser (pixelwiseoperations)A) Meget letteB) LetteC) PassendeD) SvaeligreE) Meget svaeligre

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                                                                                    Denne uges brug af clickersA) click click click ndash jeg bliver

                                                                                    sindssygB) For meget clickC) PassendeD) Jeg vil gerne have lidt mereE) Jeg kan ikrsquo faring nok

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                                                                                    What can you do after today Describe the difference between point processing and neighbourhood

                                                                                    processing Compute a rank filtered image using the min max median and

                                                                                    difference rank filters Compute a mean filtered image Decide if median or average filtering should be used for noise removal Choose the appropriate image border handling based on a given input

                                                                                    image Implement and apply template matching Compute the normalised cross correlation and explain why it should be

                                                                                    used Apply given image filter kernels to images Use edge filters on images Describe finite difference approximation of image gradients Describe the concept of edge detection

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                                                                                    Oslashvelsesrapport over oslashvelse 4 - 02511 Oslashvelser taeligller cirka 30 af karakteren Skal afleveres senest den 7 marts kl 2359 Kan afleveres af 1 eller 2 personer

                                                                                    ndash I skal skrive jeres egen oslashvelsesrapportndash Brug mindst et af jeres egne billeder

                                                                                    Afleveres som PDF Lad vaeligre med at kopiere opgaveteksten ind i jeres

                                                                                    opgave Put Matlab kode i et Appendix og henvis fra teksten Eksempel rapport over oslashvelse findes paring

                                                                                    hjemmesiden under eksamen

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                                                                                    Exercises

                                                                                    • Introduction to Medical Image Analysis
                                                                                    • Lecture 4 ndash Neighbourhood Processing
                                                                                    • What can you do after today
                                                                                    • Point processing
                                                                                    • Point processing
                                                                                    • Neighbourhood processing
                                                                                    • Use of filtering
                                                                                    • Salt and pepper noise
                                                                                    • Salt and pepper noise
                                                                                    • What is so special about noise
                                                                                    • Noise ndash go away
                                                                                    • What is the median Value
                                                                                    • The median value
                                                                                    • Noise away ndash the median filter
                                                                                    • Noise removal ndash average filter
                                                                                    • Noise removal ndash median filter
                                                                                    • Image Filtering
                                                                                    • Median filter
                                                                                    • Rank filters
                                                                                    • Median filter
                                                                                    • Correlation
                                                                                    • Why do we need similarity
                                                                                    • Correlation (1D)
                                                                                    • Correlation (1D)
                                                                                    • Normalisation
                                                                                    • Normalisation
                                                                                    • Correlation on images
                                                                                    • Correlation on images
                                                                                    • Correlation on images
                                                                                    • Draw your filter
                                                                                    • Correlation on images ndash no normalisation
                                                                                    • Correlation on images ndash no normalisation 2
                                                                                    • Mathematics of 2D Correlation
                                                                                    • Mathematics of 2D Correlation
                                                                                    • Mathematics of 2D Correlation
                                                                                    • Slide Number 40
                                                                                    • 2D Kernel Normalisation
                                                                                    • Correlation
                                                                                    • Smoothing filters
                                                                                    • Use of smoothing
                                                                                    • Use of smoothing
                                                                                    • Mean filter
                                                                                    • Border handling
                                                                                    • Border handling ndash extend the input
                                                                                    • Correlation with zero padding
                                                                                    • Border handling ndash extend the input
                                                                                    • Template Matching
                                                                                    • Template Matching
                                                                                    • Template Matching
                                                                                    • Template Matching
                                                                                    • Problematic Correlation
                                                                                    • Normalised Cross Correlation
                                                                                    • Length of template
                                                                                    • Length of image patch
                                                                                    • Normalised Cross Correlation
                                                                                    • Normalised Cross Correlation
                                                                                    • Normalised Cross Correlation
                                                                                    • Edges
                                                                                    • Edges
                                                                                    • Finite Difference
                                                                                    • Edges
                                                                                    • Edges in 2D
                                                                                    • Edge filter kernel
                                                                                    • Prewitt filter
                                                                                    • Edge detection
                                                                                    • Edge filtering
                                                                                    • 02511 - Niveau af dagens emne forelaeligsing
                                                                                    • 02512 - Niveau af dagens emne forelaeligsing
                                                                                    • 02511 - Mit eget udbytte af dagen
                                                                                    • 02512 - Mit eget udbytte af dagen
                                                                                    • 02511 - Sidste uges oslashvelser (pixelwise operations)
                                                                                    • 02512 - Sidste uges oslashvelser (pixelwise operations)
                                                                                    • Denne uges brug af clickers
                                                                                    • What can you do after today
                                                                                    • Oslashvelsesrapport over oslashvelse 4 - 02511
                                                                                    • Exercises
                                                                                      A0
                                                                                      B0
                                                                                      C5
                                                                                      D0
                                                                                      E6
                                                                                      A
                                                                                      B
                                                                                      C
                                                                                      D
                                                                                      E
                                                                                      A3
                                                                                      B0
                                                                                      C3
                                                                                      D0
                                                                                      E0
                                                                                      A
                                                                                      B
                                                                                      C
                                                                                      D
                                                                                      E
                                                                                      A0
                                                                                      B0
                                                                                      C1
                                                                                      D4
                                                                                      E1
                                                                                      A
                                                                                      B
                                                                                      C
                                                                                      D
                                                                                      E
                                                                                      A2
                                                                                      B1
                                                                                      C3
                                                                                      D2
                                                                                      E0
                                                                                      A
                                                                                      B
                                                                                      C
                                                                                      D
                                                                                      E
                                                                                      A0
                                                                                      B0
                                                                                      C2
                                                                                      D6
                                                                                      E0
                                                                                      A
                                                                                      B
                                                                                      C
                                                                                      D
                                                                                      E
                                                                                      A0
                                                                                      B0
                                                                                      C1
                                                                                      D0
                                                                                      E0
                                                                                      A
                                                                                      B
                                                                                      C
                                                                                      D
                                                                                      E
                                                                                      A2
                                                                                      B3
                                                                                      C6
                                                                                      D1
                                                                                      E0
                                                                                      A
                                                                                      B
                                                                                      C
                                                                                      D
                                                                                      E
                                                                                      A0
                                                                                      B8
                                                                                      C1
                                                                                      D1
                                                                                      E0
                                                                                      A
                                                                                      B
                                                                                      C
                                                                                      D
                                                                                      E
                                                                                      A1
                                                                                      B2
                                                                                      C2
                                                                                      D3
                                                                                      E2
                                                                                      A
                                                                                      B
                                                                                      C
                                                                                      D
                                                                                      E
                                                                                      A0
                                                                                      B13
                                                                                      C0
                                                                                      D0
                                                                                      E0
                                                                                      A
                                                                                      B
                                                                                      C
                                                                                      D
                                                                                      E
                                                                                      A12
                                                                                      B0
                                                                                      C0
                                                                                      D0
                                                                                      E0
                                                                                      A
                                                                                      B
                                                                                      C
                                                                                      D
                                                                                      E
                                                                                      A0
                                                                                      B0
                                                                                      C0
                                                                                      D0
                                                                                      E13
                                                                                      A
                                                                                      B
                                                                                      C
                                                                                      D
                                                                                      E
                                                                                      A13
                                                                                      B0
                                                                                      C0
                                                                                      D0
                                                                                      E0

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                                                                                      Mathematics of 2D Correlation

                                                                                      h

                                                                                      f

                                                                                      Correlation operator

                                                                                      1 2 11 3 11 2 1

                                                                                      0 2 4

                                                                                      1 2 2

                                                                                      1 6 3

                                                                                      1 2 1

                                                                                      2 5 3

                                                                                      2 1 3

                                                                                      1 3 1

                                                                                      2 2 2

                                                                                      0 1 3

                                                                                      1 2 0

                                                                                      2 1 4

                                                                                      1 0 1

                                                                                      119892119892 119909119909119910119910 = 119891119891 119909119909119910119910 ∘ ℎ(119909119909119910119910)

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                                                                                      Mathematics of 2D Correlation

                                                                                      1 2 11 3 11 2 1

                                                                                      0 2 4

                                                                                      1 2 2

                                                                                      1 6 3

                                                                                      1 2 1

                                                                                      2 5 3

                                                                                      2 1 3

                                                                                      1 3 1

                                                                                      2 2 2

                                                                                      0 1 3

                                                                                      1 2 0

                                                                                      2 1 4

                                                                                      1 0 1

                                                                                      h

                                                                                      fh(00)

                                                                                      f(21)

                                                                                      Example g(21)

                                                                                      i = -1 j = -1

                                                                                      i = 1 j = 0

                                                                                      119892119892 119909119909119910119910 = 119895119895=minus119877119877

                                                                                      119877119877

                                                                                      119894119894=minus119877119877

                                                                                      119877119877

                                                                                      ℎ(119894119894 119895119895) 119891119891(119909119909 + 119894119894119910119910 + 119895119895)

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                                                                                      Mathematics of 2D Correlation

                                                                                      1 2 11 3 11 2 1

                                                                                      0 2 4

                                                                                      1 2 2

                                                                                      1 6 3

                                                                                      1 2 1

                                                                                      2 5 3

                                                                                      2 1 3

                                                                                      1 3 1

                                                                                      2 2 2

                                                                                      0 1 3

                                                                                      1 2 0

                                                                                      2 1 4

                                                                                      1 0 1

                                                                                      h

                                                                                      f

                                                                                      119892119892 119909119909119910119910 = 119895119895=minus119877119877

                                                                                      119877119877

                                                                                      119894119894=minus119877119877

                                                                                      119877119877

                                                                                      ℎ(119894119894 119895119895) 119891119891(119909119909 + 119894119894119910119910 + 119895119895)

                                                                                      119892119892(119909119909119910119910 = 1 2 + 2 0 + 1 1 + 1 1 + 3 4 + 1 2 + 1 0 + 2 1 + 1 0

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                                                                                      119892119892 119909119909 119910119910 = 119895119895=minus119877119877

                                                                                      119877119877

                                                                                      119894119894=minus119877119877

                                                                                      119877119877

                                                                                      ℎ(119894119894 119895119895) 119891119891(119909119909 + 119894119894119910119910 + 119895119895)

                                                                                      119892119892 22 =ℎ minus1minus1 sdot 119891119891 11 + ℎ 0minus1 sdot 119891119891 21 + ℎ 1minus1 sdot 119891119891 31 +ℎ minus10 sdot 119891119891 12 + ℎ 00 sdot 119891119891 22 + ℎ 10 sdot 119891119891 32 +ℎ minus11 sdot 119891119891 13 + ℎ 01 sdot 119891119891 23 + ℎ 11 sdot 119891119891 33

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                                                                                      2D Kernel Normalisation

                                                                                      1 2 11 3 11 2 1

                                                                                      h

                                                                                      Normalisation factor

                                                                                      1 + 2 + 1 + 1 + 3 + 1 + 1 + 2 + 1 = 13

                                                                                      119909119909

                                                                                      119910119910

                                                                                      ℎ(119909119909119910119910)

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                                                                                      CorrelationA) 50122B) 123001C) 11233D) 2550E) 90454

                                                                                      0 0 0 0

                                                                                      13

                                                                                      A B C D E

                                                                                      Chart1

                                                                                      0
                                                                                      0
                                                                                      0
                                                                                      0
                                                                                      13

                                                                                      Sheet1

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                                                                                      Smoothing filters

                                                                                      Also know as ndash Smoothing kernel Mean filter Low pass filter blurring

                                                                                      The simplest filter ndash Spatial low pass filterndash Removes high frequencies

                                                                                      Another mask ndash Gaussian filter

                                                                                      1 1 1

                                                                                      1 1 1

                                                                                      1 1 191

                                                                                      1 2 1

                                                                                      2 4 2

                                                                                      1 2 1161

                                                                                      Why Gaussian

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                                                                                      Use of smoothing

                                                                                      3x3 7x7 11x11 15x15

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                                                                                      Use of smoothing Large kernels smooth more Removes high frequency information Good at enhancing big structures

                                                                                      3x3 15x15

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                                                                                      Mean filterA) 166B) 113C) 12D) 51E) 245

                                                                                      0 0 0 0

                                                                                      A B C D E

                                                                                      Chart1

                                                                                      12
                                                                                      0
                                                                                      0
                                                                                      0
                                                                                      0

                                                                                      Sheet1

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                                                                                      Border handling

                                                                                      0 2 41 2 2

                                                                                      1 6 3

                                                                                      1 2 12 5 3

                                                                                      2 1 3

                                                                                      1 3 1

                                                                                      2 2 2

                                                                                      0 1 3

                                                                                      1 2 0

                                                                                      2 1 4

                                                                                      1 0 1

                                                                                      Input Output

                                                                                      No values at the border

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                                                                                      Border handling ndash extend the input

                                                                                      0 2 41 2 2

                                                                                      1 6 3

                                                                                      1 2 12 5 3

                                                                                      2 1 3

                                                                                      1 3 1

                                                                                      2 2 2

                                                                                      0 1 3

                                                                                      1 2 0

                                                                                      2 1 4

                                                                                      1 0 1

                                                                                      Input

                                                                                      0 0 0 0 000000

                                                                                      bull Zero padding ndash what happens

                                                                                      bull Zero is black ndash creates dark border around the image

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                                                                                      Correlation with zero paddingA) 5 8B) 12 16C) 13 3D) 15 21E) 17 12

                                                                                      1 2 11 3 11 2 1

                                                                                      0 2 41 2 2

                                                                                      1 6 3

                                                                                      1 2 12 5 3

                                                                                      2 1 3

                                                                                      1 3 1

                                                                                      2 2 2

                                                                                      0 1 3

                                                                                      1 2 0

                                                                                      2 1 4

                                                                                      1 0 1

                                                                                      0

                                                                                      13

                                                                                      0 0 0

                                                                                      A B C D E

                                                                                      Chart1

                                                                                      0
                                                                                      13
                                                                                      0
                                                                                      0
                                                                                      0

                                                                                      Sheet1

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                                                                                      Border handling ndash extend the input

                                                                                      0 2 41 2 2

                                                                                      1 6 3

                                                                                      1 2 12 5 3

                                                                                      2 1 3

                                                                                      1 3 1

                                                                                      2 2 2

                                                                                      0 1 3

                                                                                      1 2 0

                                                                                      2 1 4

                                                                                      1 0 1

                                                                                      Input

                                                                                      1 2 0 1 311211

                                                                                      bull Reflection

                                                                                      bull Normally better than zero padding

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                                                                                      Template Matching Template

                                                                                      ndash Skabelon paring dansk Locates objects in images

                                                                                      Input

                                                                                      Template

                                                                                      Output Correlation image

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                                                                                      2122018Introduction to Medical Image Analysis55 DTU Compute Technical University of Denmark

                                                                                      Template Matching The correlation between the template and the input

                                                                                      image is computed for each pixel

                                                                                      Input

                                                                                      Template

                                                                                      Output Correlation image

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                                                                                      Template Matching The pixel with the highest value is found in the

                                                                                      output imagendash Here is the highest correlation

                                                                                      Input

                                                                                      Template

                                                                                      Output Correlation image

                                                                                      DTU Compute

                                                                                      2122018Introduction to Medical Image Analysis57 DTU Compute Technical University of Denmark

                                                                                      Template Matching This corresponds to the found pattern in the input

                                                                                      image

                                                                                      Input

                                                                                      Template

                                                                                      Output Correlation image

                                                                                      DTU Compute

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                                                                                      Problematic Correlation Correlation matching has problem with light areas ndash

                                                                                      why

                                                                                      Input (f)

                                                                                      Template (h)

                                                                                      Output Correlation imageFake max

                                                                                      Real max

                                                                                      Very High119892119892 119909119909119910119910 = 119895119895=minus119877119877

                                                                                      119877119877

                                                                                      119894119894=minus119877119877

                                                                                      119877119877

                                                                                      ℎ(119894119894 119895119895) 119891119891(119909119909 + 119894119894119910119910 + 119895119895)

                                                                                      DTU Compute

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                                                                                      Normalised Cross Correlation

                                                                                      Input (f)

                                                                                      Template (h)

                                                                                      Output Correlation image

                                                                                      Real max

                                                                                      NCC x y =Correlation

                                                                                      Length of image patch sdot Length of template

                                                                                      DTU Compute

                                                                                      2122018Introduction to Medical Image Analysis60 DTU Compute Technical University of Denmark

                                                                                      Length of template Vector length

                                                                                      ndash Put all pixel values into a vectorndash Compute the length of this vector

                                                                                      Describes the intensity of the templatendash Bright template has a large lengthndash Dark template has a small length

                                                                                      Template (h)

                                                                                      Length of template = 119895119895=minus119877119877

                                                                                      119877119877

                                                                                      119894119894=minus119877119877

                                                                                      119877119877

                                                                                      ℎ(119894119894 119895119895) ℎ(119894119894 119895119895)

                                                                                      DTU Compute

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                                                                                      Length of image patch Vector length based on pixel values in image patch Describes the intensity of the image patch

                                                                                      Template (h)

                                                                                      Input (f) with patch

                                                                                      DTU Compute

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                                                                                      Normalised Cross Correlation The length of the image patch and the length of

                                                                                      template normalise the NCC If the image is very bright the NCC will be ldquopulled

                                                                                      downrdquo

                                                                                      NCC x y =Correlation

                                                                                      Length of image patch sdot Length of template

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                                                                                      Normalised Cross Correlation NCC will be between

                                                                                      ndash 0 No similarity between template and image patchndash 1 Template and image patch are identical

                                                                                      Input (f)

                                                                                      Template (h)

                                                                                      Output Correlation image

                                                                                      Real max

                                                                                      NCC x y =Correlation

                                                                                      Length of image patch sdot Length of template

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                                                                                      Normalised Cross Correlation

                                                                                      A) 010B) 033C) 083D) 062E) 098

                                                                                      Der udfoslashres template matching med og normalized crosscorrelation (NCC) beregnes Hvad bliver NNC i den markerede pixel

                                                                                      1

                                                                                      2 2

                                                                                      3

                                                                                      2

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                                                                                      Edges An edge is where there is a

                                                                                      high change in gray level values

                                                                                      Objects are often separated from the background by edgesGray level profile

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                                                                                      Edges The profile as a function f(d) What value is high when there

                                                                                      is an edgendash The slope of fndash The slope of the tangent at d

                                                                                      f(d)

                                                                                      119891119891prime(119889119889)

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                                                                                      Finite Difference Definition of slope

                                                                                      Approximation

                                                                                      Simpler approximationh = 1

                                                                                      119891119891prime 119889119889 = limℎrarr0

                                                                                      119891119891 119889119889 + ℎ minus 119891119891(119889119889)ℎ

                                                                                      119891119891prime 119889119889 asymp119891119891 119889119889 + ℎ minus 119891119891(119889119889)

                                                                                      ℎ

                                                                                      119891119891prime 119889119889 asymp 119891119891 119889119889 + 1 minus 119891119891(119889119889)

                                                                                      DTU Compute

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                                                                                      Edges Discrete approximation of frsquo(d) Can be implemented as a filter

                                                                                      -1 0 1

                                                                                      f(d-2) f(d-1) f(d) f(d+1) f(d+2) f(d+3)

                                                                                      f(d)

                                                                                      119891119891prime 119889119889 asymp 119891119891 119889119889 + 1 minus 119891119891(119889119889)

                                                                                      DTU Compute

                                                                                      2122018Introduction to Medical Image Analysis70 DTU Compute Technical University of Denmark

                                                                                      Edges in 2D Changes in gray level values

                                                                                      ndash Image gradientndash Gradient is the 2D derivative of a 2D function f(xy)ndash Equal to the slope of the imagendash A steep slope is equal to an edge

                                                                                      120571120571119891119891 119909119909119910119910 = 119866(119892119892119909119909119892119892119910119910)

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                                                                                      Edge filter kernel The Prewitt filter is a typical

                                                                                      edge filter Output image has high

                                                                                      values where there are edges

                                                                                      -1 0 1

                                                                                      -1 0 1

                                                                                      -1 0 1Vertical Prewitt filter

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                                                                                      Prewitt filter

                                                                                      Original Prewitt Prewitt

                                                                                      Hot colormapSmooth 15x15

                                                                                      Smooth 15x15

                                                                                      Prewitt

                                                                                      DTU Compute

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                                                                                      Edge detection Edge filter

                                                                                      ndash Prewitt for example Thresholding

                                                                                      ndash Separate edges from non-edges

                                                                                      Output is binary imagendash Edges are white

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                                                                                      Edge filtering

                                                                                      A) MeanB) Horizontal SobelC) Vertical PrewittD) Horisontal PrewittE) Median

                                                                                      Der udfoslashres en filtrering (correlation) med et filter paring billedet Der bruges ikke coefficient normalization Den filtrerede vaeligrdi i den markerede pixel bliver -119 Hvilket et 3x3 filter blev benyttet

                                                                                      0

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                                                                                      02511 - Niveau af dagens emne forelaeligsingA) Meget letB) LetC) PassendeD) SvaeligrtE) Meget svaeligrt

                                                                                      23

                                                                                      6

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                                                                                      02512 - Niveau af dagens emne forelaeligsingA) Meget letB) LetC) PassendeD) SvaeligrtE) Meget svaeligrt

                                                                                      0 0

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                                                                                      02511 - Mit eget udbytte af dagenA) Jeg har laeligrt meget lidtB) Lidt laeligringC) PassendeD) God laeligringE) Jeg har laeligrt meget

                                                                                      0 0

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                                                                                      02512 - Mit eget udbytte af dagenA) Jeg har laeligrt meget lidtB) Lidt laeligringC) PassendeD) God laeligringE) Jeg har laeligrt meget

                                                                                      2

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                                                                                      02511 - Sidste uges oslashvelser (pixelwiseoperations)A) Meget letteB) LetteC) PassendeD) SvaeligreE) Meget svaeligre

                                                                                      0 0

                                                                                      1

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                                                                                      02512 - Sidste uges oslashvelser (pixelwiseoperations)A) Meget letteB) LetteC) PassendeD) SvaeligreE) Meget svaeligre

                                                                                      3

                                                                                      0

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                                                                                      Denne uges brug af clickersA) click click click ndash jeg bliver

                                                                                      sindssygB) For meget clickC) PassendeD) Jeg vil gerne have lidt mereE) Jeg kan ikrsquo faring nok

                                                                                      0 0

                                                                                      5

                                                                                      0

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                                                                                      What can you do after today Describe the difference between point processing and neighbourhood

                                                                                      processing Compute a rank filtered image using the min max median and

                                                                                      difference rank filters Compute a mean filtered image Decide if median or average filtering should be used for noise removal Choose the appropriate image border handling based on a given input

                                                                                      image Implement and apply template matching Compute the normalised cross correlation and explain why it should be

                                                                                      used Apply given image filter kernels to images Use edge filters on images Describe finite difference approximation of image gradients Describe the concept of edge detection

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                                                                                      Oslashvelsesrapport over oslashvelse 4 - 02511 Oslashvelser taeligller cirka 30 af karakteren Skal afleveres senest den 7 marts kl 2359 Kan afleveres af 1 eller 2 personer

                                                                                      ndash I skal skrive jeres egen oslashvelsesrapportndash Brug mindst et af jeres egne billeder

                                                                                      Afleveres som PDF Lad vaeligre med at kopiere opgaveteksten ind i jeres

                                                                                      opgave Put Matlab kode i et Appendix og henvis fra teksten Eksempel rapport over oslashvelse findes paring

                                                                                      hjemmesiden under eksamen

                                                                                      DTU Compute

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                                                                                      Exercises

                                                                                      • Introduction to Medical Image Analysis
                                                                                      • Lecture 4 ndash Neighbourhood Processing
                                                                                      • What can you do after today
                                                                                      • Point processing
                                                                                      • Point processing
                                                                                      • Neighbourhood processing
                                                                                      • Use of filtering
                                                                                      • Salt and pepper noise
                                                                                      • Salt and pepper noise
                                                                                      • What is so special about noise
                                                                                      • Noise ndash go away
                                                                                      • What is the median Value
                                                                                      • The median value
                                                                                      • Noise away ndash the median filter
                                                                                      • Noise removal ndash average filter
                                                                                      • Noise removal ndash median filter
                                                                                      • Image Filtering
                                                                                      • Median filter
                                                                                      • Rank filters
                                                                                      • Median filter
                                                                                      • Correlation
                                                                                      • Why do we need similarity
                                                                                      • Correlation (1D)
                                                                                      • Correlation (1D)
                                                                                      • Normalisation
                                                                                      • Normalisation
                                                                                      • Correlation on images
                                                                                      • Correlation on images
                                                                                      • Correlation on images
                                                                                      • Draw your filter
                                                                                      • Correlation on images ndash no normalisation
                                                                                      • Correlation on images ndash no normalisation 2
                                                                                      • Mathematics of 2D Correlation
                                                                                      • Mathematics of 2D Correlation
                                                                                      • Mathematics of 2D Correlation
                                                                                      • Slide Number 40
                                                                                      • 2D Kernel Normalisation
                                                                                      • Correlation
                                                                                      • Smoothing filters
                                                                                      • Use of smoothing
                                                                                      • Use of smoothing
                                                                                      • Mean filter
                                                                                      • Border handling
                                                                                      • Border handling ndash extend the input
                                                                                      • Correlation with zero padding
                                                                                      • Border handling ndash extend the input
                                                                                      • Template Matching
                                                                                      • Template Matching
                                                                                      • Template Matching
                                                                                      • Template Matching
                                                                                      • Problematic Correlation
                                                                                      • Normalised Cross Correlation
                                                                                      • Length of template
                                                                                      • Length of image patch
                                                                                      • Normalised Cross Correlation
                                                                                      • Normalised Cross Correlation
                                                                                      • Normalised Cross Correlation
                                                                                      • Edges
                                                                                      • Edges
                                                                                      • Finite Difference
                                                                                      • Edges
                                                                                      • Edges in 2D
                                                                                      • Edge filter kernel
                                                                                      • Prewitt filter
                                                                                      • Edge detection
                                                                                      • Edge filtering
                                                                                      • 02511 - Niveau af dagens emne forelaeligsing
                                                                                      • 02512 - Niveau af dagens emne forelaeligsing
                                                                                      • 02511 - Mit eget udbytte af dagen
                                                                                      • 02512 - Mit eget udbytte af dagen
                                                                                      • 02511 - Sidste uges oslashvelser (pixelwise operations)
                                                                                      • 02512 - Sidste uges oslashvelser (pixelwise operations)
                                                                                      • Denne uges brug af clickers
                                                                                      • What can you do after today
                                                                                      • Oslashvelsesrapport over oslashvelse 4 - 02511
                                                                                      • Exercises
                                                                                        A0
                                                                                        B0
                                                                                        C5
                                                                                        D0
                                                                                        E6
                                                                                        A
                                                                                        B
                                                                                        C
                                                                                        D
                                                                                        E
                                                                                        A3
                                                                                        B0
                                                                                        C3
                                                                                        D0
                                                                                        E0
                                                                                        A
                                                                                        B
                                                                                        C
                                                                                        D
                                                                                        E
                                                                                        A0
                                                                                        B0
                                                                                        C1
                                                                                        D4
                                                                                        E1
                                                                                        A
                                                                                        B
                                                                                        C
                                                                                        D
                                                                                        E
                                                                                        A2
                                                                                        B1
                                                                                        C3
                                                                                        D2
                                                                                        E0
                                                                                        A
                                                                                        B
                                                                                        C
                                                                                        D
                                                                                        E
                                                                                        A0
                                                                                        B0
                                                                                        C2
                                                                                        D6
                                                                                        E0
                                                                                        A
                                                                                        B
                                                                                        C
                                                                                        D
                                                                                        E
                                                                                        A0
                                                                                        B0
                                                                                        C1
                                                                                        D0
                                                                                        E0
                                                                                        A
                                                                                        B
                                                                                        C
                                                                                        D
                                                                                        E
                                                                                        A2
                                                                                        B3
                                                                                        C6
                                                                                        D1
                                                                                        E0
                                                                                        A
                                                                                        B
                                                                                        C
                                                                                        D
                                                                                        E
                                                                                        A0
                                                                                        B8
                                                                                        C1
                                                                                        D1
                                                                                        E0
                                                                                        A
                                                                                        B
                                                                                        C
                                                                                        D
                                                                                        E
                                                                                        A1
                                                                                        B2
                                                                                        C2
                                                                                        D3
                                                                                        E2
                                                                                        A
                                                                                        B
                                                                                        C
                                                                                        D
                                                                                        E
                                                                                        A0
                                                                                        B13
                                                                                        C0
                                                                                        D0
                                                                                        E0
                                                                                        A
                                                                                        B
                                                                                        C
                                                                                        D
                                                                                        E
                                                                                        A12
                                                                                        B0
                                                                                        C0
                                                                                        D0
                                                                                        E0
                                                                                        A
                                                                                        B
                                                                                        C
                                                                                        D
                                                                                        E
                                                                                        A0
                                                                                        B0
                                                                                        C0
                                                                                        D0
                                                                                        E13
                                                                                        A
                                                                                        B
                                                                                        C
                                                                                        D
                                                                                        E

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                                                                                        2122018Introduction to Medical Image Analysis38 DTU Compute Technical University of Denmark

                                                                                        Mathematics of 2D Correlation

                                                                                        1 2 11 3 11 2 1

                                                                                        0 2 4

                                                                                        1 2 2

                                                                                        1 6 3

                                                                                        1 2 1

                                                                                        2 5 3

                                                                                        2 1 3

                                                                                        1 3 1

                                                                                        2 2 2

                                                                                        0 1 3

                                                                                        1 2 0

                                                                                        2 1 4

                                                                                        1 0 1

                                                                                        h

                                                                                        fh(00)

                                                                                        f(21)

                                                                                        Example g(21)

                                                                                        i = -1 j = -1

                                                                                        i = 1 j = 0

                                                                                        119892119892 119909119909119910119910 = 119895119895=minus119877119877

                                                                                        119877119877

                                                                                        119894119894=minus119877119877

                                                                                        119877119877

                                                                                        ℎ(119894119894 119895119895) 119891119891(119909119909 + 119894119894119910119910 + 119895119895)

                                                                                        DTU Compute

                                                                                        2122018Introduction to Medical Image Analysis39 DTU Compute Technical University of Denmark

                                                                                        Mathematics of 2D Correlation

                                                                                        1 2 11 3 11 2 1

                                                                                        0 2 4

                                                                                        1 2 2

                                                                                        1 6 3

                                                                                        1 2 1

                                                                                        2 5 3

                                                                                        2 1 3

                                                                                        1 3 1

                                                                                        2 2 2

                                                                                        0 1 3

                                                                                        1 2 0

                                                                                        2 1 4

                                                                                        1 0 1

                                                                                        h

                                                                                        f

                                                                                        119892119892 119909119909119910119910 = 119895119895=minus119877119877

                                                                                        119877119877

                                                                                        119894119894=minus119877119877

                                                                                        119877119877

                                                                                        ℎ(119894119894 119895119895) 119891119891(119909119909 + 119894119894119910119910 + 119895119895)

                                                                                        119892119892(119909119909119910119910 = 1 2 + 2 0 + 1 1 + 1 1 + 3 4 + 1 2 + 1 0 + 2 1 + 1 0

                                                                                        DTU Compute

                                                                                        2122018Introduction to Medical Image Analysis40 DTU Compute Technical University of Denmark

                                                                                        119892119892 119909119909 119910119910 = 119895119895=minus119877119877

                                                                                        119877119877

                                                                                        119894119894=minus119877119877

                                                                                        119877119877

                                                                                        ℎ(119894119894 119895119895) 119891119891(119909119909 + 119894119894119910119910 + 119895119895)

                                                                                        119892119892 22 =ℎ minus1minus1 sdot 119891119891 11 + ℎ 0minus1 sdot 119891119891 21 + ℎ 1minus1 sdot 119891119891 31 +ℎ minus10 sdot 119891119891 12 + ℎ 00 sdot 119891119891 22 + ℎ 10 sdot 119891119891 32 +ℎ minus11 sdot 119891119891 13 + ℎ 01 sdot 119891119891 23 + ℎ 11 sdot 119891119891 33

                                                                                        DTU Compute

                                                                                        2122018Introduction to Medical Image Analysis41 DTU Compute Technical University of Denmark

                                                                                        2D Kernel Normalisation

                                                                                        1 2 11 3 11 2 1

                                                                                        h

                                                                                        Normalisation factor

                                                                                        1 + 2 + 1 + 1 + 3 + 1 + 1 + 2 + 1 = 13

                                                                                        119909119909

                                                                                        119910119910

                                                                                        ℎ(119909119909119910119910)

                                                                                        DTU Compute

                                                                                        2122018Introduction to Medical Image Analysis42 DTU Compute Technical University of Denmark

                                                                                        CorrelationA) 50122B) 123001C) 11233D) 2550E) 90454

                                                                                        0 0 0 0

                                                                                        13

                                                                                        A B C D E

                                                                                        Chart1

                                                                                        0
                                                                                        0
                                                                                        0
                                                                                        0
                                                                                        13

                                                                                        Sheet1

                                                                                        DTU Compute

                                                                                        2122018Introduction to Medical Image Analysis44 DTU Compute Technical University of Denmark

                                                                                        Smoothing filters

                                                                                        Also know as ndash Smoothing kernel Mean filter Low pass filter blurring

                                                                                        The simplest filter ndash Spatial low pass filterndash Removes high frequencies

                                                                                        Another mask ndash Gaussian filter

                                                                                        1 1 1

                                                                                        1 1 1

                                                                                        1 1 191

                                                                                        1 2 1

                                                                                        2 4 2

                                                                                        1 2 1161

                                                                                        Why Gaussian

                                                                                        DTU Compute

                                                                                        2122018Introduction to Medical Image Analysis45 DTU Compute Technical University of Denmark

                                                                                        Use of smoothing

                                                                                        3x3 7x7 11x11 15x15

                                                                                        DTU Compute

                                                                                        2122018Introduction to Medical Image Analysis46 DTU Compute Technical University of Denmark

                                                                                        Use of smoothing Large kernels smooth more Removes high frequency information Good at enhancing big structures

                                                                                        3x3 15x15

                                                                                        DTU Compute

                                                                                        2122018Introduction to Medical Image Analysis47 DTU Compute Technical University of Denmark

                                                                                        Mean filterA) 166B) 113C) 12D) 51E) 245

                                                                                        0 0 0 0

                                                                                        A B C D E

                                                                                        Chart1

                                                                                        12
                                                                                        0
                                                                                        0
                                                                                        0
                                                                                        0

                                                                                        Sheet1

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                                                                                        Border handling

                                                                                        0 2 41 2 2

                                                                                        1 6 3

                                                                                        1 2 12 5 3

                                                                                        2 1 3

                                                                                        1 3 1

                                                                                        2 2 2

                                                                                        0 1 3

                                                                                        1 2 0

                                                                                        2 1 4

                                                                                        1 0 1

                                                                                        Input Output

                                                                                        No values at the border

                                                                                        DTU Compute

                                                                                        2122018Introduction to Medical Image Analysis50 DTU Compute Technical University of Denmark

                                                                                        Border handling ndash extend the input

                                                                                        0 2 41 2 2

                                                                                        1 6 3

                                                                                        1 2 12 5 3

                                                                                        2 1 3

                                                                                        1 3 1

                                                                                        2 2 2

                                                                                        0 1 3

                                                                                        1 2 0

                                                                                        2 1 4

                                                                                        1 0 1

                                                                                        Input

                                                                                        0 0 0 0 000000

                                                                                        bull Zero padding ndash what happens

                                                                                        bull Zero is black ndash creates dark border around the image

                                                                                        DTU Compute

                                                                                        2122018Introduction to Medical Image Analysis51 DTU Compute Technical University of Denmark

                                                                                        Correlation with zero paddingA) 5 8B) 12 16C) 13 3D) 15 21E) 17 12

                                                                                        1 2 11 3 11 2 1

                                                                                        0 2 41 2 2

                                                                                        1 6 3

                                                                                        1 2 12 5 3

                                                                                        2 1 3

                                                                                        1 3 1

                                                                                        2 2 2

                                                                                        0 1 3

                                                                                        1 2 0

                                                                                        2 1 4

                                                                                        1 0 1

                                                                                        0

                                                                                        13

                                                                                        0 0 0

                                                                                        A B C D E

                                                                                        Chart1

                                                                                        0
                                                                                        13
                                                                                        0
                                                                                        0
                                                                                        0

                                                                                        Sheet1

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                                                                                        Border handling ndash extend the input

                                                                                        0 2 41 2 2

                                                                                        1 6 3

                                                                                        1 2 12 5 3

                                                                                        2 1 3

                                                                                        1 3 1

                                                                                        2 2 2

                                                                                        0 1 3

                                                                                        1 2 0

                                                                                        2 1 4

                                                                                        1 0 1

                                                                                        Input

                                                                                        1 2 0 1 311211

                                                                                        bull Reflection

                                                                                        bull Normally better than zero padding

                                                                                        DTU Compute

                                                                                        2122018Introduction to Medical Image Analysis54 DTU Compute Technical University of Denmark

                                                                                        Template Matching Template

                                                                                        ndash Skabelon paring dansk Locates objects in images

                                                                                        Input

                                                                                        Template

                                                                                        Output Correlation image

                                                                                        DTU Compute

                                                                                        2122018Introduction to Medical Image Analysis55 DTU Compute Technical University of Denmark

                                                                                        Template Matching The correlation between the template and the input

                                                                                        image is computed for each pixel

                                                                                        Input

                                                                                        Template

                                                                                        Output Correlation image

                                                                                        DTU Compute

                                                                                        2122018Introduction to Medical Image Analysis56 DTU Compute Technical University of Denmark

                                                                                        Template Matching The pixel with the highest value is found in the

                                                                                        output imagendash Here is the highest correlation

                                                                                        Input

                                                                                        Template

                                                                                        Output Correlation image

                                                                                        DTU Compute

                                                                                        2122018Introduction to Medical Image Analysis57 DTU Compute Technical University of Denmark

                                                                                        Template Matching This corresponds to the found pattern in the input

                                                                                        image

                                                                                        Input

                                                                                        Template

                                                                                        Output Correlation image

                                                                                        DTU Compute

                                                                                        2122018Introduction to Medical Image Analysis58 DTU Compute Technical University of Denmark

                                                                                        Problematic Correlation Correlation matching has problem with light areas ndash

                                                                                        why

                                                                                        Input (f)

                                                                                        Template (h)

                                                                                        Output Correlation imageFake max

                                                                                        Real max

                                                                                        Very High119892119892 119909119909119910119910 = 119895119895=minus119877119877

                                                                                        119877119877

                                                                                        119894119894=minus119877119877

                                                                                        119877119877

                                                                                        ℎ(119894119894 119895119895) 119891119891(119909119909 + 119894119894119910119910 + 119895119895)

                                                                                        DTU Compute

                                                                                        2122018Introduction to Medical Image Analysis59 DTU Compute Technical University of Denmark

                                                                                        Normalised Cross Correlation

                                                                                        Input (f)

                                                                                        Template (h)

                                                                                        Output Correlation image

                                                                                        Real max

                                                                                        NCC x y =Correlation

                                                                                        Length of image patch sdot Length of template

                                                                                        DTU Compute

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                                                                                        Length of template Vector length

                                                                                        ndash Put all pixel values into a vectorndash Compute the length of this vector

                                                                                        Describes the intensity of the templatendash Bright template has a large lengthndash Dark template has a small length

                                                                                        Template (h)

                                                                                        Length of template = 119895119895=minus119877119877

                                                                                        119877119877

                                                                                        119894119894=minus119877119877

                                                                                        119877119877

                                                                                        ℎ(119894119894 119895119895) ℎ(119894119894 119895119895)

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                                                                                        Length of image patch Vector length based on pixel values in image patch Describes the intensity of the image patch

                                                                                        Template (h)

                                                                                        Input (f) with patch

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                                                                                        Normalised Cross Correlation The length of the image patch and the length of

                                                                                        template normalise the NCC If the image is very bright the NCC will be ldquopulled

                                                                                        downrdquo

                                                                                        NCC x y =Correlation

                                                                                        Length of image patch sdot Length of template

                                                                                        DTU Compute

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                                                                                        Normalised Cross Correlation NCC will be between

                                                                                        ndash 0 No similarity between template and image patchndash 1 Template and image patch are identical

                                                                                        Input (f)

                                                                                        Template (h)

                                                                                        Output Correlation image

                                                                                        Real max

                                                                                        NCC x y =Correlation

                                                                                        Length of image patch sdot Length of template

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                                                                                        Normalised Cross Correlation

                                                                                        A) 010B) 033C) 083D) 062E) 098

                                                                                        Der udfoslashres template matching med og normalized crosscorrelation (NCC) beregnes Hvad bliver NNC i den markerede pixel

                                                                                        1

                                                                                        2 2

                                                                                        3

                                                                                        2

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                                                                                        Edges An edge is where there is a

                                                                                        high change in gray level values

                                                                                        Objects are often separated from the background by edgesGray level profile

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                                                                                        Edges The profile as a function f(d) What value is high when there

                                                                                        is an edgendash The slope of fndash The slope of the tangent at d

                                                                                        f(d)

                                                                                        119891119891prime(119889119889)

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                                                                                        Finite Difference Definition of slope

                                                                                        Approximation

                                                                                        Simpler approximationh = 1

                                                                                        119891119891prime 119889119889 = limℎrarr0

                                                                                        119891119891 119889119889 + ℎ minus 119891119891(119889119889)ℎ

                                                                                        119891119891prime 119889119889 asymp119891119891 119889119889 + ℎ minus 119891119891(119889119889)

                                                                                        ℎ

                                                                                        119891119891prime 119889119889 asymp 119891119891 119889119889 + 1 minus 119891119891(119889119889)

                                                                                        DTU Compute

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                                                                                        Edges Discrete approximation of frsquo(d) Can be implemented as a filter

                                                                                        -1 0 1

                                                                                        f(d-2) f(d-1) f(d) f(d+1) f(d+2) f(d+3)

                                                                                        f(d)

                                                                                        119891119891prime 119889119889 asymp 119891119891 119889119889 + 1 minus 119891119891(119889119889)

                                                                                        DTU Compute

                                                                                        2122018Introduction to Medical Image Analysis70 DTU Compute Technical University of Denmark

                                                                                        Edges in 2D Changes in gray level values

                                                                                        ndash Image gradientndash Gradient is the 2D derivative of a 2D function f(xy)ndash Equal to the slope of the imagendash A steep slope is equal to an edge

                                                                                        120571120571119891119891 119909119909119910119910 = 119866(119892119892119909119909119892119892119910119910)

                                                                                        DTU Compute

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                                                                                        Edge filter kernel The Prewitt filter is a typical

                                                                                        edge filter Output image has high

                                                                                        values where there are edges

                                                                                        -1 0 1

                                                                                        -1 0 1

                                                                                        -1 0 1Vertical Prewitt filter

                                                                                        DTU Compute

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                                                                                        Prewitt filter

                                                                                        Original Prewitt Prewitt

                                                                                        Hot colormapSmooth 15x15

                                                                                        Smooth 15x15

                                                                                        Prewitt

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                                                                                        Edge detection Edge filter

                                                                                        ndash Prewitt for example Thresholding

                                                                                        ndash Separate edges from non-edges

                                                                                        Output is binary imagendash Edges are white

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                                                                                        Edge filtering

                                                                                        A) MeanB) Horizontal SobelC) Vertical PrewittD) Horisontal PrewittE) Median

                                                                                        Der udfoslashres en filtrering (correlation) med et filter paring billedet Der bruges ikke coefficient normalization Den filtrerede vaeligrdi i den markerede pixel bliver -119 Hvilket et 3x3 filter blev benyttet

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                                                                                        02511 - Niveau af dagens emne forelaeligsingA) Meget letB) LetC) PassendeD) SvaeligrtE) Meget svaeligrt

                                                                                        23

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                                                                                        02512 - Niveau af dagens emne forelaeligsingA) Meget letB) LetC) PassendeD) SvaeligrtE) Meget svaeligrt

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                                                                                        02511 - Mit eget udbytte af dagenA) Jeg har laeligrt meget lidtB) Lidt laeligringC) PassendeD) God laeligringE) Jeg har laeligrt meget

                                                                                        0 0

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                                                                                        02512 - Mit eget udbytte af dagenA) Jeg har laeligrt meget lidtB) Lidt laeligringC) PassendeD) God laeligringE) Jeg har laeligrt meget

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                                                                                        02511 - Sidste uges oslashvelser (pixelwiseoperations)A) Meget letteB) LetteC) PassendeD) SvaeligreE) Meget svaeligre

                                                                                        0 0

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                                                                                        02512 - Sidste uges oslashvelser (pixelwiseoperations)A) Meget letteB) LetteC) PassendeD) SvaeligreE) Meget svaeligre

                                                                                        3

                                                                                        0

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                                                                                        Denne uges brug af clickersA) click click click ndash jeg bliver

                                                                                        sindssygB) For meget clickC) PassendeD) Jeg vil gerne have lidt mereE) Jeg kan ikrsquo faring nok

                                                                                        0 0

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                                                                                        What can you do after today Describe the difference between point processing and neighbourhood

                                                                                        processing Compute a rank filtered image using the min max median and

                                                                                        difference rank filters Compute a mean filtered image Decide if median or average filtering should be used for noise removal Choose the appropriate image border handling based on a given input

                                                                                        image Implement and apply template matching Compute the normalised cross correlation and explain why it should be

                                                                                        used Apply given image filter kernels to images Use edge filters on images Describe finite difference approximation of image gradients Describe the concept of edge detection

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                                                                                        Oslashvelsesrapport over oslashvelse 4 - 02511 Oslashvelser taeligller cirka 30 af karakteren Skal afleveres senest den 7 marts kl 2359 Kan afleveres af 1 eller 2 personer

                                                                                        ndash I skal skrive jeres egen oslashvelsesrapportndash Brug mindst et af jeres egne billeder

                                                                                        Afleveres som PDF Lad vaeligre med at kopiere opgaveteksten ind i jeres

                                                                                        opgave Put Matlab kode i et Appendix og henvis fra teksten Eksempel rapport over oslashvelse findes paring

                                                                                        hjemmesiden under eksamen

                                                                                        DTU Compute

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                                                                                        Exercises

                                                                                        • Introduction to Medical Image Analysis
                                                                                        • Lecture 4 ndash Neighbourhood Processing
                                                                                        • What can you do after today
                                                                                        • Point processing
                                                                                        • Point processing
                                                                                        • Neighbourhood processing
                                                                                        • Use of filtering
                                                                                        • Salt and pepper noise
                                                                                        • Salt and pepper noise
                                                                                        • What is so special about noise
                                                                                        • Noise ndash go away
                                                                                        • What is the median Value
                                                                                        • The median value
                                                                                        • Noise away ndash the median filter
                                                                                        • Noise removal ndash average filter
                                                                                        • Noise removal ndash median filter
                                                                                        • Image Filtering
                                                                                        • Median filter
                                                                                        • Rank filters
                                                                                        • Median filter
                                                                                        • Correlation
                                                                                        • Why do we need similarity
                                                                                        • Correlation (1D)
                                                                                        • Correlation (1D)
                                                                                        • Normalisation
                                                                                        • Normalisation
                                                                                        • Correlation on images
                                                                                        • Correlation on images
                                                                                        • Correlation on images
                                                                                        • Draw your filter
                                                                                        • Correlation on images ndash no normalisation
                                                                                        • Correlation on images ndash no normalisation 2
                                                                                        • Mathematics of 2D Correlation
                                                                                        • Mathematics of 2D Correlation
                                                                                        • Mathematics of 2D Correlation
                                                                                        • Slide Number 40
                                                                                        • 2D Kernel Normalisation
                                                                                        • Correlation
                                                                                        • Smoothing filters
                                                                                        • Use of smoothing
                                                                                        • Use of smoothing
                                                                                        • Mean filter
                                                                                        • Border handling
                                                                                        • Border handling ndash extend the input
                                                                                        • Correlation with zero padding
                                                                                        • Border handling ndash extend the input
                                                                                        • Template Matching
                                                                                        • Template Matching
                                                                                        • Template Matching
                                                                                        • Template Matching
                                                                                        • Problematic Correlation
                                                                                        • Normalised Cross Correlation
                                                                                        • Length of template
                                                                                        • Length of image patch
                                                                                        • Normalised Cross Correlation
                                                                                        • Normalised Cross Correlation
                                                                                        • Normalised Cross Correlation
                                                                                        • Edges
                                                                                        • Edges
                                                                                        • Finite Difference
                                                                                        • Edges
                                                                                        • Edges in 2D
                                                                                        • Edge filter kernel
                                                                                        • Prewitt filter
                                                                                        • Edge detection
                                                                                        • Edge filtering
                                                                                        • 02511 - Niveau af dagens emne forelaeligsing
                                                                                        • 02512 - Niveau af dagens emne forelaeligsing
                                                                                        • 02511 - Mit eget udbytte af dagen
                                                                                        • 02512 - Mit eget udbytte af dagen
                                                                                        • 02511 - Sidste uges oslashvelser (pixelwise operations)
                                                                                        • 02512 - Sidste uges oslashvelser (pixelwise operations)
                                                                                        • Denne uges brug af clickers
                                                                                        • What can you do after today
                                                                                        • Oslashvelsesrapport over oslashvelse 4 - 02511
                                                                                        • Exercises
                                                                                          A0
                                                                                          B0
                                                                                          C5
                                                                                          D0
                                                                                          E6
                                                                                          A
                                                                                          B
                                                                                          C
                                                                                          D
                                                                                          E
                                                                                          A3
                                                                                          B0
                                                                                          C3
                                                                                          D0
                                                                                          E0
                                                                                          A
                                                                                          B
                                                                                          C
                                                                                          D
                                                                                          E
                                                                                          A0
                                                                                          B0
                                                                                          C1
                                                                                          D4
                                                                                          E1
                                                                                          A
                                                                                          B
                                                                                          C
                                                                                          D
                                                                                          E
                                                                                          A2
                                                                                          B1
                                                                                          C3
                                                                                          D2
                                                                                          E0
                                                                                          A
                                                                                          B
                                                                                          C
                                                                                          D
                                                                                          E
                                                                                          A0
                                                                                          B0
                                                                                          C2
                                                                                          D6
                                                                                          E0
                                                                                          A
                                                                                          B
                                                                                          C
                                                                                          D
                                                                                          E
                                                                                          A0
                                                                                          B0
                                                                                          C1
                                                                                          D0
                                                                                          E0
                                                                                          A
                                                                                          B
                                                                                          C
                                                                                          D
                                                                                          E
                                                                                          A2
                                                                                          B3
                                                                                          C6
                                                                                          D1
                                                                                          E0
                                                                                          A
                                                                                          B
                                                                                          C
                                                                                          D
                                                                                          E
                                                                                          A0
                                                                                          B8
                                                                                          C1
                                                                                          D1
                                                                                          E0
                                                                                          A
                                                                                          B
                                                                                          C
                                                                                          D
                                                                                          E
                                                                                          A1
                                                                                          B2
                                                                                          C2
                                                                                          D3
                                                                                          E2
                                                                                          A
                                                                                          B
                                                                                          C
                                                                                          D
                                                                                          E
                                                                                          A0
                                                                                          B13
                                                                                          C0
                                                                                          D0
                                                                                          E0
                                                                                          A
                                                                                          B
                                                                                          C
                                                                                          D
                                                                                          E
                                                                                          A12
                                                                                          B0
                                                                                          C0
                                                                                          D0
                                                                                          E0
                                                                                          A
                                                                                          B
                                                                                          C
                                                                                          D
                                                                                          E
                                                                                          A0
                                                                                          B0
                                                                                          C0
                                                                                          D0
                                                                                          E13
                                                                                          A
                                                                                          B
                                                                                          C
                                                                                          D
                                                                                          E

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                                                                                          Mathematics of 2D Correlation

                                                                                          1 2 11 3 11 2 1

                                                                                          0 2 4

                                                                                          1 2 2

                                                                                          1 6 3

                                                                                          1 2 1

                                                                                          2 5 3

                                                                                          2 1 3

                                                                                          1 3 1

                                                                                          2 2 2

                                                                                          0 1 3

                                                                                          1 2 0

                                                                                          2 1 4

                                                                                          1 0 1

                                                                                          h

                                                                                          f

                                                                                          119892119892 119909119909119910119910 = 119895119895=minus119877119877

                                                                                          119877119877

                                                                                          119894119894=minus119877119877

                                                                                          119877119877

                                                                                          ℎ(119894119894 119895119895) 119891119891(119909119909 + 119894119894119910119910 + 119895119895)

                                                                                          119892119892(119909119909119910119910 = 1 2 + 2 0 + 1 1 + 1 1 + 3 4 + 1 2 + 1 0 + 2 1 + 1 0

                                                                                          DTU Compute

                                                                                          2122018Introduction to Medical Image Analysis40 DTU Compute Technical University of Denmark

                                                                                          119892119892 119909119909 119910119910 = 119895119895=minus119877119877

                                                                                          119877119877

                                                                                          119894119894=minus119877119877

                                                                                          119877119877

                                                                                          ℎ(119894119894 119895119895) 119891119891(119909119909 + 119894119894119910119910 + 119895119895)

                                                                                          119892119892 22 =ℎ minus1minus1 sdot 119891119891 11 + ℎ 0minus1 sdot 119891119891 21 + ℎ 1minus1 sdot 119891119891 31 +ℎ minus10 sdot 119891119891 12 + ℎ 00 sdot 119891119891 22 + ℎ 10 sdot 119891119891 32 +ℎ minus11 sdot 119891119891 13 + ℎ 01 sdot 119891119891 23 + ℎ 11 sdot 119891119891 33

                                                                                          DTU Compute

                                                                                          2122018Introduction to Medical Image Analysis41 DTU Compute Technical University of Denmark

                                                                                          2D Kernel Normalisation

                                                                                          1 2 11 3 11 2 1

                                                                                          h

                                                                                          Normalisation factor

                                                                                          1 + 2 + 1 + 1 + 3 + 1 + 1 + 2 + 1 = 13

                                                                                          119909119909

                                                                                          119910119910

                                                                                          ℎ(119909119909119910119910)

                                                                                          DTU Compute

                                                                                          2122018Introduction to Medical Image Analysis42 DTU Compute Technical University of Denmark

                                                                                          CorrelationA) 50122B) 123001C) 11233D) 2550E) 90454

                                                                                          0 0 0 0

                                                                                          13

                                                                                          A B C D E

                                                                                          Chart1

                                                                                          0
                                                                                          0
                                                                                          0
                                                                                          0
                                                                                          13

                                                                                          Sheet1

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                                                                                          2122018Introduction to Medical Image Analysis44 DTU Compute Technical University of Denmark

                                                                                          Smoothing filters

                                                                                          Also know as ndash Smoothing kernel Mean filter Low pass filter blurring

                                                                                          The simplest filter ndash Spatial low pass filterndash Removes high frequencies

                                                                                          Another mask ndash Gaussian filter

                                                                                          1 1 1

                                                                                          1 1 1

                                                                                          1 1 191

                                                                                          1 2 1

                                                                                          2 4 2

                                                                                          1 2 1161

                                                                                          Why Gaussian

                                                                                          DTU Compute

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                                                                                          Use of smoothing

                                                                                          3x3 7x7 11x11 15x15

                                                                                          DTU Compute

                                                                                          2122018Introduction to Medical Image Analysis46 DTU Compute Technical University of Denmark

                                                                                          Use of smoothing Large kernels smooth more Removes high frequency information Good at enhancing big structures

                                                                                          3x3 15x15

                                                                                          DTU Compute

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                                                                                          Mean filterA) 166B) 113C) 12D) 51E) 245

                                                                                          0 0 0 0

                                                                                          A B C D E

                                                                                          Chart1

                                                                                          12
                                                                                          0
                                                                                          0
                                                                                          0
                                                                                          0

                                                                                          Sheet1

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                                                                                          Border handling

                                                                                          0 2 41 2 2

                                                                                          1 6 3

                                                                                          1 2 12 5 3

                                                                                          2 1 3

                                                                                          1 3 1

                                                                                          2 2 2

                                                                                          0 1 3

                                                                                          1 2 0

                                                                                          2 1 4

                                                                                          1 0 1

                                                                                          Input Output

                                                                                          No values at the border

                                                                                          DTU Compute

                                                                                          2122018Introduction to Medical Image Analysis50 DTU Compute Technical University of Denmark

                                                                                          Border handling ndash extend the input

                                                                                          0 2 41 2 2

                                                                                          1 6 3

                                                                                          1 2 12 5 3

                                                                                          2 1 3

                                                                                          1 3 1

                                                                                          2 2 2

                                                                                          0 1 3

                                                                                          1 2 0

                                                                                          2 1 4

                                                                                          1 0 1

                                                                                          Input

                                                                                          0 0 0 0 000000

                                                                                          bull Zero padding ndash what happens

                                                                                          bull Zero is black ndash creates dark border around the image

                                                                                          DTU Compute

                                                                                          2122018Introduction to Medical Image Analysis51 DTU Compute Technical University of Denmark

                                                                                          Correlation with zero paddingA) 5 8B) 12 16C) 13 3D) 15 21E) 17 12

                                                                                          1 2 11 3 11 2 1

                                                                                          0 2 41 2 2

                                                                                          1 6 3

                                                                                          1 2 12 5 3

                                                                                          2 1 3

                                                                                          1 3 1

                                                                                          2 2 2

                                                                                          0 1 3

                                                                                          1 2 0

                                                                                          2 1 4

                                                                                          1 0 1

                                                                                          0

                                                                                          13

                                                                                          0 0 0

                                                                                          A B C D E

                                                                                          Chart1

                                                                                          0
                                                                                          13
                                                                                          0
                                                                                          0
                                                                                          0

                                                                                          Sheet1

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                                                                                          Border handling ndash extend the input

                                                                                          0 2 41 2 2

                                                                                          1 6 3

                                                                                          1 2 12 5 3

                                                                                          2 1 3

                                                                                          1 3 1

                                                                                          2 2 2

                                                                                          0 1 3

                                                                                          1 2 0

                                                                                          2 1 4

                                                                                          1 0 1

                                                                                          Input

                                                                                          1 2 0 1 311211

                                                                                          bull Reflection

                                                                                          bull Normally better than zero padding

                                                                                          DTU Compute

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                                                                                          Template Matching Template

                                                                                          ndash Skabelon paring dansk Locates objects in images

                                                                                          Input

                                                                                          Template

                                                                                          Output Correlation image

                                                                                          DTU Compute

                                                                                          2122018Introduction to Medical Image Analysis55 DTU Compute Technical University of Denmark

                                                                                          Template Matching The correlation between the template and the input

                                                                                          image is computed for each pixel

                                                                                          Input

                                                                                          Template

                                                                                          Output Correlation image

                                                                                          DTU Compute

                                                                                          2122018Introduction to Medical Image Analysis56 DTU Compute Technical University of Denmark

                                                                                          Template Matching The pixel with the highest value is found in the

                                                                                          output imagendash Here is the highest correlation

                                                                                          Input

                                                                                          Template

                                                                                          Output Correlation image

                                                                                          DTU Compute

                                                                                          2122018Introduction to Medical Image Analysis57 DTU Compute Technical University of Denmark

                                                                                          Template Matching This corresponds to the found pattern in the input

                                                                                          image

                                                                                          Input

                                                                                          Template

                                                                                          Output Correlation image

                                                                                          DTU Compute

                                                                                          2122018Introduction to Medical Image Analysis58 DTU Compute Technical University of Denmark

                                                                                          Problematic Correlation Correlation matching has problem with light areas ndash

                                                                                          why

                                                                                          Input (f)

                                                                                          Template (h)

                                                                                          Output Correlation imageFake max

                                                                                          Real max

                                                                                          Very High119892119892 119909119909119910119910 = 119895119895=minus119877119877

                                                                                          119877119877

                                                                                          119894119894=minus119877119877

                                                                                          119877119877

                                                                                          ℎ(119894119894 119895119895) 119891119891(119909119909 + 119894119894119910119910 + 119895119895)

                                                                                          DTU Compute

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                                                                                          Normalised Cross Correlation

                                                                                          Input (f)

                                                                                          Template (h)

                                                                                          Output Correlation image

                                                                                          Real max

                                                                                          NCC x y =Correlation

                                                                                          Length of image patch sdot Length of template

                                                                                          DTU Compute

                                                                                          2122018Introduction to Medical Image Analysis60 DTU Compute Technical University of Denmark

                                                                                          Length of template Vector length

                                                                                          ndash Put all pixel values into a vectorndash Compute the length of this vector

                                                                                          Describes the intensity of the templatendash Bright template has a large lengthndash Dark template has a small length

                                                                                          Template (h)

                                                                                          Length of template = 119895119895=minus119877119877

                                                                                          119877119877

                                                                                          119894119894=minus119877119877

                                                                                          119877119877

                                                                                          ℎ(119894119894 119895119895) ℎ(119894119894 119895119895)

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                                                                                          Length of image patch Vector length based on pixel values in image patch Describes the intensity of the image patch

                                                                                          Template (h)

                                                                                          Input (f) with patch

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                                                                                          Normalised Cross Correlation The length of the image patch and the length of

                                                                                          template normalise the NCC If the image is very bright the NCC will be ldquopulled

                                                                                          downrdquo

                                                                                          NCC x y =Correlation

                                                                                          Length of image patch sdot Length of template

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                                                                                          Normalised Cross Correlation NCC will be between

                                                                                          ndash 0 No similarity between template and image patchndash 1 Template and image patch are identical

                                                                                          Input (f)

                                                                                          Template (h)

                                                                                          Output Correlation image

                                                                                          Real max

                                                                                          NCC x y =Correlation

                                                                                          Length of image patch sdot Length of template

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                                                                                          Normalised Cross Correlation

                                                                                          A) 010B) 033C) 083D) 062E) 098

                                                                                          Der udfoslashres template matching med og normalized crosscorrelation (NCC) beregnes Hvad bliver NNC i den markerede pixel

                                                                                          1

                                                                                          2 2

                                                                                          3

                                                                                          2

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                                                                                          2
                                                                                          3
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                                                                                          Edges An edge is where there is a

                                                                                          high change in gray level values

                                                                                          Objects are often separated from the background by edgesGray level profile

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                                                                                          Edges The profile as a function f(d) What value is high when there

                                                                                          is an edgendash The slope of fndash The slope of the tangent at d

                                                                                          f(d)

                                                                                          119891119891prime(119889119889)

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                                                                                          Finite Difference Definition of slope

                                                                                          Approximation

                                                                                          Simpler approximationh = 1

                                                                                          119891119891prime 119889119889 = limℎrarr0

                                                                                          119891119891 119889119889 + ℎ minus 119891119891(119889119889)ℎ

                                                                                          119891119891prime 119889119889 asymp119891119891 119889119889 + ℎ minus 119891119891(119889119889)

                                                                                          ℎ

                                                                                          119891119891prime 119889119889 asymp 119891119891 119889119889 + 1 minus 119891119891(119889119889)

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                                                                                          Edges Discrete approximation of frsquo(d) Can be implemented as a filter

                                                                                          -1 0 1

                                                                                          f(d-2) f(d-1) f(d) f(d+1) f(d+2) f(d+3)

                                                                                          f(d)

                                                                                          119891119891prime 119889119889 asymp 119891119891 119889119889 + 1 minus 119891119891(119889119889)

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                                                                                          Edges in 2D Changes in gray level values

                                                                                          ndash Image gradientndash Gradient is the 2D derivative of a 2D function f(xy)ndash Equal to the slope of the imagendash A steep slope is equal to an edge

                                                                                          120571120571119891119891 119909119909119910119910 = 119866(119892119892119909119909119892119892119910119910)

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                                                                                          Edge filter kernel The Prewitt filter is a typical

                                                                                          edge filter Output image has high

                                                                                          values where there are edges

                                                                                          -1 0 1

                                                                                          -1 0 1

                                                                                          -1 0 1Vertical Prewitt filter

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                                                                                          Prewitt filter

                                                                                          Original Prewitt Prewitt

                                                                                          Hot colormapSmooth 15x15

                                                                                          Smooth 15x15

                                                                                          Prewitt

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                                                                                          Edge detection Edge filter

                                                                                          ndash Prewitt for example Thresholding

                                                                                          ndash Separate edges from non-edges

                                                                                          Output is binary imagendash Edges are white

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                                                                                          Edge filtering

                                                                                          A) MeanB) Horizontal SobelC) Vertical PrewittD) Horisontal PrewittE) Median

                                                                                          Der udfoslashres en filtrering (correlation) med et filter paring billedet Der bruges ikke coefficient normalization Den filtrerede vaeligrdi i den markerede pixel bliver -119 Hvilket et 3x3 filter blev benyttet

                                                                                          0

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                                                                                          02511 - Niveau af dagens emne forelaeligsingA) Meget letB) LetC) PassendeD) SvaeligrtE) Meget svaeligrt

                                                                                          23

                                                                                          6

                                                                                          10

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                                                                                          02512 - Niveau af dagens emne forelaeligsingA) Meget letB) LetC) PassendeD) SvaeligrtE) Meget svaeligrt

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                                                                                          02511 - Mit eget udbytte af dagenA) Jeg har laeligrt meget lidtB) Lidt laeligringC) PassendeD) God laeligringE) Jeg har laeligrt meget

                                                                                          0 0

                                                                                          2

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                                                                                          02512 - Mit eget udbytte af dagenA) Jeg har laeligrt meget lidtB) Lidt laeligringC) PassendeD) God laeligringE) Jeg har laeligrt meget

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                                                                                          1

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                                                                                          02511 - Sidste uges oslashvelser (pixelwiseoperations)A) Meget letteB) LetteC) PassendeD) SvaeligreE) Meget svaeligre

                                                                                          0 0

                                                                                          1

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                                                                                          02512 - Sidste uges oslashvelser (pixelwiseoperations)A) Meget letteB) LetteC) PassendeD) SvaeligreE) Meget svaeligre

                                                                                          3

                                                                                          0

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                                                                                          Denne uges brug af clickersA) click click click ndash jeg bliver

                                                                                          sindssygB) For meget clickC) PassendeD) Jeg vil gerne have lidt mereE) Jeg kan ikrsquo faring nok

                                                                                          0 0

                                                                                          5

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                                                                                          What can you do after today Describe the difference between point processing and neighbourhood

                                                                                          processing Compute a rank filtered image using the min max median and

                                                                                          difference rank filters Compute a mean filtered image Decide if median or average filtering should be used for noise removal Choose the appropriate image border handling based on a given input

                                                                                          image Implement and apply template matching Compute the normalised cross correlation and explain why it should be

                                                                                          used Apply given image filter kernels to images Use edge filters on images Describe finite difference approximation of image gradients Describe the concept of edge detection

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                                                                                          Oslashvelsesrapport over oslashvelse 4 - 02511 Oslashvelser taeligller cirka 30 af karakteren Skal afleveres senest den 7 marts kl 2359 Kan afleveres af 1 eller 2 personer

                                                                                          ndash I skal skrive jeres egen oslashvelsesrapportndash Brug mindst et af jeres egne billeder

                                                                                          Afleveres som PDF Lad vaeligre med at kopiere opgaveteksten ind i jeres

                                                                                          opgave Put Matlab kode i et Appendix og henvis fra teksten Eksempel rapport over oslashvelse findes paring

                                                                                          hjemmesiden under eksamen

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                                                                                          Exercises

                                                                                          • Introduction to Medical Image Analysis
                                                                                          • Lecture 4 ndash Neighbourhood Processing
                                                                                          • What can you do after today
                                                                                          • Point processing
                                                                                          • Point processing
                                                                                          • Neighbourhood processing
                                                                                          • Use of filtering
                                                                                          • Salt and pepper noise
                                                                                          • Salt and pepper noise
                                                                                          • What is so special about noise
                                                                                          • Noise ndash go away
                                                                                          • What is the median Value
                                                                                          • The median value
                                                                                          • Noise away ndash the median filter
                                                                                          • Noise removal ndash average filter
                                                                                          • Noise removal ndash median filter
                                                                                          • Image Filtering
                                                                                          • Median filter
                                                                                          • Rank filters
                                                                                          • Median filter
                                                                                          • Correlation
                                                                                          • Why do we need similarity
                                                                                          • Correlation (1D)
                                                                                          • Correlation (1D)
                                                                                          • Normalisation
                                                                                          • Normalisation
                                                                                          • Correlation on images
                                                                                          • Correlation on images
                                                                                          • Correlation on images
                                                                                          • Draw your filter
                                                                                          • Correlation on images ndash no normalisation
                                                                                          • Correlation on images ndash no normalisation 2
                                                                                          • Mathematics of 2D Correlation
                                                                                          • Mathematics of 2D Correlation
                                                                                          • Mathematics of 2D Correlation
                                                                                          • Slide Number 40
                                                                                          • 2D Kernel Normalisation
                                                                                          • Correlation
                                                                                          • Smoothing filters
                                                                                          • Use of smoothing
                                                                                          • Use of smoothing
                                                                                          • Mean filter
                                                                                          • Border handling
                                                                                          • Border handling ndash extend the input
                                                                                          • Correlation with zero padding
                                                                                          • Border handling ndash extend the input
                                                                                          • Template Matching
                                                                                          • Template Matching
                                                                                          • Template Matching
                                                                                          • Template Matching
                                                                                          • Problematic Correlation
                                                                                          • Normalised Cross Correlation
                                                                                          • Length of template
                                                                                          • Length of image patch
                                                                                          • Normalised Cross Correlation
                                                                                          • Normalised Cross Correlation
                                                                                          • Normalised Cross Correlation
                                                                                          • Edges
                                                                                          • Edges
                                                                                          • Finite Difference
                                                                                          • Edges
                                                                                          • Edges in 2D
                                                                                          • Edge filter kernel
                                                                                          • Prewitt filter
                                                                                          • Edge detection
                                                                                          • Edge filtering
                                                                                          • 02511 - Niveau af dagens emne forelaeligsing
                                                                                          • 02512 - Niveau af dagens emne forelaeligsing
                                                                                          • 02511 - Mit eget udbytte af dagen
                                                                                          • 02512 - Mit eget udbytte af dagen
                                                                                          • 02511 - Sidste uges oslashvelser (pixelwise operations)
                                                                                          • 02512 - Sidste uges oslashvelser (pixelwise operations)
                                                                                          • Denne uges brug af clickers
                                                                                          • What can you do after today
                                                                                          • Oslashvelsesrapport over oslashvelse 4 - 02511
                                                                                          • Exercises
                                                                                            A0
                                                                                            B0
                                                                                            C5
                                                                                            D0
                                                                                            E6
                                                                                            A
                                                                                            B
                                                                                            C
                                                                                            D
                                                                                            E
                                                                                            A3
                                                                                            B0
                                                                                            C3
                                                                                            D0
                                                                                            E0
                                                                                            A
                                                                                            B
                                                                                            C
                                                                                            D
                                                                                            E
                                                                                            A0
                                                                                            B0
                                                                                            C1
                                                                                            D4
                                                                                            E1
                                                                                            A
                                                                                            B
                                                                                            C
                                                                                            D
                                                                                            E
                                                                                            A2
                                                                                            B1
                                                                                            C3
                                                                                            D2
                                                                                            E0
                                                                                            A
                                                                                            B
                                                                                            C
                                                                                            D
                                                                                            E
                                                                                            A0
                                                                                            B0
                                                                                            C2
                                                                                            D6
                                                                                            E0
                                                                                            A
                                                                                            B
                                                                                            C
                                                                                            D
                                                                                            E
                                                                                            A0
                                                                                            B0
                                                                                            C1
                                                                                            D0
                                                                                            E0
                                                                                            A
                                                                                            B
                                                                                            C
                                                                                            D
                                                                                            E
                                                                                            A2
                                                                                            B3
                                                                                            C6
                                                                                            D1
                                                                                            E0
                                                                                            A
                                                                                            B
                                                                                            C
                                                                                            D
                                                                                            E
                                                                                            A0
                                                                                            B8
                                                                                            C1
                                                                                            D1
                                                                                            E0
                                                                                            A
                                                                                            B
                                                                                            C
                                                                                            D
                                                                                            E
                                                                                            A1
                                                                                            B2
                                                                                            C2
                                                                                            D3
                                                                                            E2
                                                                                            A
                                                                                            B
                                                                                            C
                                                                                            D
                                                                                            E
                                                                                            A0
                                                                                            B13
                                                                                            C0
                                                                                            D0
                                                                                            E0
                                                                                            A
                                                                                            B
                                                                                            C
                                                                                            D
                                                                                            E
                                                                                            A12
                                                                                            B0
                                                                                            C0
                                                                                            D0
                                                                                            E0
                                                                                            A
                                                                                            B
                                                                                            C
                                                                                            D
                                                                                            E
                                                                                            A0
                                                                                            B0
                                                                                            C0
                                                                                            D0
                                                                                            E13
                                                                                            A
                                                                                            B
                                                                                            C
                                                                                            D
                                                                                            E

                                                                                            DTU Compute

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                                                                                            119892119892 119909119909 119910119910 = 119895119895=minus119877119877

                                                                                            119877119877

                                                                                            119894119894=minus119877119877

                                                                                            119877119877

                                                                                            ℎ(119894119894 119895119895) 119891119891(119909119909 + 119894119894119910119910 + 119895119895)

                                                                                            119892119892 22 =ℎ minus1minus1 sdot 119891119891 11 + ℎ 0minus1 sdot 119891119891 21 + ℎ 1minus1 sdot 119891119891 31 +ℎ minus10 sdot 119891119891 12 + ℎ 00 sdot 119891119891 22 + ℎ 10 sdot 119891119891 32 +ℎ minus11 sdot 119891119891 13 + ℎ 01 sdot 119891119891 23 + ℎ 11 sdot 119891119891 33

                                                                                            DTU Compute

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                                                                                            2D Kernel Normalisation

                                                                                            1 2 11 3 11 2 1

                                                                                            h

                                                                                            Normalisation factor

                                                                                            1 + 2 + 1 + 1 + 3 + 1 + 1 + 2 + 1 = 13

                                                                                            119909119909

                                                                                            119910119910

                                                                                            ℎ(119909119909119910119910)

                                                                                            DTU Compute

                                                                                            2122018Introduction to Medical Image Analysis42 DTU Compute Technical University of Denmark

                                                                                            CorrelationA) 50122B) 123001C) 11233D) 2550E) 90454

                                                                                            0 0 0 0

                                                                                            13

                                                                                            A B C D E

                                                                                            Chart1

                                                                                            0
                                                                                            0
                                                                                            0
                                                                                            0
                                                                                            13

                                                                                            Sheet1

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                                                                                            Smoothing filters

                                                                                            Also know as ndash Smoothing kernel Mean filter Low pass filter blurring

                                                                                            The simplest filter ndash Spatial low pass filterndash Removes high frequencies

                                                                                            Another mask ndash Gaussian filter

                                                                                            1 1 1

                                                                                            1 1 1

                                                                                            1 1 191

                                                                                            1 2 1

                                                                                            2 4 2

                                                                                            1 2 1161

                                                                                            Why Gaussian

                                                                                            DTU Compute

                                                                                            2122018Introduction to Medical Image Analysis45 DTU Compute Technical University of Denmark

                                                                                            Use of smoothing

                                                                                            3x3 7x7 11x11 15x15

                                                                                            DTU Compute

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                                                                                            Use of smoothing Large kernels smooth more Removes high frequency information Good at enhancing big structures

                                                                                            3x3 15x15

                                                                                            DTU Compute

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                                                                                            Mean filterA) 166B) 113C) 12D) 51E) 245

                                                                                            0 0 0 0

                                                                                            A B C D E

                                                                                            Chart1

                                                                                            12
                                                                                            0
                                                                                            0
                                                                                            0
                                                                                            0

                                                                                            Sheet1

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                                                                                            Border handling

                                                                                            0 2 41 2 2

                                                                                            1 6 3

                                                                                            1 2 12 5 3

                                                                                            2 1 3

                                                                                            1 3 1

                                                                                            2 2 2

                                                                                            0 1 3

                                                                                            1 2 0

                                                                                            2 1 4

                                                                                            1 0 1

                                                                                            Input Output

                                                                                            No values at the border

                                                                                            DTU Compute

                                                                                            2122018Introduction to Medical Image Analysis50 DTU Compute Technical University of Denmark

                                                                                            Border handling ndash extend the input

                                                                                            0 2 41 2 2

                                                                                            1 6 3

                                                                                            1 2 12 5 3

                                                                                            2 1 3

                                                                                            1 3 1

                                                                                            2 2 2

                                                                                            0 1 3

                                                                                            1 2 0

                                                                                            2 1 4

                                                                                            1 0 1

                                                                                            Input

                                                                                            0 0 0 0 000000

                                                                                            bull Zero padding ndash what happens

                                                                                            bull Zero is black ndash creates dark border around the image

                                                                                            DTU Compute

                                                                                            2122018Introduction to Medical Image Analysis51 DTU Compute Technical University of Denmark

                                                                                            Correlation with zero paddingA) 5 8B) 12 16C) 13 3D) 15 21E) 17 12

                                                                                            1 2 11 3 11 2 1

                                                                                            0 2 41 2 2

                                                                                            1 6 3

                                                                                            1 2 12 5 3

                                                                                            2 1 3

                                                                                            1 3 1

                                                                                            2 2 2

                                                                                            0 1 3

                                                                                            1 2 0

                                                                                            2 1 4

                                                                                            1 0 1

                                                                                            0

                                                                                            13

                                                                                            0 0 0

                                                                                            A B C D E

                                                                                            Chart1

                                                                                            0
                                                                                            13
                                                                                            0
                                                                                            0
                                                                                            0

                                                                                            Sheet1

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                                                                                            Border handling ndash extend the input

                                                                                            0 2 41 2 2

                                                                                            1 6 3

                                                                                            1 2 12 5 3

                                                                                            2 1 3

                                                                                            1 3 1

                                                                                            2 2 2

                                                                                            0 1 3

                                                                                            1 2 0

                                                                                            2 1 4

                                                                                            1 0 1

                                                                                            Input

                                                                                            1 2 0 1 311211

                                                                                            bull Reflection

                                                                                            bull Normally better than zero padding

                                                                                            DTU Compute

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                                                                                            Template Matching Template

                                                                                            ndash Skabelon paring dansk Locates objects in images

                                                                                            Input

                                                                                            Template

                                                                                            Output Correlation image

                                                                                            DTU Compute

                                                                                            2122018Introduction to Medical Image Analysis55 DTU Compute Technical University of Denmark

                                                                                            Template Matching The correlation between the template and the input

                                                                                            image is computed for each pixel

                                                                                            Input

                                                                                            Template

                                                                                            Output Correlation image

                                                                                            DTU Compute

                                                                                            2122018Introduction to Medical Image Analysis56 DTU Compute Technical University of Denmark

                                                                                            Template Matching The pixel with the highest value is found in the

                                                                                            output imagendash Here is the highest correlation

                                                                                            Input

                                                                                            Template

                                                                                            Output Correlation image

                                                                                            DTU Compute

                                                                                            2122018Introduction to Medical Image Analysis57 DTU Compute Technical University of Denmark

                                                                                            Template Matching This corresponds to the found pattern in the input

                                                                                            image

                                                                                            Input

                                                                                            Template

                                                                                            Output Correlation image

                                                                                            DTU Compute

                                                                                            2122018Introduction to Medical Image Analysis58 DTU Compute Technical University of Denmark

                                                                                            Problematic Correlation Correlation matching has problem with light areas ndash

                                                                                            why

                                                                                            Input (f)

                                                                                            Template (h)

                                                                                            Output Correlation imageFake max

                                                                                            Real max

                                                                                            Very High119892119892 119909119909119910119910 = 119895119895=minus119877119877

                                                                                            119877119877

                                                                                            119894119894=minus119877119877

                                                                                            119877119877

                                                                                            ℎ(119894119894 119895119895) 119891119891(119909119909 + 119894119894119910119910 + 119895119895)

                                                                                            DTU Compute

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                                                                                            Normalised Cross Correlation

                                                                                            Input (f)

                                                                                            Template (h)

                                                                                            Output Correlation image

                                                                                            Real max

                                                                                            NCC x y =Correlation

                                                                                            Length of image patch sdot Length of template

                                                                                            DTU Compute

                                                                                            2122018Introduction to Medical Image Analysis60 DTU Compute Technical University of Denmark

                                                                                            Length of template Vector length

                                                                                            ndash Put all pixel values into a vectorndash Compute the length of this vector

                                                                                            Describes the intensity of the templatendash Bright template has a large lengthndash Dark template has a small length

                                                                                            Template (h)

                                                                                            Length of template = 119895119895=minus119877119877

                                                                                            119877119877

                                                                                            119894119894=minus119877119877

                                                                                            119877119877

                                                                                            ℎ(119894119894 119895119895) ℎ(119894119894 119895119895)

                                                                                            DTU Compute

                                                                                            2122018Introduction to Medical Image Analysis61 DTU Compute Technical University of Denmark

                                                                                            Length of image patch Vector length based on pixel values in image patch Describes the intensity of the image patch

                                                                                            Template (h)

                                                                                            Input (f) with patch

                                                                                            DTU Compute

                                                                                            2122018Introduction to Medical Image Analysis62 DTU Compute Technical University of Denmark

                                                                                            Normalised Cross Correlation The length of the image patch and the length of

                                                                                            template normalise the NCC If the image is very bright the NCC will be ldquopulled

                                                                                            downrdquo

                                                                                            NCC x y =Correlation

                                                                                            Length of image patch sdot Length of template

                                                                                            DTU Compute

                                                                                            2122018Introduction to Medical Image Analysis63 DTU Compute Technical University of Denmark

                                                                                            Normalised Cross Correlation NCC will be between

                                                                                            ndash 0 No similarity between template and image patchndash 1 Template and image patch are identical

                                                                                            Input (f)

                                                                                            Template (h)

                                                                                            Output Correlation image

                                                                                            Real max

                                                                                            NCC x y =Correlation

                                                                                            Length of image patch sdot Length of template

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                                                                                            Normalised Cross Correlation

                                                                                            A) 010B) 033C) 083D) 062E) 098

                                                                                            Der udfoslashres template matching med og normalized crosscorrelation (NCC) beregnes Hvad bliver NNC i den markerede pixel

                                                                                            1

                                                                                            2 2

                                                                                            3

                                                                                            2

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                                                                                            Edges An edge is where there is a

                                                                                            high change in gray level values

                                                                                            Objects are often separated from the background by edgesGray level profile

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                                                                                            Edges The profile as a function f(d) What value is high when there

                                                                                            is an edgendash The slope of fndash The slope of the tangent at d

                                                                                            f(d)

                                                                                            119891119891prime(119889119889)

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                                                                                            Finite Difference Definition of slope

                                                                                            Approximation

                                                                                            Simpler approximationh = 1

                                                                                            119891119891prime 119889119889 = limℎrarr0

                                                                                            119891119891 119889119889 + ℎ minus 119891119891(119889119889)ℎ

                                                                                            119891119891prime 119889119889 asymp119891119891 119889119889 + ℎ minus 119891119891(119889119889)

                                                                                            ℎ

                                                                                            119891119891prime 119889119889 asymp 119891119891 119889119889 + 1 minus 119891119891(119889119889)

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                                                                                            Edges Discrete approximation of frsquo(d) Can be implemented as a filter

                                                                                            -1 0 1

                                                                                            f(d-2) f(d-1) f(d) f(d+1) f(d+2) f(d+3)

                                                                                            f(d)

                                                                                            119891119891prime 119889119889 asymp 119891119891 119889119889 + 1 minus 119891119891(119889119889)

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                                                                                            Edges in 2D Changes in gray level values

                                                                                            ndash Image gradientndash Gradient is the 2D derivative of a 2D function f(xy)ndash Equal to the slope of the imagendash A steep slope is equal to an edge

                                                                                            120571120571119891119891 119909119909119910119910 = 119866(119892119892119909119909119892119892119910119910)

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                                                                                            Edge filter kernel The Prewitt filter is a typical

                                                                                            edge filter Output image has high

                                                                                            values where there are edges

                                                                                            -1 0 1

                                                                                            -1 0 1

                                                                                            -1 0 1Vertical Prewitt filter

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                                                                                            Prewitt filter

                                                                                            Original Prewitt Prewitt

                                                                                            Hot colormapSmooth 15x15

                                                                                            Smooth 15x15

                                                                                            Prewitt

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                                                                                            Edge detection Edge filter

                                                                                            ndash Prewitt for example Thresholding

                                                                                            ndash Separate edges from non-edges

                                                                                            Output is binary imagendash Edges are white

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                                                                                            Edge filtering

                                                                                            A) MeanB) Horizontal SobelC) Vertical PrewittD) Horisontal PrewittE) Median

                                                                                            Der udfoslashres en filtrering (correlation) med et filter paring billedet Der bruges ikke coefficient normalization Den filtrerede vaeligrdi i den markerede pixel bliver -119 Hvilket et 3x3 filter blev benyttet

                                                                                            0

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                                                                                            02511 - Niveau af dagens emne forelaeligsingA) Meget letB) LetC) PassendeD) SvaeligrtE) Meget svaeligrt

                                                                                            23

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                                                                                            02512 - Niveau af dagens emne forelaeligsingA) Meget letB) LetC) PassendeD) SvaeligrtE) Meget svaeligrt

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                                                                                            02511 - Mit eget udbytte af dagenA) Jeg har laeligrt meget lidtB) Lidt laeligringC) PassendeD) God laeligringE) Jeg har laeligrt meget

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                                                                                            02512 - Mit eget udbytte af dagenA) Jeg har laeligrt meget lidtB) Lidt laeligringC) PassendeD) God laeligringE) Jeg har laeligrt meget

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                                                                                            02511 - Sidste uges oslashvelser (pixelwiseoperations)A) Meget letteB) LetteC) PassendeD) SvaeligreE) Meget svaeligre

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                                                                                            02512 - Sidste uges oslashvelser (pixelwiseoperations)A) Meget letteB) LetteC) PassendeD) SvaeligreE) Meget svaeligre

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                                                                                            Denne uges brug af clickersA) click click click ndash jeg bliver

                                                                                            sindssygB) For meget clickC) PassendeD) Jeg vil gerne have lidt mereE) Jeg kan ikrsquo faring nok

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                                                                                            What can you do after today Describe the difference between point processing and neighbourhood

                                                                                            processing Compute a rank filtered image using the min max median and

                                                                                            difference rank filters Compute a mean filtered image Decide if median or average filtering should be used for noise removal Choose the appropriate image border handling based on a given input

                                                                                            image Implement and apply template matching Compute the normalised cross correlation and explain why it should be

                                                                                            used Apply given image filter kernels to images Use edge filters on images Describe finite difference approximation of image gradients Describe the concept of edge detection

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                                                                                            Oslashvelsesrapport over oslashvelse 4 - 02511 Oslashvelser taeligller cirka 30 af karakteren Skal afleveres senest den 7 marts kl 2359 Kan afleveres af 1 eller 2 personer

                                                                                            ndash I skal skrive jeres egen oslashvelsesrapportndash Brug mindst et af jeres egne billeder

                                                                                            Afleveres som PDF Lad vaeligre med at kopiere opgaveteksten ind i jeres

                                                                                            opgave Put Matlab kode i et Appendix og henvis fra teksten Eksempel rapport over oslashvelse findes paring

                                                                                            hjemmesiden under eksamen

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                                                                                            Exercises

                                                                                            • Introduction to Medical Image Analysis
                                                                                            • Lecture 4 ndash Neighbourhood Processing
                                                                                            • What can you do after today
                                                                                            • Point processing
                                                                                            • Point processing
                                                                                            • Neighbourhood processing
                                                                                            • Use of filtering
                                                                                            • Salt and pepper noise
                                                                                            • Salt and pepper noise
                                                                                            • What is so special about noise
                                                                                            • Noise ndash go away
                                                                                            • What is the median Value
                                                                                            • The median value
                                                                                            • Noise away ndash the median filter
                                                                                            • Noise removal ndash average filter
                                                                                            • Noise removal ndash median filter
                                                                                            • Image Filtering
                                                                                            • Median filter
                                                                                            • Rank filters
                                                                                            • Median filter
                                                                                            • Correlation
                                                                                            • Why do we need similarity
                                                                                            • Correlation (1D)
                                                                                            • Correlation (1D)
                                                                                            • Normalisation
                                                                                            • Normalisation
                                                                                            • Correlation on images
                                                                                            • Correlation on images
                                                                                            • Correlation on images
                                                                                            • Draw your filter
                                                                                            • Correlation on images ndash no normalisation
                                                                                            • Correlation on images ndash no normalisation 2
                                                                                            • Mathematics of 2D Correlation
                                                                                            • Mathematics of 2D Correlation
                                                                                            • Mathematics of 2D Correlation
                                                                                            • Slide Number 40
                                                                                            • 2D Kernel Normalisation
                                                                                            • Correlation
                                                                                            • Smoothing filters
                                                                                            • Use of smoothing
                                                                                            • Use of smoothing
                                                                                            • Mean filter
                                                                                            • Border handling
                                                                                            • Border handling ndash extend the input
                                                                                            • Correlation with zero padding
                                                                                            • Border handling ndash extend the input
                                                                                            • Template Matching
                                                                                            • Template Matching
                                                                                            • Template Matching
                                                                                            • Template Matching
                                                                                            • Problematic Correlation
                                                                                            • Normalised Cross Correlation
                                                                                            • Length of template
                                                                                            • Length of image patch
                                                                                            • Normalised Cross Correlation
                                                                                            • Normalised Cross Correlation
                                                                                            • Normalised Cross Correlation
                                                                                            • Edges
                                                                                            • Edges
                                                                                            • Finite Difference
                                                                                            • Edges
                                                                                            • Edges in 2D
                                                                                            • Edge filter kernel
                                                                                            • Prewitt filter
                                                                                            • Edge detection
                                                                                            • Edge filtering
                                                                                            • 02511 - Niveau af dagens emne forelaeligsing
                                                                                            • 02512 - Niveau af dagens emne forelaeligsing
                                                                                            • 02511 - Mit eget udbytte af dagen
                                                                                            • 02512 - Mit eget udbytte af dagen
                                                                                            • 02511 - Sidste uges oslashvelser (pixelwise operations)
                                                                                            • 02512 - Sidste uges oslashvelser (pixelwise operations)
                                                                                            • Denne uges brug af clickers
                                                                                            • What can you do after today
                                                                                            • Oslashvelsesrapport over oslashvelse 4 - 02511
                                                                                            • Exercises
                                                                                              A0
                                                                                              B0
                                                                                              C5
                                                                                              D0
                                                                                              E6
                                                                                              A
                                                                                              B
                                                                                              C
                                                                                              D
                                                                                              E
                                                                                              A3
                                                                                              B0
                                                                                              C3
                                                                                              D0
                                                                                              E0
                                                                                              A
                                                                                              B
                                                                                              C
                                                                                              D
                                                                                              E
                                                                                              A0
                                                                                              B0
                                                                                              C1
                                                                                              D4
                                                                                              E1
                                                                                              A
                                                                                              B
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                                                                                              A2
                                                                                              B1
                                                                                              C3
                                                                                              D2
                                                                                              E0
                                                                                              A
                                                                                              B
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                                                                                              A0
                                                                                              B0
                                                                                              C2
                                                                                              D6
                                                                                              E0
                                                                                              A
                                                                                              B
                                                                                              C
                                                                                              D
                                                                                              E
                                                                                              A0
                                                                                              B0
                                                                                              C1
                                                                                              D0
                                                                                              E0
                                                                                              A
                                                                                              B
                                                                                              C
                                                                                              D
                                                                                              E
                                                                                              A2
                                                                                              B3
                                                                                              C6
                                                                                              D1
                                                                                              E0
                                                                                              A
                                                                                              B
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                                                                                              A0
                                                                                              B8
                                                                                              C1
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                                                                                              E0
                                                                                              A
                                                                                              B
                                                                                              C
                                                                                              D
                                                                                              E
                                                                                              A1
                                                                                              B2
                                                                                              C2
                                                                                              D3
                                                                                              E2
                                                                                              A
                                                                                              B
                                                                                              C
                                                                                              D
                                                                                              E
                                                                                              A0
                                                                                              B13
                                                                                              C0
                                                                                              D0
                                                                                              E0
                                                                                              A
                                                                                              B
                                                                                              C
                                                                                              D
                                                                                              E
                                                                                              A12
                                                                                              B0
                                                                                              C0
                                                                                              D0
                                                                                              E0
                                                                                              A
                                                                                              B
                                                                                              C
                                                                                              D
                                                                                              E
                                                                                              A0
                                                                                              B0
                                                                                              C0
                                                                                              D0
                                                                                              E13
                                                                                              A
                                                                                              B
                                                                                              C
                                                                                              D
                                                                                              E

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                                                                                              2D Kernel Normalisation

                                                                                              1 2 11 3 11 2 1

                                                                                              h

                                                                                              Normalisation factor

                                                                                              1 + 2 + 1 + 1 + 3 + 1 + 1 + 2 + 1 = 13

                                                                                              119909119909

                                                                                              119910119910

                                                                                              ℎ(119909119909119910119910)

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                                                                                              CorrelationA) 50122B) 123001C) 11233D) 2550E) 90454

                                                                                              0 0 0 0

                                                                                              13

                                                                                              A B C D E

                                                                                              Chart1

                                                                                              0
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                                                                                              0
                                                                                              0
                                                                                              13

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                                                                                              Smoothing filters

                                                                                              Also know as ndash Smoothing kernel Mean filter Low pass filter blurring

                                                                                              The simplest filter ndash Spatial low pass filterndash Removes high frequencies

                                                                                              Another mask ndash Gaussian filter

                                                                                              1 1 1

                                                                                              1 1 1

                                                                                              1 1 191

                                                                                              1 2 1

                                                                                              2 4 2

                                                                                              1 2 1161

                                                                                              Why Gaussian

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                                                                                              Use of smoothing

                                                                                              3x3 7x7 11x11 15x15

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                                                                                              Use of smoothing Large kernels smooth more Removes high frequency information Good at enhancing big structures

                                                                                              3x3 15x15

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                                                                                              Mean filterA) 166B) 113C) 12D) 51E) 245

                                                                                              0 0 0 0

                                                                                              A B C D E

                                                                                              Chart1

                                                                                              12
                                                                                              0
                                                                                              0
                                                                                              0
                                                                                              0

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                                                                                              Border handling

                                                                                              0 2 41 2 2

                                                                                              1 6 3

                                                                                              1 2 12 5 3

                                                                                              2 1 3

                                                                                              1 3 1

                                                                                              2 2 2

                                                                                              0 1 3

                                                                                              1 2 0

                                                                                              2 1 4

                                                                                              1 0 1

                                                                                              Input Output

                                                                                              No values at the border

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                                                                                              Border handling ndash extend the input

                                                                                              0 2 41 2 2

                                                                                              1 6 3

                                                                                              1 2 12 5 3

                                                                                              2 1 3

                                                                                              1 3 1

                                                                                              2 2 2

                                                                                              0 1 3

                                                                                              1 2 0

                                                                                              2 1 4

                                                                                              1 0 1

                                                                                              Input

                                                                                              0 0 0 0 000000

                                                                                              bull Zero padding ndash what happens

                                                                                              bull Zero is black ndash creates dark border around the image

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                                                                                              Correlation with zero paddingA) 5 8B) 12 16C) 13 3D) 15 21E) 17 12

                                                                                              1 2 11 3 11 2 1

                                                                                              0 2 41 2 2

                                                                                              1 6 3

                                                                                              1 2 12 5 3

                                                                                              2 1 3

                                                                                              1 3 1

                                                                                              2 2 2

                                                                                              0 1 3

                                                                                              1 2 0

                                                                                              2 1 4

                                                                                              1 0 1

                                                                                              0

                                                                                              13

                                                                                              0 0 0

                                                                                              A B C D E

                                                                                              Chart1

                                                                                              0
                                                                                              13
                                                                                              0
                                                                                              0
                                                                                              0

                                                                                              Sheet1

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                                                                                              Border handling ndash extend the input

                                                                                              0 2 41 2 2

                                                                                              1 6 3

                                                                                              1 2 12 5 3

                                                                                              2 1 3

                                                                                              1 3 1

                                                                                              2 2 2

                                                                                              0 1 3

                                                                                              1 2 0

                                                                                              2 1 4

                                                                                              1 0 1

                                                                                              Input

                                                                                              1 2 0 1 311211

                                                                                              bull Reflection

                                                                                              bull Normally better than zero padding

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                                                                                              Template Matching Template

                                                                                              ndash Skabelon paring dansk Locates objects in images

                                                                                              Input

                                                                                              Template

                                                                                              Output Correlation image

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                                                                                              Template Matching The correlation between the template and the input

                                                                                              image is computed for each pixel

                                                                                              Input

                                                                                              Template

                                                                                              Output Correlation image

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                                                                                              Template Matching The pixel with the highest value is found in the

                                                                                              output imagendash Here is the highest correlation

                                                                                              Input

                                                                                              Template

                                                                                              Output Correlation image

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                                                                                              Template Matching This corresponds to the found pattern in the input

                                                                                              image

                                                                                              Input

                                                                                              Template

                                                                                              Output Correlation image

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                                                                                              Problematic Correlation Correlation matching has problem with light areas ndash

                                                                                              why

                                                                                              Input (f)

                                                                                              Template (h)

                                                                                              Output Correlation imageFake max

                                                                                              Real max

                                                                                              Very High119892119892 119909119909119910119910 = 119895119895=minus119877119877

                                                                                              119877119877

                                                                                              119894119894=minus119877119877

                                                                                              119877119877

                                                                                              ℎ(119894119894 119895119895) 119891119891(119909119909 + 119894119894119910119910 + 119895119895)

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                                                                                              Normalised Cross Correlation

                                                                                              Input (f)

                                                                                              Template (h)

                                                                                              Output Correlation image

                                                                                              Real max

                                                                                              NCC x y =Correlation

                                                                                              Length of image patch sdot Length of template

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                                                                                              Length of template Vector length

                                                                                              ndash Put all pixel values into a vectorndash Compute the length of this vector

                                                                                              Describes the intensity of the templatendash Bright template has a large lengthndash Dark template has a small length

                                                                                              Template (h)

                                                                                              Length of template = 119895119895=minus119877119877

                                                                                              119877119877

                                                                                              119894119894=minus119877119877

                                                                                              119877119877

                                                                                              ℎ(119894119894 119895119895) ℎ(119894119894 119895119895)

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                                                                                              Length of image patch Vector length based on pixel values in image patch Describes the intensity of the image patch

                                                                                              Template (h)

                                                                                              Input (f) with patch

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                                                                                              Normalised Cross Correlation The length of the image patch and the length of

                                                                                              template normalise the NCC If the image is very bright the NCC will be ldquopulled

                                                                                              downrdquo

                                                                                              NCC x y =Correlation

                                                                                              Length of image patch sdot Length of template

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                                                                                              Normalised Cross Correlation NCC will be between

                                                                                              ndash 0 No similarity between template and image patchndash 1 Template and image patch are identical

                                                                                              Input (f)

                                                                                              Template (h)

                                                                                              Output Correlation image

                                                                                              Real max

                                                                                              NCC x y =Correlation

                                                                                              Length of image patch sdot Length of template

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                                                                                              Normalised Cross Correlation

                                                                                              A) 010B) 033C) 083D) 062E) 098

                                                                                              Der udfoslashres template matching med og normalized crosscorrelation (NCC) beregnes Hvad bliver NNC i den markerede pixel

                                                                                              1

                                                                                              2 2

                                                                                              3

                                                                                              2

                                                                                              A B C D E

                                                                                              Chart1

                                                                                              1
                                                                                              2
                                                                                              2
                                                                                              3
                                                                                              2

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                                                                                              Edges An edge is where there is a

                                                                                              high change in gray level values

                                                                                              Objects are often separated from the background by edgesGray level profile

                                                                                              DTU Compute

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                                                                                              Edges The profile as a function f(d) What value is high when there

                                                                                              is an edgendash The slope of fndash The slope of the tangent at d

                                                                                              f(d)

                                                                                              119891119891prime(119889119889)

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                                                                                              Finite Difference Definition of slope

                                                                                              Approximation

                                                                                              Simpler approximationh = 1

                                                                                              119891119891prime 119889119889 = limℎrarr0

                                                                                              119891119891 119889119889 + ℎ minus 119891119891(119889119889)ℎ

                                                                                              119891119891prime 119889119889 asymp119891119891 119889119889 + ℎ minus 119891119891(119889119889)

                                                                                              ℎ

                                                                                              119891119891prime 119889119889 asymp 119891119891 119889119889 + 1 minus 119891119891(119889119889)

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                                                                                              Edges Discrete approximation of frsquo(d) Can be implemented as a filter

                                                                                              -1 0 1

                                                                                              f(d-2) f(d-1) f(d) f(d+1) f(d+2) f(d+3)

                                                                                              f(d)

                                                                                              119891119891prime 119889119889 asymp 119891119891 119889119889 + 1 minus 119891119891(119889119889)

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                                                                                              Edges in 2D Changes in gray level values

                                                                                              ndash Image gradientndash Gradient is the 2D derivative of a 2D function f(xy)ndash Equal to the slope of the imagendash A steep slope is equal to an edge

                                                                                              120571120571119891119891 119909119909119910119910 = 119866(119892119892119909119909119892119892119910119910)

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                                                                                              Edge filter kernel The Prewitt filter is a typical

                                                                                              edge filter Output image has high

                                                                                              values where there are edges

                                                                                              -1 0 1

                                                                                              -1 0 1

                                                                                              -1 0 1Vertical Prewitt filter

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                                                                                              Prewitt filter

                                                                                              Original Prewitt Prewitt

                                                                                              Hot colormapSmooth 15x15

                                                                                              Smooth 15x15

                                                                                              Prewitt

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                                                                                              Edge detection Edge filter

                                                                                              ndash Prewitt for example Thresholding

                                                                                              ndash Separate edges from non-edges

                                                                                              Output is binary imagendash Edges are white

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                                                                                              Edge filtering

                                                                                              A) MeanB) Horizontal SobelC) Vertical PrewittD) Horisontal PrewittE) Median

                                                                                              Der udfoslashres en filtrering (correlation) med et filter paring billedet Der bruges ikke coefficient normalization Den filtrerede vaeligrdi i den markerede pixel bliver -119 Hvilket et 3x3 filter blev benyttet

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                                                                                              02511 - Niveau af dagens emne forelaeligsingA) Meget letB) LetC) PassendeD) SvaeligrtE) Meget svaeligrt

                                                                                              23

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                                                                                              02512 - Niveau af dagens emne forelaeligsingA) Meget letB) LetC) PassendeD) SvaeligrtE) Meget svaeligrt

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                                                                                              02511 - Mit eget udbytte af dagenA) Jeg har laeligrt meget lidtB) Lidt laeligringC) PassendeD) God laeligringE) Jeg har laeligrt meget

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                                                                                              02512 - Mit eget udbytte af dagenA) Jeg har laeligrt meget lidtB) Lidt laeligringC) PassendeD) God laeligringE) Jeg har laeligrt meget

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                                                                                              02511 - Sidste uges oslashvelser (pixelwiseoperations)A) Meget letteB) LetteC) PassendeD) SvaeligreE) Meget svaeligre

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                                                                                              02512 - Sidste uges oslashvelser (pixelwiseoperations)A) Meget letteB) LetteC) PassendeD) SvaeligreE) Meget svaeligre

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                                                                                              Denne uges brug af clickersA) click click click ndash jeg bliver

                                                                                              sindssygB) For meget clickC) PassendeD) Jeg vil gerne have lidt mereE) Jeg kan ikrsquo faring nok

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                                                                                              What can you do after today Describe the difference between point processing and neighbourhood

                                                                                              processing Compute a rank filtered image using the min max median and

                                                                                              difference rank filters Compute a mean filtered image Decide if median or average filtering should be used for noise removal Choose the appropriate image border handling based on a given input

                                                                                              image Implement and apply template matching Compute the normalised cross correlation and explain why it should be

                                                                                              used Apply given image filter kernels to images Use edge filters on images Describe finite difference approximation of image gradients Describe the concept of edge detection

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                                                                                              Oslashvelsesrapport over oslashvelse 4 - 02511 Oslashvelser taeligller cirka 30 af karakteren Skal afleveres senest den 7 marts kl 2359 Kan afleveres af 1 eller 2 personer

                                                                                              ndash I skal skrive jeres egen oslashvelsesrapportndash Brug mindst et af jeres egne billeder

                                                                                              Afleveres som PDF Lad vaeligre med at kopiere opgaveteksten ind i jeres

                                                                                              opgave Put Matlab kode i et Appendix og henvis fra teksten Eksempel rapport over oslashvelse findes paring

                                                                                              hjemmesiden under eksamen

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                                                                                              Exercises

                                                                                              • Introduction to Medical Image Analysis
                                                                                              • Lecture 4 ndash Neighbourhood Processing
                                                                                              • What can you do after today
                                                                                              • Point processing
                                                                                              • Point processing
                                                                                              • Neighbourhood processing
                                                                                              • Use of filtering
                                                                                              • Salt and pepper noise
                                                                                              • Salt and pepper noise
                                                                                              • What is so special about noise
                                                                                              • Noise ndash go away
                                                                                              • What is the median Value
                                                                                              • The median value
                                                                                              • Noise away ndash the median filter
                                                                                              • Noise removal ndash average filter
                                                                                              • Noise removal ndash median filter
                                                                                              • Image Filtering
                                                                                              • Median filter
                                                                                              • Rank filters
                                                                                              • Median filter
                                                                                              • Correlation
                                                                                              • Why do we need similarity
                                                                                              • Correlation (1D)
                                                                                              • Correlation (1D)
                                                                                              • Normalisation
                                                                                              • Normalisation
                                                                                              • Correlation on images
                                                                                              • Correlation on images
                                                                                              • Correlation on images
                                                                                              • Draw your filter
                                                                                              • Correlation on images ndash no normalisation
                                                                                              • Correlation on images ndash no normalisation 2
                                                                                              • Mathematics of 2D Correlation
                                                                                              • Mathematics of 2D Correlation
                                                                                              • Mathematics of 2D Correlation
                                                                                              • Slide Number 40
                                                                                              • 2D Kernel Normalisation
                                                                                              • Correlation
                                                                                              • Smoothing filters
                                                                                              • Use of smoothing
                                                                                              • Use of smoothing
                                                                                              • Mean filter
                                                                                              • Border handling
                                                                                              • Border handling ndash extend the input
                                                                                              • Correlation with zero padding
                                                                                              • Border handling ndash extend the input
                                                                                              • Template Matching
                                                                                              • Template Matching
                                                                                              • Template Matching
                                                                                              • Template Matching
                                                                                              • Problematic Correlation
                                                                                              • Normalised Cross Correlation
                                                                                              • Length of template
                                                                                              • Length of image patch
                                                                                              • Normalised Cross Correlation
                                                                                              • Normalised Cross Correlation
                                                                                              • Normalised Cross Correlation
                                                                                              • Edges
                                                                                              • Edges
                                                                                              • Finite Difference
                                                                                              • Edges
                                                                                              • Edges in 2D
                                                                                              • Edge filter kernel
                                                                                              • Prewitt filter
                                                                                              • Edge detection
                                                                                              • Edge filtering
                                                                                              • 02511 - Niveau af dagens emne forelaeligsing
                                                                                              • 02512 - Niveau af dagens emne forelaeligsing
                                                                                              • 02511 - Mit eget udbytte af dagen
                                                                                              • 02512 - Mit eget udbytte af dagen
                                                                                              • 02511 - Sidste uges oslashvelser (pixelwise operations)
                                                                                              • 02512 - Sidste uges oslashvelser (pixelwise operations)
                                                                                              • Denne uges brug af clickers
                                                                                              • What can you do after today
                                                                                              • Oslashvelsesrapport over oslashvelse 4 - 02511
                                                                                              • Exercises
                                                                                                A0
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                                                                                                E0
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                                                                                                E0
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                                                                                                CorrelationA) 50122B) 123001C) 11233D) 2550E) 90454

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                                                                                                Smoothing filters

                                                                                                Also know as ndash Smoothing kernel Mean filter Low pass filter blurring

                                                                                                The simplest filter ndash Spatial low pass filterndash Removes high frequencies

                                                                                                Another mask ndash Gaussian filter

                                                                                                1 1 1

                                                                                                1 1 1

                                                                                                1 1 191

                                                                                                1 2 1

                                                                                                2 4 2

                                                                                                1 2 1161

                                                                                                Why Gaussian

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                                                                                                Use of smoothing

                                                                                                3x3 7x7 11x11 15x15

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                                                                                                Use of smoothing Large kernels smooth more Removes high frequency information Good at enhancing big structures

                                                                                                3x3 15x15

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                                                                                                Mean filterA) 166B) 113C) 12D) 51E) 245

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                                                                                                Border handling

                                                                                                0 2 41 2 2

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                                                                                                1 2 12 5 3

                                                                                                2 1 3

                                                                                                1 3 1

                                                                                                2 2 2

                                                                                                0 1 3

                                                                                                1 2 0

                                                                                                2 1 4

                                                                                                1 0 1

                                                                                                Input Output

                                                                                                No values at the border

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                                                                                                Border handling ndash extend the input

                                                                                                0 2 41 2 2

                                                                                                1 6 3

                                                                                                1 2 12 5 3

                                                                                                2 1 3

                                                                                                1 3 1

                                                                                                2 2 2

                                                                                                0 1 3

                                                                                                1 2 0

                                                                                                2 1 4

                                                                                                1 0 1

                                                                                                Input

                                                                                                0 0 0 0 000000

                                                                                                bull Zero padding ndash what happens

                                                                                                bull Zero is black ndash creates dark border around the image

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                                                                                                Correlation with zero paddingA) 5 8B) 12 16C) 13 3D) 15 21E) 17 12

                                                                                                1 2 11 3 11 2 1

                                                                                                0 2 41 2 2

                                                                                                1 6 3

                                                                                                1 2 12 5 3

                                                                                                2 1 3

                                                                                                1 3 1

                                                                                                2 2 2

                                                                                                0 1 3

                                                                                                1 2 0

                                                                                                2 1 4

                                                                                                1 0 1

                                                                                                0

                                                                                                13

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                                                                                                Border handling ndash extend the input

                                                                                                0 2 41 2 2

                                                                                                1 6 3

                                                                                                1 2 12 5 3

                                                                                                2 1 3

                                                                                                1 3 1

                                                                                                2 2 2

                                                                                                0 1 3

                                                                                                1 2 0

                                                                                                2 1 4

                                                                                                1 0 1

                                                                                                Input

                                                                                                1 2 0 1 311211

                                                                                                bull Reflection

                                                                                                bull Normally better than zero padding

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                                                                                                Template Matching Template

                                                                                                ndash Skabelon paring dansk Locates objects in images

                                                                                                Input

                                                                                                Template

                                                                                                Output Correlation image

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                                                                                                Template Matching The correlation between the template and the input

                                                                                                image is computed for each pixel

                                                                                                Input

                                                                                                Template

                                                                                                Output Correlation image

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                                                                                                Template Matching The pixel with the highest value is found in the

                                                                                                output imagendash Here is the highest correlation

                                                                                                Input

                                                                                                Template

                                                                                                Output Correlation image

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                                                                                                Template Matching This corresponds to the found pattern in the input

                                                                                                image

                                                                                                Input

                                                                                                Template

                                                                                                Output Correlation image

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                                                                                                Problematic Correlation Correlation matching has problem with light areas ndash

                                                                                                why

                                                                                                Input (f)

                                                                                                Template (h)

                                                                                                Output Correlation imageFake max

                                                                                                Real max

                                                                                                Very High119892119892 119909119909119910119910 = 119895119895=minus119877119877

                                                                                                119877119877

                                                                                                119894119894=minus119877119877

                                                                                                119877119877

                                                                                                ℎ(119894119894 119895119895) 119891119891(119909119909 + 119894119894119910119910 + 119895119895)

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                                                                                                Normalised Cross Correlation

                                                                                                Input (f)

                                                                                                Template (h)

                                                                                                Output Correlation image

                                                                                                Real max

                                                                                                NCC x y =Correlation

                                                                                                Length of image patch sdot Length of template

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                                                                                                Length of template Vector length

                                                                                                ndash Put all pixel values into a vectorndash Compute the length of this vector

                                                                                                Describes the intensity of the templatendash Bright template has a large lengthndash Dark template has a small length

                                                                                                Template (h)

                                                                                                Length of template = 119895119895=minus119877119877

                                                                                                119877119877

                                                                                                119894119894=minus119877119877

                                                                                                119877119877

                                                                                                ℎ(119894119894 119895119895) ℎ(119894119894 119895119895)

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                                                                                                Length of image patch Vector length based on pixel values in image patch Describes the intensity of the image patch

                                                                                                Template (h)

                                                                                                Input (f) with patch

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                                                                                                Normalised Cross Correlation The length of the image patch and the length of

                                                                                                template normalise the NCC If the image is very bright the NCC will be ldquopulled

                                                                                                downrdquo

                                                                                                NCC x y =Correlation

                                                                                                Length of image patch sdot Length of template

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                                                                                                Normalised Cross Correlation NCC will be between

                                                                                                ndash 0 No similarity between template and image patchndash 1 Template and image patch are identical

                                                                                                Input (f)

                                                                                                Template (h)

                                                                                                Output Correlation image

                                                                                                Real max

                                                                                                NCC x y =Correlation

                                                                                                Length of image patch sdot Length of template

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                                                                                                Normalised Cross Correlation

                                                                                                A) 010B) 033C) 083D) 062E) 098

                                                                                                Der udfoslashres template matching med og normalized crosscorrelation (NCC) beregnes Hvad bliver NNC i den markerede pixel

                                                                                                1

                                                                                                2 2

                                                                                                3

                                                                                                2

                                                                                                A B C D E

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                                                                                                Edges An edge is where there is a

                                                                                                high change in gray level values

                                                                                                Objects are often separated from the background by edgesGray level profile

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                                                                                                Edges The profile as a function f(d) What value is high when there

                                                                                                is an edgendash The slope of fndash The slope of the tangent at d

                                                                                                f(d)

                                                                                                119891119891prime(119889119889)

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                                                                                                Finite Difference Definition of slope

                                                                                                Approximation

                                                                                                Simpler approximationh = 1

                                                                                                119891119891prime 119889119889 = limℎrarr0

                                                                                                119891119891 119889119889 + ℎ minus 119891119891(119889119889)ℎ

                                                                                                119891119891prime 119889119889 asymp119891119891 119889119889 + ℎ minus 119891119891(119889119889)

                                                                                                ℎ

                                                                                                119891119891prime 119889119889 asymp 119891119891 119889119889 + 1 minus 119891119891(119889119889)

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                                                                                                Edges Discrete approximation of frsquo(d) Can be implemented as a filter

                                                                                                -1 0 1

                                                                                                f(d-2) f(d-1) f(d) f(d+1) f(d+2) f(d+3)

                                                                                                f(d)

                                                                                                119891119891prime 119889119889 asymp 119891119891 119889119889 + 1 minus 119891119891(119889119889)

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                                                                                                Edges in 2D Changes in gray level values

                                                                                                ndash Image gradientndash Gradient is the 2D derivative of a 2D function f(xy)ndash Equal to the slope of the imagendash A steep slope is equal to an edge

                                                                                                120571120571119891119891 119909119909119910119910 = 119866(119892119892119909119909119892119892119910119910)

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                                                                                                Edge filter kernel The Prewitt filter is a typical

                                                                                                edge filter Output image has high

                                                                                                values where there are edges

                                                                                                -1 0 1

                                                                                                -1 0 1

                                                                                                -1 0 1Vertical Prewitt filter

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                                                                                                Prewitt filter

                                                                                                Original Prewitt Prewitt

                                                                                                Hot colormapSmooth 15x15

                                                                                                Smooth 15x15

                                                                                                Prewitt

                                                                                                DTU Compute

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                                                                                                Edge detection Edge filter

                                                                                                ndash Prewitt for example Thresholding

                                                                                                ndash Separate edges from non-edges

                                                                                                Output is binary imagendash Edges are white

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                                                                                                Edge filtering

                                                                                                A) MeanB) Horizontal SobelC) Vertical PrewittD) Horisontal PrewittE) Median

                                                                                                Der udfoslashres en filtrering (correlation) med et filter paring billedet Der bruges ikke coefficient normalization Den filtrerede vaeligrdi i den markerede pixel bliver -119 Hvilket et 3x3 filter blev benyttet

                                                                                                0

                                                                                                8

                                                                                                1 10

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                                                                                                02511 - Niveau af dagens emne forelaeligsingA) Meget letB) LetC) PassendeD) SvaeligrtE) Meget svaeligrt

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                                                                                                02511 - Mit eget udbytte af dagenA) Jeg har laeligrt meget lidtB) Lidt laeligringC) PassendeD) God laeligringE) Jeg har laeligrt meget

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                                                                                                02512 - Mit eget udbytte af dagenA) Jeg har laeligrt meget lidtB) Lidt laeligringC) PassendeD) God laeligringE) Jeg har laeligrt meget

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                                                                                                02511 - Sidste uges oslashvelser (pixelwiseoperations)A) Meget letteB) LetteC) PassendeD) SvaeligreE) Meget svaeligre

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                                                                                                02512 - Sidste uges oslashvelser (pixelwiseoperations)A) Meget letteB) LetteC) PassendeD) SvaeligreE) Meget svaeligre

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                                                                                                Denne uges brug af clickersA) click click click ndash jeg bliver

                                                                                                sindssygB) For meget clickC) PassendeD) Jeg vil gerne have lidt mereE) Jeg kan ikrsquo faring nok

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                                                                                                What can you do after today Describe the difference between point processing and neighbourhood

                                                                                                processing Compute a rank filtered image using the min max median and

                                                                                                difference rank filters Compute a mean filtered image Decide if median or average filtering should be used for noise removal Choose the appropriate image border handling based on a given input

                                                                                                image Implement and apply template matching Compute the normalised cross correlation and explain why it should be

                                                                                                used Apply given image filter kernels to images Use edge filters on images Describe finite difference approximation of image gradients Describe the concept of edge detection

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                                                                                                Oslashvelsesrapport over oslashvelse 4 - 02511 Oslashvelser taeligller cirka 30 af karakteren Skal afleveres senest den 7 marts kl 2359 Kan afleveres af 1 eller 2 personer

                                                                                                ndash I skal skrive jeres egen oslashvelsesrapportndash Brug mindst et af jeres egne billeder

                                                                                                Afleveres som PDF Lad vaeligre med at kopiere opgaveteksten ind i jeres

                                                                                                opgave Put Matlab kode i et Appendix og henvis fra teksten Eksempel rapport over oslashvelse findes paring

                                                                                                hjemmesiden under eksamen

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                                                                                                2122018Introduction to Medical Image Analysis85 DTU Compute Technical University of Denmark

                                                                                                Exercises

                                                                                                • Introduction to Medical Image Analysis
                                                                                                • Lecture 4 ndash Neighbourhood Processing
                                                                                                • What can you do after today
                                                                                                • Point processing
                                                                                                • Point processing
                                                                                                • Neighbourhood processing
                                                                                                • Use of filtering
                                                                                                • Salt and pepper noise
                                                                                                • Salt and pepper noise
                                                                                                • What is so special about noise
                                                                                                • Noise ndash go away
                                                                                                • What is the median Value
                                                                                                • The median value
                                                                                                • Noise away ndash the median filter
                                                                                                • Noise removal ndash average filter
                                                                                                • Noise removal ndash median filter
                                                                                                • Image Filtering
                                                                                                • Median filter
                                                                                                • Rank filters
                                                                                                • Median filter
                                                                                                • Correlation
                                                                                                • Why do we need similarity
                                                                                                • Correlation (1D)
                                                                                                • Correlation (1D)
                                                                                                • Normalisation
                                                                                                • Normalisation
                                                                                                • Correlation on images
                                                                                                • Correlation on images
                                                                                                • Correlation on images
                                                                                                • Draw your filter
                                                                                                • Correlation on images ndash no normalisation
                                                                                                • Correlation on images ndash no normalisation 2
                                                                                                • Mathematics of 2D Correlation
                                                                                                • Mathematics of 2D Correlation
                                                                                                • Mathematics of 2D Correlation
                                                                                                • Slide Number 40
                                                                                                • 2D Kernel Normalisation
                                                                                                • Correlation
                                                                                                • Smoothing filters
                                                                                                • Use of smoothing
                                                                                                • Use of smoothing
                                                                                                • Mean filter
                                                                                                • Border handling
                                                                                                • Border handling ndash extend the input
                                                                                                • Correlation with zero padding
                                                                                                • Border handling ndash extend the input
                                                                                                • Template Matching
                                                                                                • Template Matching
                                                                                                • Template Matching
                                                                                                • Template Matching
                                                                                                • Problematic Correlation
                                                                                                • Normalised Cross Correlation
                                                                                                • Length of template
                                                                                                • Length of image patch
                                                                                                • Normalised Cross Correlation
                                                                                                • Normalised Cross Correlation
                                                                                                • Normalised Cross Correlation
                                                                                                • Edges
                                                                                                • Edges
                                                                                                • Finite Difference
                                                                                                • Edges
                                                                                                • Edges in 2D
                                                                                                • Edge filter kernel
                                                                                                • Prewitt filter
                                                                                                • Edge detection
                                                                                                • Edge filtering
                                                                                                • 02511 - Niveau af dagens emne forelaeligsing
                                                                                                • 02512 - Niveau af dagens emne forelaeligsing
                                                                                                • 02511 - Mit eget udbytte af dagen
                                                                                                • 02512 - Mit eget udbytte af dagen
                                                                                                • 02511 - Sidste uges oslashvelser (pixelwise operations)
                                                                                                • 02512 - Sidste uges oslashvelser (pixelwise operations)
                                                                                                • Denne uges brug af clickers
                                                                                                • What can you do after today
                                                                                                • Oslashvelsesrapport over oslashvelse 4 - 02511
                                                                                                • Exercises
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                                                                                                  Smoothing filters

                                                                                                  Also know as ndash Smoothing kernel Mean filter Low pass filter blurring

                                                                                                  The simplest filter ndash Spatial low pass filterndash Removes high frequencies

                                                                                                  Another mask ndash Gaussian filter

                                                                                                  1 1 1

                                                                                                  1 1 1

                                                                                                  1 1 191

                                                                                                  1 2 1

                                                                                                  2 4 2

                                                                                                  1 2 1161

                                                                                                  Why Gaussian

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                                                                                                  Use of smoothing

                                                                                                  3x3 7x7 11x11 15x15

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                                                                                                  Use of smoothing Large kernels smooth more Removes high frequency information Good at enhancing big structures

                                                                                                  3x3 15x15

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                                                                                                  Mean filterA) 166B) 113C) 12D) 51E) 245

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                                                                                                  Border handling

                                                                                                  0 2 41 2 2

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                                                                                                  2 1 3

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                                                                                                  2 2 2

                                                                                                  0 1 3

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                                                                                                  1 0 1

                                                                                                  Input Output

                                                                                                  No values at the border

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                                                                                                  Border handling ndash extend the input

                                                                                                  0 2 41 2 2

                                                                                                  1 6 3

                                                                                                  1 2 12 5 3

                                                                                                  2 1 3

                                                                                                  1 3 1

                                                                                                  2 2 2

                                                                                                  0 1 3

                                                                                                  1 2 0

                                                                                                  2 1 4

                                                                                                  1 0 1

                                                                                                  Input

                                                                                                  0 0 0 0 000000

                                                                                                  bull Zero padding ndash what happens

                                                                                                  bull Zero is black ndash creates dark border around the image

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                                                                                                  Correlation with zero paddingA) 5 8B) 12 16C) 13 3D) 15 21E) 17 12

                                                                                                  1 2 11 3 11 2 1

                                                                                                  0 2 41 2 2

                                                                                                  1 6 3

                                                                                                  1 2 12 5 3

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                                                                                                  Border handling ndash extend the input

                                                                                                  0 2 41 2 2

                                                                                                  1 6 3

                                                                                                  1 2 12 5 3

                                                                                                  2 1 3

                                                                                                  1 3 1

                                                                                                  2 2 2

                                                                                                  0 1 3

                                                                                                  1 2 0

                                                                                                  2 1 4

                                                                                                  1 0 1

                                                                                                  Input

                                                                                                  1 2 0 1 311211

                                                                                                  bull Reflection

                                                                                                  bull Normally better than zero padding

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                                                                                                  Template Matching Template

                                                                                                  ndash Skabelon paring dansk Locates objects in images

                                                                                                  Input

                                                                                                  Template

                                                                                                  Output Correlation image

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                                                                                                  2122018Introduction to Medical Image Analysis55 DTU Compute Technical University of Denmark

                                                                                                  Template Matching The correlation between the template and the input

                                                                                                  image is computed for each pixel

                                                                                                  Input

                                                                                                  Template

                                                                                                  Output Correlation image

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                                                                                                  Template Matching The pixel with the highest value is found in the

                                                                                                  output imagendash Here is the highest correlation

                                                                                                  Input

                                                                                                  Template

                                                                                                  Output Correlation image

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                                                                                                  Template Matching This corresponds to the found pattern in the input

                                                                                                  image

                                                                                                  Input

                                                                                                  Template

                                                                                                  Output Correlation image

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                                                                                                  Problematic Correlation Correlation matching has problem with light areas ndash

                                                                                                  why

                                                                                                  Input (f)

                                                                                                  Template (h)

                                                                                                  Output Correlation imageFake max

                                                                                                  Real max

                                                                                                  Very High119892119892 119909119909119910119910 = 119895119895=minus119877119877

                                                                                                  119877119877

                                                                                                  119894119894=minus119877119877

                                                                                                  119877119877

                                                                                                  ℎ(119894119894 119895119895) 119891119891(119909119909 + 119894119894119910119910 + 119895119895)

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                                                                                                  Normalised Cross Correlation

                                                                                                  Input (f)

                                                                                                  Template (h)

                                                                                                  Output Correlation image

                                                                                                  Real max

                                                                                                  NCC x y =Correlation

                                                                                                  Length of image patch sdot Length of template

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                                                                                                  Length of template Vector length

                                                                                                  ndash Put all pixel values into a vectorndash Compute the length of this vector

                                                                                                  Describes the intensity of the templatendash Bright template has a large lengthndash Dark template has a small length

                                                                                                  Template (h)

                                                                                                  Length of template = 119895119895=minus119877119877

                                                                                                  119877119877

                                                                                                  119894119894=minus119877119877

                                                                                                  119877119877

                                                                                                  ℎ(119894119894 119895119895) ℎ(119894119894 119895119895)

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                                                                                                  Length of image patch Vector length based on pixel values in image patch Describes the intensity of the image patch

                                                                                                  Template (h)

                                                                                                  Input (f) with patch

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                                                                                                  Normalised Cross Correlation The length of the image patch and the length of

                                                                                                  template normalise the NCC If the image is very bright the NCC will be ldquopulled

                                                                                                  downrdquo

                                                                                                  NCC x y =Correlation

                                                                                                  Length of image patch sdot Length of template

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                                                                                                  Normalised Cross Correlation NCC will be between

                                                                                                  ndash 0 No similarity between template and image patchndash 1 Template and image patch are identical

                                                                                                  Input (f)

                                                                                                  Template (h)

                                                                                                  Output Correlation image

                                                                                                  Real max

                                                                                                  NCC x y =Correlation

                                                                                                  Length of image patch sdot Length of template

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                                                                                                  Normalised Cross Correlation

                                                                                                  A) 010B) 033C) 083D) 062E) 098

                                                                                                  Der udfoslashres template matching med og normalized crosscorrelation (NCC) beregnes Hvad bliver NNC i den markerede pixel

                                                                                                  1

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                                                                                                  3

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                                                                                                  Edges An edge is where there is a

                                                                                                  high change in gray level values

                                                                                                  Objects are often separated from the background by edgesGray level profile

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                                                                                                  Edges The profile as a function f(d) What value is high when there

                                                                                                  is an edgendash The slope of fndash The slope of the tangent at d

                                                                                                  f(d)

                                                                                                  119891119891prime(119889119889)

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                                                                                                  Finite Difference Definition of slope

                                                                                                  Approximation

                                                                                                  Simpler approximationh = 1

                                                                                                  119891119891prime 119889119889 = limℎrarr0

                                                                                                  119891119891 119889119889 + ℎ minus 119891119891(119889119889)ℎ

                                                                                                  119891119891prime 119889119889 asymp119891119891 119889119889 + ℎ minus 119891119891(119889119889)

                                                                                                  ℎ

                                                                                                  119891119891prime 119889119889 asymp 119891119891 119889119889 + 1 minus 119891119891(119889119889)

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                                                                                                  Edges Discrete approximation of frsquo(d) Can be implemented as a filter

                                                                                                  -1 0 1

                                                                                                  f(d-2) f(d-1) f(d) f(d+1) f(d+2) f(d+3)

                                                                                                  f(d)

                                                                                                  119891119891prime 119889119889 asymp 119891119891 119889119889 + 1 minus 119891119891(119889119889)

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                                                                                                  Edges in 2D Changes in gray level values

                                                                                                  ndash Image gradientndash Gradient is the 2D derivative of a 2D function f(xy)ndash Equal to the slope of the imagendash A steep slope is equal to an edge

                                                                                                  120571120571119891119891 119909119909119910119910 = 119866(119892119892119909119909119892119892119910119910)

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                                                                                                  Edge filter kernel The Prewitt filter is a typical

                                                                                                  edge filter Output image has high

                                                                                                  values where there are edges

                                                                                                  -1 0 1

                                                                                                  -1 0 1

                                                                                                  -1 0 1Vertical Prewitt filter

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                                                                                                  Prewitt filter

                                                                                                  Original Prewitt Prewitt

                                                                                                  Hot colormapSmooth 15x15

                                                                                                  Smooth 15x15

                                                                                                  Prewitt

                                                                                                  DTU Compute

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                                                                                                  Edge detection Edge filter

                                                                                                  ndash Prewitt for example Thresholding

                                                                                                  ndash Separate edges from non-edges

                                                                                                  Output is binary imagendash Edges are white

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                                                                                                  Edge filtering

                                                                                                  A) MeanB) Horizontal SobelC) Vertical PrewittD) Horisontal PrewittE) Median

                                                                                                  Der udfoslashres en filtrering (correlation) med et filter paring billedet Der bruges ikke coefficient normalization Den filtrerede vaeligrdi i den markerede pixel bliver -119 Hvilket et 3x3 filter blev benyttet

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                                                                                                  02511 - Niveau af dagens emne forelaeligsingA) Meget letB) LetC) PassendeD) SvaeligrtE) Meget svaeligrt

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                                                                                                  02512 - Niveau af dagens emne forelaeligsingA) Meget letB) LetC) PassendeD) SvaeligrtE) Meget svaeligrt

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                                                                                                  02511 - Mit eget udbytte af dagenA) Jeg har laeligrt meget lidtB) Lidt laeligringC) PassendeD) God laeligringE) Jeg har laeligrt meget

                                                                                                  0 0

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                                                                                                  02512 - Mit eget udbytte af dagenA) Jeg har laeligrt meget lidtB) Lidt laeligringC) PassendeD) God laeligringE) Jeg har laeligrt meget

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                                                                                                  02511 - Sidste uges oslashvelser (pixelwiseoperations)A) Meget letteB) LetteC) PassendeD) SvaeligreE) Meget svaeligre

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                                                                                                  02512 - Sidste uges oslashvelser (pixelwiseoperations)A) Meget letteB) LetteC) PassendeD) SvaeligreE) Meget svaeligre

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                                                                                                  Denne uges brug af clickersA) click click click ndash jeg bliver

                                                                                                  sindssygB) For meget clickC) PassendeD) Jeg vil gerne have lidt mereE) Jeg kan ikrsquo faring nok

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                                                                                                  What can you do after today Describe the difference between point processing and neighbourhood

                                                                                                  processing Compute a rank filtered image using the min max median and

                                                                                                  difference rank filters Compute a mean filtered image Decide if median or average filtering should be used for noise removal Choose the appropriate image border handling based on a given input

                                                                                                  image Implement and apply template matching Compute the normalised cross correlation and explain why it should be

                                                                                                  used Apply given image filter kernels to images Use edge filters on images Describe finite difference approximation of image gradients Describe the concept of edge detection

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                                                                                                  Oslashvelsesrapport over oslashvelse 4 - 02511 Oslashvelser taeligller cirka 30 af karakteren Skal afleveres senest den 7 marts kl 2359 Kan afleveres af 1 eller 2 personer

                                                                                                  ndash I skal skrive jeres egen oslashvelsesrapportndash Brug mindst et af jeres egne billeder

                                                                                                  Afleveres som PDF Lad vaeligre med at kopiere opgaveteksten ind i jeres

                                                                                                  opgave Put Matlab kode i et Appendix og henvis fra teksten Eksempel rapport over oslashvelse findes paring

                                                                                                  hjemmesiden under eksamen

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                                                                                                  Exercises

                                                                                                  • Introduction to Medical Image Analysis
                                                                                                  • Lecture 4 ndash Neighbourhood Processing
                                                                                                  • What can you do after today
                                                                                                  • Point processing
                                                                                                  • Point processing
                                                                                                  • Neighbourhood processing
                                                                                                  • Use of filtering
                                                                                                  • Salt and pepper noise
                                                                                                  • Salt and pepper noise
                                                                                                  • What is so special about noise
                                                                                                  • Noise ndash go away
                                                                                                  • What is the median Value
                                                                                                  • The median value
                                                                                                  • Noise away ndash the median filter
                                                                                                  • Noise removal ndash average filter
                                                                                                  • Noise removal ndash median filter
                                                                                                  • Image Filtering
                                                                                                  • Median filter
                                                                                                  • Rank filters
                                                                                                  • Median filter
                                                                                                  • Correlation
                                                                                                  • Why do we need similarity
                                                                                                  • Correlation (1D)
                                                                                                  • Correlation (1D)
                                                                                                  • Normalisation
                                                                                                  • Normalisation
                                                                                                  • Correlation on images
                                                                                                  • Correlation on images
                                                                                                  • Correlation on images
                                                                                                  • Draw your filter
                                                                                                  • Correlation on images ndash no normalisation
                                                                                                  • Correlation on images ndash no normalisation 2
                                                                                                  • Mathematics of 2D Correlation
                                                                                                  • Mathematics of 2D Correlation
                                                                                                  • Mathematics of 2D Correlation
                                                                                                  • Slide Number 40
                                                                                                  • 2D Kernel Normalisation
                                                                                                  • Correlation
                                                                                                  • Smoothing filters
                                                                                                  • Use of smoothing
                                                                                                  • Use of smoothing
                                                                                                  • Mean filter
                                                                                                  • Border handling
                                                                                                  • Border handling ndash extend the input
                                                                                                  • Correlation with zero padding
                                                                                                  • Border handling ndash extend the input
                                                                                                  • Template Matching
                                                                                                  • Template Matching
                                                                                                  • Template Matching
                                                                                                  • Template Matching
                                                                                                  • Problematic Correlation
                                                                                                  • Normalised Cross Correlation
                                                                                                  • Length of template
                                                                                                  • Length of image patch
                                                                                                  • Normalised Cross Correlation
                                                                                                  • Normalised Cross Correlation
                                                                                                  • Normalised Cross Correlation
                                                                                                  • Edges
                                                                                                  • Edges
                                                                                                  • Finite Difference
                                                                                                  • Edges
                                                                                                  • Edges in 2D
                                                                                                  • Edge filter kernel
                                                                                                  • Prewitt filter
                                                                                                  • Edge detection
                                                                                                  • Edge filtering
                                                                                                  • 02511 - Niveau af dagens emne forelaeligsing
                                                                                                  • 02512 - Niveau af dagens emne forelaeligsing
                                                                                                  • 02511 - Mit eget udbytte af dagen
                                                                                                  • 02512 - Mit eget udbytte af dagen
                                                                                                  • 02511 - Sidste uges oslashvelser (pixelwise operations)
                                                                                                  • 02512 - Sidste uges oslashvelser (pixelwise operations)
                                                                                                  • Denne uges brug af clickers
                                                                                                  • What can you do after today
                                                                                                  • Oslashvelsesrapport over oslashvelse 4 - 02511
                                                                                                  • Exercises
                                                                                                    A0
                                                                                                    B0
                                                                                                    C5
                                                                                                    D0
                                                                                                    E6
                                                                                                    A
                                                                                                    B
                                                                                                    C
                                                                                                    D
                                                                                                    E
                                                                                                    A3
                                                                                                    B0
                                                                                                    C3
                                                                                                    D0
                                                                                                    E0
                                                                                                    A
                                                                                                    B
                                                                                                    C
                                                                                                    D
                                                                                                    E
                                                                                                    A0
                                                                                                    B0
                                                                                                    C1
                                                                                                    D4
                                                                                                    E1
                                                                                                    A
                                                                                                    B
                                                                                                    C
                                                                                                    D
                                                                                                    E
                                                                                                    A2
                                                                                                    B1
                                                                                                    C3
                                                                                                    D2
                                                                                                    E0
                                                                                                    A
                                                                                                    B
                                                                                                    C
                                                                                                    D
                                                                                                    E
                                                                                                    A0
                                                                                                    B0
                                                                                                    C2
                                                                                                    D6
                                                                                                    E0
                                                                                                    A
                                                                                                    B
                                                                                                    C
                                                                                                    D
                                                                                                    E
                                                                                                    A0
                                                                                                    B0
                                                                                                    C1
                                                                                                    D0
                                                                                                    E0
                                                                                                    A
                                                                                                    B
                                                                                                    C
                                                                                                    D
                                                                                                    E
                                                                                                    A2
                                                                                                    B3
                                                                                                    C6
                                                                                                    D1
                                                                                                    E0
                                                                                                    A
                                                                                                    B
                                                                                                    C
                                                                                                    D
                                                                                                    E
                                                                                                    A0
                                                                                                    B8
                                                                                                    C1
                                                                                                    D1
                                                                                                    E0
                                                                                                    A
                                                                                                    B
                                                                                                    C
                                                                                                    D
                                                                                                    E
                                                                                                    A1
                                                                                                    B2
                                                                                                    C2
                                                                                                    D3
                                                                                                    E2
                                                                                                    A
                                                                                                    B
                                                                                                    C
                                                                                                    D
                                                                                                    E
                                                                                                    A0
                                                                                                    B13
                                                                                                    C0
                                                                                                    D0
                                                                                                    E0
                                                                                                    A
                                                                                                    B
                                                                                                    C
                                                                                                    D
                                                                                                    E
                                                                                                    A12
                                                                                                    B0
                                                                                                    C0
                                                                                                    D0
                                                                                                    E0
                                                                                                    A
                                                                                                    B
                                                                                                    C
                                                                                                    D
                                                                                                    E
                                                                                                    A0
                                                                                                    B0
                                                                                                    C0
                                                                                                    D0
                                                                                                    E13
                                                                                                    A
                                                                                                    B
                                                                                                    C
                                                                                                    D
                                                                                                    E

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                                                                                                    Smoothing filters

                                                                                                    Also know as ndash Smoothing kernel Mean filter Low pass filter blurring

                                                                                                    The simplest filter ndash Spatial low pass filterndash Removes high frequencies

                                                                                                    Another mask ndash Gaussian filter

                                                                                                    1 1 1

                                                                                                    1 1 1

                                                                                                    1 1 191

                                                                                                    1 2 1

                                                                                                    2 4 2

                                                                                                    1 2 1161

                                                                                                    Why Gaussian

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                                                                                                    Use of smoothing

                                                                                                    3x3 7x7 11x11 15x15

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                                                                                                    Use of smoothing Large kernels smooth more Removes high frequency information Good at enhancing big structures

                                                                                                    3x3 15x15

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                                                                                                    Mean filterA) 166B) 113C) 12D) 51E) 245

                                                                                                    0 0 0 0

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                                                                                                    Border handling

                                                                                                    0 2 41 2 2

                                                                                                    1 6 3

                                                                                                    1 2 12 5 3

                                                                                                    2 1 3

                                                                                                    1 3 1

                                                                                                    2 2 2

                                                                                                    0 1 3

                                                                                                    1 2 0

                                                                                                    2 1 4

                                                                                                    1 0 1

                                                                                                    Input Output

                                                                                                    No values at the border

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                                                                                                    Border handling ndash extend the input

                                                                                                    0 2 41 2 2

                                                                                                    1 6 3

                                                                                                    1 2 12 5 3

                                                                                                    2 1 3

                                                                                                    1 3 1

                                                                                                    2 2 2

                                                                                                    0 1 3

                                                                                                    1 2 0

                                                                                                    2 1 4

                                                                                                    1 0 1

                                                                                                    Input

                                                                                                    0 0 0 0 000000

                                                                                                    bull Zero padding ndash what happens

                                                                                                    bull Zero is black ndash creates dark border around the image

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                                                                                                    Correlation with zero paddingA) 5 8B) 12 16C) 13 3D) 15 21E) 17 12

                                                                                                    1 2 11 3 11 2 1

                                                                                                    0 2 41 2 2

                                                                                                    1 6 3

                                                                                                    1 2 12 5 3

                                                                                                    2 1 3

                                                                                                    1 3 1

                                                                                                    2 2 2

                                                                                                    0 1 3

                                                                                                    1 2 0

                                                                                                    2 1 4

                                                                                                    1 0 1

                                                                                                    0

                                                                                                    13

                                                                                                    0 0 0

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                                                                                                    Border handling ndash extend the input

                                                                                                    0 2 41 2 2

                                                                                                    1 6 3

                                                                                                    1 2 12 5 3

                                                                                                    2 1 3

                                                                                                    1 3 1

                                                                                                    2 2 2

                                                                                                    0 1 3

                                                                                                    1 2 0

                                                                                                    2 1 4

                                                                                                    1 0 1

                                                                                                    Input

                                                                                                    1 2 0 1 311211

                                                                                                    bull Reflection

                                                                                                    bull Normally better than zero padding

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                                                                                                    Template Matching Template

                                                                                                    ndash Skabelon paring dansk Locates objects in images

                                                                                                    Input

                                                                                                    Template

                                                                                                    Output Correlation image

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                                                                                                    Template Matching The correlation between the template and the input

                                                                                                    image is computed for each pixel

                                                                                                    Input

                                                                                                    Template

                                                                                                    Output Correlation image

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                                                                                                    Template Matching The pixel with the highest value is found in the

                                                                                                    output imagendash Here is the highest correlation

                                                                                                    Input

                                                                                                    Template

                                                                                                    Output Correlation image

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                                                                                                    Template Matching This corresponds to the found pattern in the input

                                                                                                    image

                                                                                                    Input

                                                                                                    Template

                                                                                                    Output Correlation image

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                                                                                                    Problematic Correlation Correlation matching has problem with light areas ndash

                                                                                                    why

                                                                                                    Input (f)

                                                                                                    Template (h)

                                                                                                    Output Correlation imageFake max

                                                                                                    Real max

                                                                                                    Very High119892119892 119909119909119910119910 = 119895119895=minus119877119877

                                                                                                    119877119877

                                                                                                    119894119894=minus119877119877

                                                                                                    119877119877

                                                                                                    ℎ(119894119894 119895119895) 119891119891(119909119909 + 119894119894119910119910 + 119895119895)

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                                                                                                    Normalised Cross Correlation

                                                                                                    Input (f)

                                                                                                    Template (h)

                                                                                                    Output Correlation image

                                                                                                    Real max

                                                                                                    NCC x y =Correlation

                                                                                                    Length of image patch sdot Length of template

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                                                                                                    Length of template Vector length

                                                                                                    ndash Put all pixel values into a vectorndash Compute the length of this vector

                                                                                                    Describes the intensity of the templatendash Bright template has a large lengthndash Dark template has a small length

                                                                                                    Template (h)

                                                                                                    Length of template = 119895119895=minus119877119877

                                                                                                    119877119877

                                                                                                    119894119894=minus119877119877

                                                                                                    119877119877

                                                                                                    ℎ(119894119894 119895119895) ℎ(119894119894 119895119895)

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                                                                                                    Length of image patch Vector length based on pixel values in image patch Describes the intensity of the image patch

                                                                                                    Template (h)

                                                                                                    Input (f) with patch

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                                                                                                    Normalised Cross Correlation The length of the image patch and the length of

                                                                                                    template normalise the NCC If the image is very bright the NCC will be ldquopulled

                                                                                                    downrdquo

                                                                                                    NCC x y =Correlation

                                                                                                    Length of image patch sdot Length of template

                                                                                                    DTU Compute

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                                                                                                    Normalised Cross Correlation NCC will be between

                                                                                                    ndash 0 No similarity between template and image patchndash 1 Template and image patch are identical

                                                                                                    Input (f)

                                                                                                    Template (h)

                                                                                                    Output Correlation image

                                                                                                    Real max

                                                                                                    NCC x y =Correlation

                                                                                                    Length of image patch sdot Length of template

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                                                                                                    Normalised Cross Correlation

                                                                                                    A) 010B) 033C) 083D) 062E) 098

                                                                                                    Der udfoslashres template matching med og normalized crosscorrelation (NCC) beregnes Hvad bliver NNC i den markerede pixel

                                                                                                    1

                                                                                                    2 2

                                                                                                    3

                                                                                                    2

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                                                                                                    Edges An edge is where there is a

                                                                                                    high change in gray level values

                                                                                                    Objects are often separated from the background by edgesGray level profile

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                                                                                                    Edges The profile as a function f(d) What value is high when there

                                                                                                    is an edgendash The slope of fndash The slope of the tangent at d

                                                                                                    f(d)

                                                                                                    119891119891prime(119889119889)

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                                                                                                    Finite Difference Definition of slope

                                                                                                    Approximation

                                                                                                    Simpler approximationh = 1

                                                                                                    119891119891prime 119889119889 = limℎrarr0

                                                                                                    119891119891 119889119889 + ℎ minus 119891119891(119889119889)ℎ

                                                                                                    119891119891prime 119889119889 asymp119891119891 119889119889 + ℎ minus 119891119891(119889119889)

                                                                                                    ℎ

                                                                                                    119891119891prime 119889119889 asymp 119891119891 119889119889 + 1 minus 119891119891(119889119889)

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                                                                                                    Edges Discrete approximation of frsquo(d) Can be implemented as a filter

                                                                                                    -1 0 1

                                                                                                    f(d-2) f(d-1) f(d) f(d+1) f(d+2) f(d+3)

                                                                                                    f(d)

                                                                                                    119891119891prime 119889119889 asymp 119891119891 119889119889 + 1 minus 119891119891(119889119889)

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                                                                                                    Edges in 2D Changes in gray level values

                                                                                                    ndash Image gradientndash Gradient is the 2D derivative of a 2D function f(xy)ndash Equal to the slope of the imagendash A steep slope is equal to an edge

                                                                                                    120571120571119891119891 119909119909119910119910 = 119866(119892119892119909119909119892119892119910119910)

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                                                                                                    Edge filter kernel The Prewitt filter is a typical

                                                                                                    edge filter Output image has high

                                                                                                    values where there are edges

                                                                                                    -1 0 1

                                                                                                    -1 0 1

                                                                                                    -1 0 1Vertical Prewitt filter

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                                                                                                    Prewitt filter

                                                                                                    Original Prewitt Prewitt

                                                                                                    Hot colormapSmooth 15x15

                                                                                                    Smooth 15x15

                                                                                                    Prewitt

                                                                                                    DTU Compute

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                                                                                                    Edge detection Edge filter

                                                                                                    ndash Prewitt for example Thresholding

                                                                                                    ndash Separate edges from non-edges

                                                                                                    Output is binary imagendash Edges are white

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                                                                                                    Edge filtering

                                                                                                    A) MeanB) Horizontal SobelC) Vertical PrewittD) Horisontal PrewittE) Median

                                                                                                    Der udfoslashres en filtrering (correlation) med et filter paring billedet Der bruges ikke coefficient normalization Den filtrerede vaeligrdi i den markerede pixel bliver -119 Hvilket et 3x3 filter blev benyttet

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                                                                                                    02511 - Niveau af dagens emne forelaeligsingA) Meget letB) LetC) PassendeD) SvaeligrtE) Meget svaeligrt

                                                                                                    23

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                                                                                                    02512 - Niveau af dagens emne forelaeligsingA) Meget letB) LetC) PassendeD) SvaeligrtE) Meget svaeligrt

                                                                                                    0 0

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                                                                                                    02511 - Mit eget udbytte af dagenA) Jeg har laeligrt meget lidtB) Lidt laeligringC) PassendeD) God laeligringE) Jeg har laeligrt meget

                                                                                                    0 0

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                                                                                                    0

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                                                                                                    02512 - Mit eget udbytte af dagenA) Jeg har laeligrt meget lidtB) Lidt laeligringC) PassendeD) God laeligringE) Jeg har laeligrt meget

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                                                                                                    02511 - Sidste uges oslashvelser (pixelwiseoperations)A) Meget letteB) LetteC) PassendeD) SvaeligreE) Meget svaeligre

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                                                                                                    02512 - Sidste uges oslashvelser (pixelwiseoperations)A) Meget letteB) LetteC) PassendeD) SvaeligreE) Meget svaeligre

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                                                                                                    Denne uges brug af clickersA) click click click ndash jeg bliver

                                                                                                    sindssygB) For meget clickC) PassendeD) Jeg vil gerne have lidt mereE) Jeg kan ikrsquo faring nok

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                                                                                                    What can you do after today Describe the difference between point processing and neighbourhood

                                                                                                    processing Compute a rank filtered image using the min max median and

                                                                                                    difference rank filters Compute a mean filtered image Decide if median or average filtering should be used for noise removal Choose the appropriate image border handling based on a given input

                                                                                                    image Implement and apply template matching Compute the normalised cross correlation and explain why it should be

                                                                                                    used Apply given image filter kernels to images Use edge filters on images Describe finite difference approximation of image gradients Describe the concept of edge detection

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                                                                                                    Oslashvelsesrapport over oslashvelse 4 - 02511 Oslashvelser taeligller cirka 30 af karakteren Skal afleveres senest den 7 marts kl 2359 Kan afleveres af 1 eller 2 personer

                                                                                                    ndash I skal skrive jeres egen oslashvelsesrapportndash Brug mindst et af jeres egne billeder

                                                                                                    Afleveres som PDF Lad vaeligre med at kopiere opgaveteksten ind i jeres

                                                                                                    opgave Put Matlab kode i et Appendix og henvis fra teksten Eksempel rapport over oslashvelse findes paring

                                                                                                    hjemmesiden under eksamen

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                                                                                                    Exercises

                                                                                                    • Introduction to Medical Image Analysis
                                                                                                    • Lecture 4 ndash Neighbourhood Processing
                                                                                                    • What can you do after today
                                                                                                    • Point processing
                                                                                                    • Point processing
                                                                                                    • Neighbourhood processing
                                                                                                    • Use of filtering
                                                                                                    • Salt and pepper noise
                                                                                                    • Salt and pepper noise
                                                                                                    • What is so special about noise
                                                                                                    • Noise ndash go away
                                                                                                    • What is the median Value
                                                                                                    • The median value
                                                                                                    • Noise away ndash the median filter
                                                                                                    • Noise removal ndash average filter
                                                                                                    • Noise removal ndash median filter
                                                                                                    • Image Filtering
                                                                                                    • Median filter
                                                                                                    • Rank filters
                                                                                                    • Median filter
                                                                                                    • Correlation
                                                                                                    • Why do we need similarity
                                                                                                    • Correlation (1D)
                                                                                                    • Correlation (1D)
                                                                                                    • Normalisation
                                                                                                    • Normalisation
                                                                                                    • Correlation on images
                                                                                                    • Correlation on images
                                                                                                    • Correlation on images
                                                                                                    • Draw your filter
                                                                                                    • Correlation on images ndash no normalisation
                                                                                                    • Correlation on images ndash no normalisation 2
                                                                                                    • Mathematics of 2D Correlation
                                                                                                    • Mathematics of 2D Correlation
                                                                                                    • Mathematics of 2D Correlation
                                                                                                    • Slide Number 40
                                                                                                    • 2D Kernel Normalisation
                                                                                                    • Correlation
                                                                                                    • Smoothing filters
                                                                                                    • Use of smoothing
                                                                                                    • Use of smoothing
                                                                                                    • Mean filter
                                                                                                    • Border handling
                                                                                                    • Border handling ndash extend the input
                                                                                                    • Correlation with zero padding
                                                                                                    • Border handling ndash extend the input
                                                                                                    • Template Matching
                                                                                                    • Template Matching
                                                                                                    • Template Matching
                                                                                                    • Template Matching
                                                                                                    • Problematic Correlation
                                                                                                    • Normalised Cross Correlation
                                                                                                    • Length of template
                                                                                                    • Length of image patch
                                                                                                    • Normalised Cross Correlation
                                                                                                    • Normalised Cross Correlation
                                                                                                    • Normalised Cross Correlation
                                                                                                    • Edges
                                                                                                    • Edges
                                                                                                    • Finite Difference
                                                                                                    • Edges
                                                                                                    • Edges in 2D
                                                                                                    • Edge filter kernel
                                                                                                    • Prewitt filter
                                                                                                    • Edge detection
                                                                                                    • Edge filtering
                                                                                                    • 02511 - Niveau af dagens emne forelaeligsing
                                                                                                    • 02512 - Niveau af dagens emne forelaeligsing
                                                                                                    • 02511 - Mit eget udbytte af dagen
                                                                                                    • 02512 - Mit eget udbytte af dagen
                                                                                                    • 02511 - Sidste uges oslashvelser (pixelwise operations)
                                                                                                    • 02512 - Sidste uges oslashvelser (pixelwise operations)
                                                                                                    • Denne uges brug af clickers
                                                                                                    • What can you do after today
                                                                                                    • Oslashvelsesrapport over oslashvelse 4 - 02511
                                                                                                    • Exercises
                                                                                                      A0
                                                                                                      B0
                                                                                                      C5
                                                                                                      D0
                                                                                                      E6
                                                                                                      A
                                                                                                      B
                                                                                                      C
                                                                                                      D
                                                                                                      E
                                                                                                      A3
                                                                                                      B0
                                                                                                      C3
                                                                                                      D0
                                                                                                      E0
                                                                                                      A
                                                                                                      B
                                                                                                      C
                                                                                                      D
                                                                                                      E
                                                                                                      A0
                                                                                                      B0
                                                                                                      C1
                                                                                                      D4
                                                                                                      E1
                                                                                                      A
                                                                                                      B
                                                                                                      C
                                                                                                      D
                                                                                                      E
                                                                                                      A2
                                                                                                      B1
                                                                                                      C3
                                                                                                      D2
                                                                                                      E0
                                                                                                      A
                                                                                                      B
                                                                                                      C
                                                                                                      D
                                                                                                      E
                                                                                                      A0
                                                                                                      B0
                                                                                                      C2
                                                                                                      D6
                                                                                                      E0
                                                                                                      A
                                                                                                      B
                                                                                                      C
                                                                                                      D
                                                                                                      E
                                                                                                      A0
                                                                                                      B0
                                                                                                      C1
                                                                                                      D0
                                                                                                      E0
                                                                                                      A
                                                                                                      B
                                                                                                      C
                                                                                                      D
                                                                                                      E
                                                                                                      A2
                                                                                                      B3
                                                                                                      C6
                                                                                                      D1
                                                                                                      E0
                                                                                                      A
                                                                                                      B
                                                                                                      C
                                                                                                      D
                                                                                                      E
                                                                                                      A0
                                                                                                      B8
                                                                                                      C1
                                                                                                      D1
                                                                                                      E0
                                                                                                      A
                                                                                                      B
                                                                                                      C
                                                                                                      D
                                                                                                      E
                                                                                                      A1
                                                                                                      B2
                                                                                                      C2
                                                                                                      D3
                                                                                                      E2
                                                                                                      A
                                                                                                      B
                                                                                                      C
                                                                                                      D
                                                                                                      E
                                                                                                      A0
                                                                                                      B13
                                                                                                      C0
                                                                                                      D0
                                                                                                      E0
                                                                                                      A
                                                                                                      B
                                                                                                      C
                                                                                                      D
                                                                                                      E
                                                                                                      A12
                                                                                                      B0
                                                                                                      C0
                                                                                                      D0
                                                                                                      E0
                                                                                                      A
                                                                                                      B
                                                                                                      C
                                                                                                      D
                                                                                                      E
                                                                                                      A0
                                                                                                      B0
                                                                                                      C0
                                                                                                      D0
                                                                                                      E13

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                                                                                                      Smoothing filters

                                                                                                      Also know as ndash Smoothing kernel Mean filter Low pass filter blurring

                                                                                                      The simplest filter ndash Spatial low pass filterndash Removes high frequencies

                                                                                                      Another mask ndash Gaussian filter

                                                                                                      1 1 1

                                                                                                      1 1 1

                                                                                                      1 1 191

                                                                                                      1 2 1

                                                                                                      2 4 2

                                                                                                      1 2 1161

                                                                                                      Why Gaussian

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                                                                                                      Use of smoothing

                                                                                                      3x3 7x7 11x11 15x15

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                                                                                                      Use of smoothing Large kernels smooth more Removes high frequency information Good at enhancing big structures

                                                                                                      3x3 15x15

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                                                                                                      Mean filterA) 166B) 113C) 12D) 51E) 245

                                                                                                      0 0 0 0

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                                                                                                      Border handling

                                                                                                      0 2 41 2 2

                                                                                                      1 6 3

                                                                                                      1 2 12 5 3

                                                                                                      2 1 3

                                                                                                      1 3 1

                                                                                                      2 2 2

                                                                                                      0 1 3

                                                                                                      1 2 0

                                                                                                      2 1 4

                                                                                                      1 0 1

                                                                                                      Input Output

                                                                                                      No values at the border

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                                                                                                      Border handling ndash extend the input

                                                                                                      0 2 41 2 2

                                                                                                      1 6 3

                                                                                                      1 2 12 5 3

                                                                                                      2 1 3

                                                                                                      1 3 1

                                                                                                      2 2 2

                                                                                                      0 1 3

                                                                                                      1 2 0

                                                                                                      2 1 4

                                                                                                      1 0 1

                                                                                                      Input

                                                                                                      0 0 0 0 000000

                                                                                                      bull Zero padding ndash what happens

                                                                                                      bull Zero is black ndash creates dark border around the image

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                                                                                                      Correlation with zero paddingA) 5 8B) 12 16C) 13 3D) 15 21E) 17 12

                                                                                                      1 2 11 3 11 2 1

                                                                                                      0 2 41 2 2

                                                                                                      1 6 3

                                                                                                      1 2 12 5 3

                                                                                                      2 1 3

                                                                                                      1 3 1

                                                                                                      2 2 2

                                                                                                      0 1 3

                                                                                                      1 2 0

                                                                                                      2 1 4

                                                                                                      1 0 1

                                                                                                      0

                                                                                                      13

                                                                                                      0 0 0

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                                                                                                      Border handling ndash extend the input

                                                                                                      0 2 41 2 2

                                                                                                      1 6 3

                                                                                                      1 2 12 5 3

                                                                                                      2 1 3

                                                                                                      1 3 1

                                                                                                      2 2 2

                                                                                                      0 1 3

                                                                                                      1 2 0

                                                                                                      2 1 4

                                                                                                      1 0 1

                                                                                                      Input

                                                                                                      1 2 0 1 311211

                                                                                                      bull Reflection

                                                                                                      bull Normally better than zero padding

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                                                                                                      Template Matching Template

                                                                                                      ndash Skabelon paring dansk Locates objects in images

                                                                                                      Input

                                                                                                      Template

                                                                                                      Output Correlation image

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                                                                                                      Template Matching The correlation between the template and the input

                                                                                                      image is computed for each pixel

                                                                                                      Input

                                                                                                      Template

                                                                                                      Output Correlation image

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                                                                                                      Template Matching The pixel with the highest value is found in the

                                                                                                      output imagendash Here is the highest correlation

                                                                                                      Input

                                                                                                      Template

                                                                                                      Output Correlation image

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                                                                                                      Template Matching This corresponds to the found pattern in the input

                                                                                                      image

                                                                                                      Input

                                                                                                      Template

                                                                                                      Output Correlation image

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                                                                                                      Problematic Correlation Correlation matching has problem with light areas ndash

                                                                                                      why

                                                                                                      Input (f)

                                                                                                      Template (h)

                                                                                                      Output Correlation imageFake max

                                                                                                      Real max

                                                                                                      Very High119892119892 119909119909119910119910 = 119895119895=minus119877119877

                                                                                                      119877119877

                                                                                                      119894119894=minus119877119877

                                                                                                      119877119877

                                                                                                      ℎ(119894119894 119895119895) 119891119891(119909119909 + 119894119894119910119910 + 119895119895)

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                                                                                                      Normalised Cross Correlation

                                                                                                      Input (f)

                                                                                                      Template (h)

                                                                                                      Output Correlation image

                                                                                                      Real max

                                                                                                      NCC x y =Correlation

                                                                                                      Length of image patch sdot Length of template

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                                                                                                      Length of template Vector length

                                                                                                      ndash Put all pixel values into a vectorndash Compute the length of this vector

                                                                                                      Describes the intensity of the templatendash Bright template has a large lengthndash Dark template has a small length

                                                                                                      Template (h)

                                                                                                      Length of template = 119895119895=minus119877119877

                                                                                                      119877119877

                                                                                                      119894119894=minus119877119877

                                                                                                      119877119877

                                                                                                      ℎ(119894119894 119895119895) ℎ(119894119894 119895119895)

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                                                                                                      Length of image patch Vector length based on pixel values in image patch Describes the intensity of the image patch

                                                                                                      Template (h)

                                                                                                      Input (f) with patch

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                                                                                                      Normalised Cross Correlation The length of the image patch and the length of

                                                                                                      template normalise the NCC If the image is very bright the NCC will be ldquopulled

                                                                                                      downrdquo

                                                                                                      NCC x y =Correlation

                                                                                                      Length of image patch sdot Length of template

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                                                                                                      Normalised Cross Correlation NCC will be between

                                                                                                      ndash 0 No similarity between template and image patchndash 1 Template and image patch are identical

                                                                                                      Input (f)

                                                                                                      Template (h)

                                                                                                      Output Correlation image

                                                                                                      Real max

                                                                                                      NCC x y =Correlation

                                                                                                      Length of image patch sdot Length of template

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                                                                                                      Normalised Cross Correlation

                                                                                                      A) 010B) 033C) 083D) 062E) 098

                                                                                                      Der udfoslashres template matching med og normalized crosscorrelation (NCC) beregnes Hvad bliver NNC i den markerede pixel

                                                                                                      1

                                                                                                      2 2

                                                                                                      3

                                                                                                      2

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                                                                                                      2
                                                                                                      2
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                                                                                                      Edges An edge is where there is a

                                                                                                      high change in gray level values

                                                                                                      Objects are often separated from the background by edgesGray level profile

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                                                                                                      Edges The profile as a function f(d) What value is high when there

                                                                                                      is an edgendash The slope of fndash The slope of the tangent at d

                                                                                                      f(d)

                                                                                                      119891119891prime(119889119889)

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                                                                                                      Finite Difference Definition of slope

                                                                                                      Approximation

                                                                                                      Simpler approximationh = 1

                                                                                                      119891119891prime 119889119889 = limℎrarr0

                                                                                                      119891119891 119889119889 + ℎ minus 119891119891(119889119889)ℎ

                                                                                                      119891119891prime 119889119889 asymp119891119891 119889119889 + ℎ minus 119891119891(119889119889)

                                                                                                      ℎ

                                                                                                      119891119891prime 119889119889 asymp 119891119891 119889119889 + 1 minus 119891119891(119889119889)

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                                                                                                      Edges Discrete approximation of frsquo(d) Can be implemented as a filter

                                                                                                      -1 0 1

                                                                                                      f(d-2) f(d-1) f(d) f(d+1) f(d+2) f(d+3)

                                                                                                      f(d)

                                                                                                      119891119891prime 119889119889 asymp 119891119891 119889119889 + 1 minus 119891119891(119889119889)

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                                                                                                      Edges in 2D Changes in gray level values

                                                                                                      ndash Image gradientndash Gradient is the 2D derivative of a 2D function f(xy)ndash Equal to the slope of the imagendash A steep slope is equal to an edge

                                                                                                      120571120571119891119891 119909119909119910119910 = 119866(119892119892119909119909119892119892119910119910)

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                                                                                                      Edge filter kernel The Prewitt filter is a typical

                                                                                                      edge filter Output image has high

                                                                                                      values where there are edges

                                                                                                      -1 0 1

                                                                                                      -1 0 1

                                                                                                      -1 0 1Vertical Prewitt filter

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                                                                                                      Prewitt filter

                                                                                                      Original Prewitt Prewitt

                                                                                                      Hot colormapSmooth 15x15

                                                                                                      Smooth 15x15

                                                                                                      Prewitt

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                                                                                                      Edge detection Edge filter

                                                                                                      ndash Prewitt for example Thresholding

                                                                                                      ndash Separate edges from non-edges

                                                                                                      Output is binary imagendash Edges are white

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                                                                                                      Edge filtering

                                                                                                      A) MeanB) Horizontal SobelC) Vertical PrewittD) Horisontal PrewittE) Median

                                                                                                      Der udfoslashres en filtrering (correlation) med et filter paring billedet Der bruges ikke coefficient normalization Den filtrerede vaeligrdi i den markerede pixel bliver -119 Hvilket et 3x3 filter blev benyttet

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                                                                                                      02511 - Niveau af dagens emne forelaeligsingA) Meget letB) LetC) PassendeD) SvaeligrtE) Meget svaeligrt

                                                                                                      23

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                                                                                                      02512 - Niveau af dagens emne forelaeligsingA) Meget letB) LetC) PassendeD) SvaeligrtE) Meget svaeligrt

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                                                                                                      02511 - Mit eget udbytte af dagenA) Jeg har laeligrt meget lidtB) Lidt laeligringC) PassendeD) God laeligringE) Jeg har laeligrt meget

                                                                                                      0 0

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                                                                                                      02512 - Mit eget udbytte af dagenA) Jeg har laeligrt meget lidtB) Lidt laeligringC) PassendeD) God laeligringE) Jeg har laeligrt meget

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                                                                                                      02511 - Sidste uges oslashvelser (pixelwiseoperations)A) Meget letteB) LetteC) PassendeD) SvaeligreE) Meget svaeligre

                                                                                                      0 0

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                                                                                                      02512 - Sidste uges oslashvelser (pixelwiseoperations)A) Meget letteB) LetteC) PassendeD) SvaeligreE) Meget svaeligre

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                                                                                                      2122018Introduction to Medical Image Analysis82 DTU Compute Technical University of Denmark

                                                                                                      Denne uges brug af clickersA) click click click ndash jeg bliver

                                                                                                      sindssygB) For meget clickC) PassendeD) Jeg vil gerne have lidt mereE) Jeg kan ikrsquo faring nok

                                                                                                      0 0

                                                                                                      5

                                                                                                      0

                                                                                                      6

                                                                                                      A B C D E

                                                                                                      Chart1

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                                                                                                      What can you do after today Describe the difference between point processing and neighbourhood

                                                                                                      processing Compute a rank filtered image using the min max median and

                                                                                                      difference rank filters Compute a mean filtered image Decide if median or average filtering should be used for noise removal Choose the appropriate image border handling based on a given input

                                                                                                      image Implement and apply template matching Compute the normalised cross correlation and explain why it should be

                                                                                                      used Apply given image filter kernels to images Use edge filters on images Describe finite difference approximation of image gradients Describe the concept of edge detection

                                                                                                      DTU Compute

                                                                                                      2122018Introduction to Medical Image Analysis84 DTU Compute Technical University of Denmark

                                                                                                      Oslashvelsesrapport over oslashvelse 4 - 02511 Oslashvelser taeligller cirka 30 af karakteren Skal afleveres senest den 7 marts kl 2359 Kan afleveres af 1 eller 2 personer

                                                                                                      ndash I skal skrive jeres egen oslashvelsesrapportndash Brug mindst et af jeres egne billeder

                                                                                                      Afleveres som PDF Lad vaeligre med at kopiere opgaveteksten ind i jeres

                                                                                                      opgave Put Matlab kode i et Appendix og henvis fra teksten Eksempel rapport over oslashvelse findes paring

                                                                                                      hjemmesiden under eksamen

                                                                                                      DTU Compute

                                                                                                      2122018Introduction to Medical Image Analysis85 DTU Compute Technical University of Denmark

                                                                                                      Exercises

                                                                                                      • Introduction to Medical Image Analysis
                                                                                                      • Lecture 4 ndash Neighbourhood Processing
                                                                                                      • What can you do after today
                                                                                                      • Point processing
                                                                                                      • Point processing
                                                                                                      • Neighbourhood processing
                                                                                                      • Use of filtering
                                                                                                      • Salt and pepper noise
                                                                                                      • Salt and pepper noise
                                                                                                      • What is so special about noise
                                                                                                      • Noise ndash go away
                                                                                                      • What is the median Value
                                                                                                      • The median value
                                                                                                      • Noise away ndash the median filter
                                                                                                      • Noise removal ndash average filter
                                                                                                      • Noise removal ndash median filter
                                                                                                      • Image Filtering
                                                                                                      • Median filter
                                                                                                      • Rank filters
                                                                                                      • Median filter
                                                                                                      • Correlation
                                                                                                      • Why do we need similarity
                                                                                                      • Correlation (1D)
                                                                                                      • Correlation (1D)
                                                                                                      • Normalisation
                                                                                                      • Normalisation
                                                                                                      • Correlation on images
                                                                                                      • Correlation on images
                                                                                                      • Correlation on images
                                                                                                      • Draw your filter
                                                                                                      • Correlation on images ndash no normalisation
                                                                                                      • Correlation on images ndash no normalisation 2
                                                                                                      • Mathematics of 2D Correlation
                                                                                                      • Mathematics of 2D Correlation
                                                                                                      • Mathematics of 2D Correlation
                                                                                                      • Slide Number 40
                                                                                                      • 2D Kernel Normalisation
                                                                                                      • Correlation
                                                                                                      • Smoothing filters
                                                                                                      • Use of smoothing
                                                                                                      • Use of smoothing
                                                                                                      • Mean filter
                                                                                                      • Border handling
                                                                                                      • Border handling ndash extend the input
                                                                                                      • Correlation with zero padding
                                                                                                      • Border handling ndash extend the input
                                                                                                      • Template Matching
                                                                                                      • Template Matching
                                                                                                      • Template Matching
                                                                                                      • Template Matching
                                                                                                      • Problematic Correlation
                                                                                                      • Normalised Cross Correlation
                                                                                                      • Length of template
                                                                                                      • Length of image patch
                                                                                                      • Normalised Cross Correlation
                                                                                                      • Normalised Cross Correlation
                                                                                                      • Normalised Cross Correlation
                                                                                                      • Edges
                                                                                                      • Edges
                                                                                                      • Finite Difference
                                                                                                      • Edges
                                                                                                      • Edges in 2D
                                                                                                      • Edge filter kernel
                                                                                                      • Prewitt filter
                                                                                                      • Edge detection
                                                                                                      • Edge filtering
                                                                                                      • 02511 - Niveau af dagens emne forelaeligsing
                                                                                                      • 02512 - Niveau af dagens emne forelaeligsing
                                                                                                      • 02511 - Mit eget udbytte af dagen
                                                                                                      • 02512 - Mit eget udbytte af dagen
                                                                                                      • 02511 - Sidste uges oslashvelser (pixelwise operations)
                                                                                                      • 02512 - Sidste uges oslashvelser (pixelwise operations)
                                                                                                      • Denne uges brug af clickers
                                                                                                      • What can you do after today
                                                                                                      • Oslashvelsesrapport over oslashvelse 4 - 02511
                                                                                                      • Exercises
                                                                                                        A0
                                                                                                        B0
                                                                                                        C5
                                                                                                        D0
                                                                                                        E6
                                                                                                        A
                                                                                                        B
                                                                                                        C
                                                                                                        D
                                                                                                        E
                                                                                                        A3
                                                                                                        B0
                                                                                                        C3
                                                                                                        D0
                                                                                                        E0
                                                                                                        A
                                                                                                        B
                                                                                                        C
                                                                                                        D
                                                                                                        E
                                                                                                        A0
                                                                                                        B0
                                                                                                        C1
                                                                                                        D4
                                                                                                        E1
                                                                                                        A
                                                                                                        B
                                                                                                        C
                                                                                                        D
                                                                                                        E
                                                                                                        A2
                                                                                                        B1
                                                                                                        C3
                                                                                                        D2
                                                                                                        E0
                                                                                                        A
                                                                                                        B
                                                                                                        C
                                                                                                        D
                                                                                                        E
                                                                                                        A0
                                                                                                        B0
                                                                                                        C2
                                                                                                        D6
                                                                                                        E0
                                                                                                        A
                                                                                                        B
                                                                                                        C
                                                                                                        D
                                                                                                        E
                                                                                                        A0
                                                                                                        B0
                                                                                                        C1
                                                                                                        D0
                                                                                                        E0
                                                                                                        A
                                                                                                        B
                                                                                                        C
                                                                                                        D
                                                                                                        E
                                                                                                        A2
                                                                                                        B3
                                                                                                        C6
                                                                                                        D1
                                                                                                        E0
                                                                                                        A
                                                                                                        B
                                                                                                        C
                                                                                                        D
                                                                                                        E
                                                                                                        A0
                                                                                                        B8
                                                                                                        C1
                                                                                                        D1
                                                                                                        E0
                                                                                                        A
                                                                                                        B
                                                                                                        C
                                                                                                        D
                                                                                                        E
                                                                                                        A1
                                                                                                        B2
                                                                                                        C2
                                                                                                        D3
                                                                                                        E2
                                                                                                        A
                                                                                                        B
                                                                                                        C
                                                                                                        D
                                                                                                        E
                                                                                                        A0
                                                                                                        B13
                                                                                                        C0
                                                                                                        D0
                                                                                                        E0
                                                                                                        A
                                                                                                        B
                                                                                                        C
                                                                                                        D
                                                                                                        E
                                                                                                        A12
                                                                                                        B0
                                                                                                        C0
                                                                                                        D0
                                                                                                        E0
                                                                                                        A
                                                                                                        B
                                                                                                        C
                                                                                                        D
                                                                                                        E

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                                                                                                        2122018Introduction to Medical Image Analysis45 DTU Compute Technical University of Denmark

                                                                                                        Use of smoothing

                                                                                                        3x3 7x7 11x11 15x15

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                                                                                                        2122018Introduction to Medical Image Analysis46 DTU Compute Technical University of Denmark

                                                                                                        Use of smoothing Large kernels smooth more Removes high frequency information Good at enhancing big structures

                                                                                                        3x3 15x15

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                                                                                                        2122018Introduction to Medical Image Analysis47 DTU Compute Technical University of Denmark

                                                                                                        Mean filterA) 166B) 113C) 12D) 51E) 245

                                                                                                        0 0 0 0

                                                                                                        A B C D E

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                                                                                                        12
                                                                                                        0
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                                                                                                        Border handling

                                                                                                        0 2 41 2 2

                                                                                                        1 6 3

                                                                                                        1 2 12 5 3

                                                                                                        2 1 3

                                                                                                        1 3 1

                                                                                                        2 2 2

                                                                                                        0 1 3

                                                                                                        1 2 0

                                                                                                        2 1 4

                                                                                                        1 0 1

                                                                                                        Input Output

                                                                                                        No values at the border

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                                                                                                        2122018Introduction to Medical Image Analysis50 DTU Compute Technical University of Denmark

                                                                                                        Border handling ndash extend the input

                                                                                                        0 2 41 2 2

                                                                                                        1 6 3

                                                                                                        1 2 12 5 3

                                                                                                        2 1 3

                                                                                                        1 3 1

                                                                                                        2 2 2

                                                                                                        0 1 3

                                                                                                        1 2 0

                                                                                                        2 1 4

                                                                                                        1 0 1

                                                                                                        Input

                                                                                                        0 0 0 0 000000

                                                                                                        bull Zero padding ndash what happens

                                                                                                        bull Zero is black ndash creates dark border around the image

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                                                                                                        2122018Introduction to Medical Image Analysis51 DTU Compute Technical University of Denmark

                                                                                                        Correlation with zero paddingA) 5 8B) 12 16C) 13 3D) 15 21E) 17 12

                                                                                                        1 2 11 3 11 2 1

                                                                                                        0 2 41 2 2

                                                                                                        1 6 3

                                                                                                        1 2 12 5 3

                                                                                                        2 1 3

                                                                                                        1 3 1

                                                                                                        2 2 2

                                                                                                        0 1 3

                                                                                                        1 2 0

                                                                                                        2 1 4

                                                                                                        1 0 1

                                                                                                        0

                                                                                                        13

                                                                                                        0 0 0

                                                                                                        A B C D E

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                                                                                                        0
                                                                                                        13
                                                                                                        0
                                                                                                        0
                                                                                                        0

                                                                                                        Sheet1

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                                                                                                        2122018Introduction to Medical Image Analysis53 DTU Compute Technical University of Denmark

                                                                                                        Border handling ndash extend the input

                                                                                                        0 2 41 2 2

                                                                                                        1 6 3

                                                                                                        1 2 12 5 3

                                                                                                        2 1 3

                                                                                                        1 3 1

                                                                                                        2 2 2

                                                                                                        0 1 3

                                                                                                        1 2 0

                                                                                                        2 1 4

                                                                                                        1 0 1

                                                                                                        Input

                                                                                                        1 2 0 1 311211

                                                                                                        bull Reflection

                                                                                                        bull Normally better than zero padding

                                                                                                        DTU Compute

                                                                                                        2122018Introduction to Medical Image Analysis54 DTU Compute Technical University of Denmark

                                                                                                        Template Matching Template

                                                                                                        ndash Skabelon paring dansk Locates objects in images

                                                                                                        Input

                                                                                                        Template

                                                                                                        Output Correlation image

                                                                                                        DTU Compute

                                                                                                        2122018Introduction to Medical Image Analysis55 DTU Compute Technical University of Denmark

                                                                                                        Template Matching The correlation between the template and the input

                                                                                                        image is computed for each pixel

                                                                                                        Input

                                                                                                        Template

                                                                                                        Output Correlation image

                                                                                                        DTU Compute

                                                                                                        2122018Introduction to Medical Image Analysis56 DTU Compute Technical University of Denmark

                                                                                                        Template Matching The pixel with the highest value is found in the

                                                                                                        output imagendash Here is the highest correlation

                                                                                                        Input

                                                                                                        Template

                                                                                                        Output Correlation image

                                                                                                        DTU Compute

                                                                                                        2122018Introduction to Medical Image Analysis57 DTU Compute Technical University of Denmark

                                                                                                        Template Matching This corresponds to the found pattern in the input

                                                                                                        image

                                                                                                        Input

                                                                                                        Template

                                                                                                        Output Correlation image

                                                                                                        DTU Compute

                                                                                                        2122018Introduction to Medical Image Analysis58 DTU Compute Technical University of Denmark

                                                                                                        Problematic Correlation Correlation matching has problem with light areas ndash

                                                                                                        why

                                                                                                        Input (f)

                                                                                                        Template (h)

                                                                                                        Output Correlation imageFake max

                                                                                                        Real max

                                                                                                        Very High119892119892 119909119909119910119910 = 119895119895=minus119877119877

                                                                                                        119877119877

                                                                                                        119894119894=minus119877119877

                                                                                                        119877119877

                                                                                                        ℎ(119894119894 119895119895) 119891119891(119909119909 + 119894119894119910119910 + 119895119895)

                                                                                                        DTU Compute

                                                                                                        2122018Introduction to Medical Image Analysis59 DTU Compute Technical University of Denmark

                                                                                                        Normalised Cross Correlation

                                                                                                        Input (f)

                                                                                                        Template (h)

                                                                                                        Output Correlation image

                                                                                                        Real max

                                                                                                        NCC x y =Correlation

                                                                                                        Length of image patch sdot Length of template

                                                                                                        DTU Compute

                                                                                                        2122018Introduction to Medical Image Analysis60 DTU Compute Technical University of Denmark

                                                                                                        Length of template Vector length

                                                                                                        ndash Put all pixel values into a vectorndash Compute the length of this vector

                                                                                                        Describes the intensity of the templatendash Bright template has a large lengthndash Dark template has a small length

                                                                                                        Template (h)

                                                                                                        Length of template = 119895119895=minus119877119877

                                                                                                        119877119877

                                                                                                        119894119894=minus119877119877

                                                                                                        119877119877

                                                                                                        ℎ(119894119894 119895119895) ℎ(119894119894 119895119895)

                                                                                                        DTU Compute

                                                                                                        2122018Introduction to Medical Image Analysis61 DTU Compute Technical University of Denmark

                                                                                                        Length of image patch Vector length based on pixel values in image patch Describes the intensity of the image patch

                                                                                                        Template (h)

                                                                                                        Input (f) with patch

                                                                                                        DTU Compute

                                                                                                        2122018Introduction to Medical Image Analysis62 DTU Compute Technical University of Denmark

                                                                                                        Normalised Cross Correlation The length of the image patch and the length of

                                                                                                        template normalise the NCC If the image is very bright the NCC will be ldquopulled

                                                                                                        downrdquo

                                                                                                        NCC x y =Correlation

                                                                                                        Length of image patch sdot Length of template

                                                                                                        DTU Compute

                                                                                                        2122018Introduction to Medical Image Analysis63 DTU Compute Technical University of Denmark

                                                                                                        Normalised Cross Correlation NCC will be between

                                                                                                        ndash 0 No similarity between template and image patchndash 1 Template and image patch are identical

                                                                                                        Input (f)

                                                                                                        Template (h)

                                                                                                        Output Correlation image

                                                                                                        Real max

                                                                                                        NCC x y =Correlation

                                                                                                        Length of image patch sdot Length of template

                                                                                                        DTU Compute

                                                                                                        2122018Introduction to Medical Image Analysis64 DTU Compute Technical University of Denmark

                                                                                                        Normalised Cross Correlation

                                                                                                        A) 010B) 033C) 083D) 062E) 098

                                                                                                        Der udfoslashres template matching med og normalized crosscorrelation (NCC) beregnes Hvad bliver NNC i den markerede pixel

                                                                                                        1

                                                                                                        2 2

                                                                                                        3

                                                                                                        2

                                                                                                        A B C D E

                                                                                                        Chart1

                                                                                                        1
                                                                                                        2
                                                                                                        2
                                                                                                        3
                                                                                                        2

                                                                                                        Sheet1

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                                                                                                        Edges An edge is where there is a

                                                                                                        high change in gray level values

                                                                                                        Objects are often separated from the background by edgesGray level profile

                                                                                                        DTU Compute

                                                                                                        2122018Introduction to Medical Image Analysis67 DTU Compute Technical University of Denmark

                                                                                                        Edges The profile as a function f(d) What value is high when there

                                                                                                        is an edgendash The slope of fndash The slope of the tangent at d

                                                                                                        f(d)

                                                                                                        119891119891prime(119889119889)

                                                                                                        DTU Compute

                                                                                                        2122018Introduction to Medical Image Analysis68 DTU Compute Technical University of Denmark

                                                                                                        Finite Difference Definition of slope

                                                                                                        Approximation

                                                                                                        Simpler approximationh = 1

                                                                                                        119891119891prime 119889119889 = limℎrarr0

                                                                                                        119891119891 119889119889 + ℎ minus 119891119891(119889119889)ℎ

                                                                                                        119891119891prime 119889119889 asymp119891119891 119889119889 + ℎ minus 119891119891(119889119889)

                                                                                                        ℎ

                                                                                                        119891119891prime 119889119889 asymp 119891119891 119889119889 + 1 minus 119891119891(119889119889)

                                                                                                        DTU Compute

                                                                                                        2122018Introduction to Medical Image Analysis69 DTU Compute Technical University of Denmark

                                                                                                        Edges Discrete approximation of frsquo(d) Can be implemented as a filter

                                                                                                        -1 0 1

                                                                                                        f(d-2) f(d-1) f(d) f(d+1) f(d+2) f(d+3)

                                                                                                        f(d)

                                                                                                        119891119891prime 119889119889 asymp 119891119891 119889119889 + 1 minus 119891119891(119889119889)

                                                                                                        DTU Compute

                                                                                                        2122018Introduction to Medical Image Analysis70 DTU Compute Technical University of Denmark

                                                                                                        Edges in 2D Changes in gray level values

                                                                                                        ndash Image gradientndash Gradient is the 2D derivative of a 2D function f(xy)ndash Equal to the slope of the imagendash A steep slope is equal to an edge

                                                                                                        120571120571119891119891 119909119909119910119910 = 119866(119892119892119909119909119892119892119910119910)

                                                                                                        DTU Compute

                                                                                                        2122018Introduction to Medical Image Analysis71 DTU Compute Technical University of Denmark

                                                                                                        Edge filter kernel The Prewitt filter is a typical

                                                                                                        edge filter Output image has high

                                                                                                        values where there are edges

                                                                                                        -1 0 1

                                                                                                        -1 0 1

                                                                                                        -1 0 1Vertical Prewitt filter

                                                                                                        DTU Compute

                                                                                                        2122018Introduction to Medical Image Analysis72 DTU Compute Technical University of Denmark

                                                                                                        Prewitt filter

                                                                                                        Original Prewitt Prewitt

                                                                                                        Hot colormapSmooth 15x15

                                                                                                        Smooth 15x15

                                                                                                        Prewitt

                                                                                                        DTU Compute

                                                                                                        2122018Introduction to Medical Image Analysis73 DTU Compute Technical University of Denmark

                                                                                                        Edge detection Edge filter

                                                                                                        ndash Prewitt for example Thresholding

                                                                                                        ndash Separate edges from non-edges

                                                                                                        Output is binary imagendash Edges are white

                                                                                                        DTU Compute

                                                                                                        2122018Introduction to Medical Image Analysis74 DTU Compute Technical University of Denmark

                                                                                                        Edge filtering

                                                                                                        A) MeanB) Horizontal SobelC) Vertical PrewittD) Horisontal PrewittE) Median

                                                                                                        Der udfoslashres en filtrering (correlation) med et filter paring billedet Der bruges ikke coefficient normalization Den filtrerede vaeligrdi i den markerede pixel bliver -119 Hvilket et 3x3 filter blev benyttet

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                                                                                                        02511 - Niveau af dagens emne forelaeligsingA) Meget letB) LetC) PassendeD) SvaeligrtE) Meget svaeligrt

                                                                                                        23

                                                                                                        6

                                                                                                        10

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                                                                                                        02512 - Niveau af dagens emne forelaeligsingA) Meget letB) LetC) PassendeD) SvaeligrtE) Meget svaeligrt

                                                                                                        0 0

                                                                                                        1

                                                                                                        0 0

                                                                                                        A B C D E

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                                                                                                        02511 - Mit eget udbytte af dagenA) Jeg har laeligrt meget lidtB) Lidt laeligringC) PassendeD) God laeligringE) Jeg har laeligrt meget

                                                                                                        0 0

                                                                                                        2

                                                                                                        6

                                                                                                        0

                                                                                                        A B C D E

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                                                                                                        02512 - Mit eget udbytte af dagenA) Jeg har laeligrt meget lidtB) Lidt laeligringC) PassendeD) God laeligringE) Jeg har laeligrt meget

                                                                                                        2

                                                                                                        1

                                                                                                        3

                                                                                                        2

                                                                                                        0

                                                                                                        A B C D E

                                                                                                        Chart1

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                                                                                                        02511 - Sidste uges oslashvelser (pixelwiseoperations)A) Meget letteB) LetteC) PassendeD) SvaeligreE) Meget svaeligre

                                                                                                        0 0

                                                                                                        1

                                                                                                        4

                                                                                                        1

                                                                                                        A B C D E

                                                                                                        Chart1

                                                                                                        0
                                                                                                        0
                                                                                                        1
                                                                                                        4
                                                                                                        1

                                                                                                        Sheet1

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                                                                                                        02512 - Sidste uges oslashvelser (pixelwiseoperations)A) Meget letteB) LetteC) PassendeD) SvaeligreE) Meget svaeligre

                                                                                                        3

                                                                                                        0

                                                                                                        3

                                                                                                        0 0

                                                                                                        A B C D E

                                                                                                        Chart1

                                                                                                        3
                                                                                                        0
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                                                                                                        0

                                                                                                        Sheet1

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                                                                                                        2122018Introduction to Medical Image Analysis82 DTU Compute Technical University of Denmark

                                                                                                        Denne uges brug af clickersA) click click click ndash jeg bliver

                                                                                                        sindssygB) For meget clickC) PassendeD) Jeg vil gerne have lidt mereE) Jeg kan ikrsquo faring nok

                                                                                                        0 0

                                                                                                        5

                                                                                                        0

                                                                                                        6

                                                                                                        A B C D E

                                                                                                        Chart1

                                                                                                        0
                                                                                                        0
                                                                                                        5
                                                                                                        0
                                                                                                        6

                                                                                                        Sheet1

                                                                                                        DTU Compute

                                                                                                        2122018Introduction to Medical Image Analysis83 DTU Compute Technical University of Denmark

                                                                                                        What can you do after today Describe the difference between point processing and neighbourhood

                                                                                                        processing Compute a rank filtered image using the min max median and

                                                                                                        difference rank filters Compute a mean filtered image Decide if median or average filtering should be used for noise removal Choose the appropriate image border handling based on a given input

                                                                                                        image Implement and apply template matching Compute the normalised cross correlation and explain why it should be

                                                                                                        used Apply given image filter kernels to images Use edge filters on images Describe finite difference approximation of image gradients Describe the concept of edge detection

                                                                                                        DTU Compute

                                                                                                        2122018Introduction to Medical Image Analysis84 DTU Compute Technical University of Denmark

                                                                                                        Oslashvelsesrapport over oslashvelse 4 - 02511 Oslashvelser taeligller cirka 30 af karakteren Skal afleveres senest den 7 marts kl 2359 Kan afleveres af 1 eller 2 personer

                                                                                                        ndash I skal skrive jeres egen oslashvelsesrapportndash Brug mindst et af jeres egne billeder

                                                                                                        Afleveres som PDF Lad vaeligre med at kopiere opgaveteksten ind i jeres

                                                                                                        opgave Put Matlab kode i et Appendix og henvis fra teksten Eksempel rapport over oslashvelse findes paring

                                                                                                        hjemmesiden under eksamen

                                                                                                        DTU Compute

                                                                                                        2122018Introduction to Medical Image Analysis85 DTU Compute Technical University of Denmark

                                                                                                        Exercises

                                                                                                        • Introduction to Medical Image Analysis
                                                                                                        • Lecture 4 ndash Neighbourhood Processing
                                                                                                        • What can you do after today
                                                                                                        • Point processing
                                                                                                        • Point processing
                                                                                                        • Neighbourhood processing
                                                                                                        • Use of filtering
                                                                                                        • Salt and pepper noise
                                                                                                        • Salt and pepper noise
                                                                                                        • What is so special about noise
                                                                                                        • Noise ndash go away
                                                                                                        • What is the median Value
                                                                                                        • The median value
                                                                                                        • Noise away ndash the median filter
                                                                                                        • Noise removal ndash average filter
                                                                                                        • Noise removal ndash median filter
                                                                                                        • Image Filtering
                                                                                                        • Median filter
                                                                                                        • Rank filters
                                                                                                        • Median filter
                                                                                                        • Correlation
                                                                                                        • Why do we need similarity
                                                                                                        • Correlation (1D)
                                                                                                        • Correlation (1D)
                                                                                                        • Normalisation
                                                                                                        • Normalisation
                                                                                                        • Correlation on images
                                                                                                        • Correlation on images
                                                                                                        • Correlation on images
                                                                                                        • Draw your filter
                                                                                                        • Correlation on images ndash no normalisation
                                                                                                        • Correlation on images ndash no normalisation 2
                                                                                                        • Mathematics of 2D Correlation
                                                                                                        • Mathematics of 2D Correlation
                                                                                                        • Mathematics of 2D Correlation
                                                                                                        • Slide Number 40
                                                                                                        • 2D Kernel Normalisation
                                                                                                        • Correlation
                                                                                                        • Smoothing filters
                                                                                                        • Use of smoothing
                                                                                                        • Use of smoothing
                                                                                                        • Mean filter
                                                                                                        • Border handling
                                                                                                        • Border handling ndash extend the input
                                                                                                        • Correlation with zero padding
                                                                                                        • Border handling ndash extend the input
                                                                                                        • Template Matching
                                                                                                        • Template Matching
                                                                                                        • Template Matching
                                                                                                        • Template Matching
                                                                                                        • Problematic Correlation
                                                                                                        • Normalised Cross Correlation
                                                                                                        • Length of template
                                                                                                        • Length of image patch
                                                                                                        • Normalised Cross Correlation
                                                                                                        • Normalised Cross Correlation
                                                                                                        • Normalised Cross Correlation
                                                                                                        • Edges
                                                                                                        • Edges
                                                                                                        • Finite Difference
                                                                                                        • Edges
                                                                                                        • Edges in 2D
                                                                                                        • Edge filter kernel
                                                                                                        • Prewitt filter
                                                                                                        • Edge detection
                                                                                                        • Edge filtering
                                                                                                        • 02511 - Niveau af dagens emne forelaeligsing
                                                                                                        • 02512 - Niveau af dagens emne forelaeligsing
                                                                                                        • 02511 - Mit eget udbytte af dagen
                                                                                                        • 02512 - Mit eget udbytte af dagen
                                                                                                        • 02511 - Sidste uges oslashvelser (pixelwise operations)
                                                                                                        • 02512 - Sidste uges oslashvelser (pixelwise operations)
                                                                                                        • Denne uges brug af clickers
                                                                                                        • What can you do after today
                                                                                                        • Oslashvelsesrapport over oslashvelse 4 - 02511
                                                                                                        • Exercises
                                                                                                          A0
                                                                                                          B0
                                                                                                          C5
                                                                                                          D0
                                                                                                          E6
                                                                                                          A
                                                                                                          B
                                                                                                          C
                                                                                                          D
                                                                                                          E
                                                                                                          A3
                                                                                                          B0
                                                                                                          C3
                                                                                                          D0
                                                                                                          E0
                                                                                                          A
                                                                                                          B
                                                                                                          C
                                                                                                          D
                                                                                                          E
                                                                                                          A0
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                                                                                                          C1
                                                                                                          D4
                                                                                                          E1
                                                                                                          A
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                                                                                                          C
                                                                                                          D
                                                                                                          E
                                                                                                          A2
                                                                                                          B1
                                                                                                          C3
                                                                                                          D2
                                                                                                          E0
                                                                                                          A
                                                                                                          B
                                                                                                          C
                                                                                                          D
                                                                                                          E
                                                                                                          A0
                                                                                                          B0
                                                                                                          C2
                                                                                                          D6
                                                                                                          E0
                                                                                                          A
                                                                                                          B
                                                                                                          C
                                                                                                          D
                                                                                                          E
                                                                                                          A0
                                                                                                          B0
                                                                                                          C1
                                                                                                          D0
                                                                                                          E0
                                                                                                          A
                                                                                                          B
                                                                                                          C
                                                                                                          D
                                                                                                          E
                                                                                                          A2
                                                                                                          B3
                                                                                                          C6
                                                                                                          D1
                                                                                                          E0
                                                                                                          A
                                                                                                          B
                                                                                                          C
                                                                                                          D
                                                                                                          E
                                                                                                          A0
                                                                                                          B8
                                                                                                          C1
                                                                                                          D1
                                                                                                          E0
                                                                                                          A
                                                                                                          B
                                                                                                          C
                                                                                                          D
                                                                                                          E
                                                                                                          A1
                                                                                                          B2
                                                                                                          C2
                                                                                                          D3
                                                                                                          E2
                                                                                                          A
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                                                                                                          C
                                                                                                          D
                                                                                                          E
                                                                                                          A0
                                                                                                          B13
                                                                                                          C0
                                                                                                          D0
                                                                                                          E0
                                                                                                          A
                                                                                                          B
                                                                                                          C
                                                                                                          D
                                                                                                          E
                                                                                                          A12
                                                                                                          B0
                                                                                                          C0
                                                                                                          D0
                                                                                                          E0
                                                                                                          A
                                                                                                          B
                                                                                                          C
                                                                                                          D
                                                                                                          E

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                                                                                                          Use of smoothing Large kernels smooth more Removes high frequency information Good at enhancing big structures

                                                                                                          3x3 15x15

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                                                                                                          Mean filterA) 166B) 113C) 12D) 51E) 245

                                                                                                          0 0 0 0

                                                                                                          A B C D E

                                                                                                          Chart1

                                                                                                          12
                                                                                                          0
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                                                                                                          Border handling

                                                                                                          0 2 41 2 2

                                                                                                          1 6 3

                                                                                                          1 2 12 5 3

                                                                                                          2 1 3

                                                                                                          1 3 1

                                                                                                          2 2 2

                                                                                                          0 1 3

                                                                                                          1 2 0

                                                                                                          2 1 4

                                                                                                          1 0 1

                                                                                                          Input Output

                                                                                                          No values at the border

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                                                                                                          Border handling ndash extend the input

                                                                                                          0 2 41 2 2

                                                                                                          1 6 3

                                                                                                          1 2 12 5 3

                                                                                                          2 1 3

                                                                                                          1 3 1

                                                                                                          2 2 2

                                                                                                          0 1 3

                                                                                                          1 2 0

                                                                                                          2 1 4

                                                                                                          1 0 1

                                                                                                          Input

                                                                                                          0 0 0 0 000000

                                                                                                          bull Zero padding ndash what happens

                                                                                                          bull Zero is black ndash creates dark border around the image

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                                                                                                          Correlation with zero paddingA) 5 8B) 12 16C) 13 3D) 15 21E) 17 12

                                                                                                          1 2 11 3 11 2 1

                                                                                                          0 2 41 2 2

                                                                                                          1 6 3

                                                                                                          1 2 12 5 3

                                                                                                          2 1 3

                                                                                                          1 3 1

                                                                                                          2 2 2

                                                                                                          0 1 3

                                                                                                          1 2 0

                                                                                                          2 1 4

                                                                                                          1 0 1

                                                                                                          0

                                                                                                          13

                                                                                                          0 0 0

                                                                                                          A B C D E

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                                                                                                          13
                                                                                                          0
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                                                                                                          0

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                                                                                                          Border handling ndash extend the input

                                                                                                          0 2 41 2 2

                                                                                                          1 6 3

                                                                                                          1 2 12 5 3

                                                                                                          2 1 3

                                                                                                          1 3 1

                                                                                                          2 2 2

                                                                                                          0 1 3

                                                                                                          1 2 0

                                                                                                          2 1 4

                                                                                                          1 0 1

                                                                                                          Input

                                                                                                          1 2 0 1 311211

                                                                                                          bull Reflection

                                                                                                          bull Normally better than zero padding

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                                                                                                          Template Matching Template

                                                                                                          ndash Skabelon paring dansk Locates objects in images

                                                                                                          Input

                                                                                                          Template

                                                                                                          Output Correlation image

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                                                                                                          Template Matching The correlation between the template and the input

                                                                                                          image is computed for each pixel

                                                                                                          Input

                                                                                                          Template

                                                                                                          Output Correlation image

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                                                                                                          Template Matching The pixel with the highest value is found in the

                                                                                                          output imagendash Here is the highest correlation

                                                                                                          Input

                                                                                                          Template

                                                                                                          Output Correlation image

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                                                                                                          Template Matching This corresponds to the found pattern in the input

                                                                                                          image

                                                                                                          Input

                                                                                                          Template

                                                                                                          Output Correlation image

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                                                                                                          Problematic Correlation Correlation matching has problem with light areas ndash

                                                                                                          why

                                                                                                          Input (f)

                                                                                                          Template (h)

                                                                                                          Output Correlation imageFake max

                                                                                                          Real max

                                                                                                          Very High119892119892 119909119909119910119910 = 119895119895=minus119877119877

                                                                                                          119877119877

                                                                                                          119894119894=minus119877119877

                                                                                                          119877119877

                                                                                                          ℎ(119894119894 119895119895) 119891119891(119909119909 + 119894119894119910119910 + 119895119895)

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                                                                                                          Normalised Cross Correlation

                                                                                                          Input (f)

                                                                                                          Template (h)

                                                                                                          Output Correlation image

                                                                                                          Real max

                                                                                                          NCC x y =Correlation

                                                                                                          Length of image patch sdot Length of template

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                                                                                                          Length of template Vector length

                                                                                                          ndash Put all pixel values into a vectorndash Compute the length of this vector

                                                                                                          Describes the intensity of the templatendash Bright template has a large lengthndash Dark template has a small length

                                                                                                          Template (h)

                                                                                                          Length of template = 119895119895=minus119877119877

                                                                                                          119877119877

                                                                                                          119894119894=minus119877119877

                                                                                                          119877119877

                                                                                                          ℎ(119894119894 119895119895) ℎ(119894119894 119895119895)

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                                                                                                          Length of image patch Vector length based on pixel values in image patch Describes the intensity of the image patch

                                                                                                          Template (h)

                                                                                                          Input (f) with patch

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                                                                                                          Normalised Cross Correlation The length of the image patch and the length of

                                                                                                          template normalise the NCC If the image is very bright the NCC will be ldquopulled

                                                                                                          downrdquo

                                                                                                          NCC x y =Correlation

                                                                                                          Length of image patch sdot Length of template

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                                                                                                          Normalised Cross Correlation NCC will be between

                                                                                                          ndash 0 No similarity between template and image patchndash 1 Template and image patch are identical

                                                                                                          Input (f)

                                                                                                          Template (h)

                                                                                                          Output Correlation image

                                                                                                          Real max

                                                                                                          NCC x y =Correlation

                                                                                                          Length of image patch sdot Length of template

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                                                                                                          Normalised Cross Correlation

                                                                                                          A) 010B) 033C) 083D) 062E) 098

                                                                                                          Der udfoslashres template matching med og normalized crosscorrelation (NCC) beregnes Hvad bliver NNC i den markerede pixel

                                                                                                          1

                                                                                                          2 2

                                                                                                          3

                                                                                                          2

                                                                                                          A B C D E

                                                                                                          Chart1

                                                                                                          1
                                                                                                          2
                                                                                                          2
                                                                                                          3
                                                                                                          2

                                                                                                          Sheet1

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                                                                                                          Edges An edge is where there is a

                                                                                                          high change in gray level values

                                                                                                          Objects are often separated from the background by edgesGray level profile

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                                                                                                          Edges The profile as a function f(d) What value is high when there

                                                                                                          is an edgendash The slope of fndash The slope of the tangent at d

                                                                                                          f(d)

                                                                                                          119891119891prime(119889119889)

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                                                                                                          Finite Difference Definition of slope

                                                                                                          Approximation

                                                                                                          Simpler approximationh = 1

                                                                                                          119891119891prime 119889119889 = limℎrarr0

                                                                                                          119891119891 119889119889 + ℎ minus 119891119891(119889119889)ℎ

                                                                                                          119891119891prime 119889119889 asymp119891119891 119889119889 + ℎ minus 119891119891(119889119889)

                                                                                                          ℎ

                                                                                                          119891119891prime 119889119889 asymp 119891119891 119889119889 + 1 minus 119891119891(119889119889)

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                                                                                                          Edges Discrete approximation of frsquo(d) Can be implemented as a filter

                                                                                                          -1 0 1

                                                                                                          f(d-2) f(d-1) f(d) f(d+1) f(d+2) f(d+3)

                                                                                                          f(d)

                                                                                                          119891119891prime 119889119889 asymp 119891119891 119889119889 + 1 minus 119891119891(119889119889)

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                                                                                                          Edges in 2D Changes in gray level values

                                                                                                          ndash Image gradientndash Gradient is the 2D derivative of a 2D function f(xy)ndash Equal to the slope of the imagendash A steep slope is equal to an edge

                                                                                                          120571120571119891119891 119909119909119910119910 = 119866(119892119892119909119909119892119892119910119910)

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                                                                                                          Edge filter kernel The Prewitt filter is a typical

                                                                                                          edge filter Output image has high

                                                                                                          values where there are edges

                                                                                                          -1 0 1

                                                                                                          -1 0 1

                                                                                                          -1 0 1Vertical Prewitt filter

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                                                                                                          Prewitt filter

                                                                                                          Original Prewitt Prewitt

                                                                                                          Hot colormapSmooth 15x15

                                                                                                          Smooth 15x15

                                                                                                          Prewitt

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                                                                                                          Edge detection Edge filter

                                                                                                          ndash Prewitt for example Thresholding

                                                                                                          ndash Separate edges from non-edges

                                                                                                          Output is binary imagendash Edges are white

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                                                                                                          Edge filtering

                                                                                                          A) MeanB) Horizontal SobelC) Vertical PrewittD) Horisontal PrewittE) Median

                                                                                                          Der udfoslashres en filtrering (correlation) med et filter paring billedet Der bruges ikke coefficient normalization Den filtrerede vaeligrdi i den markerede pixel bliver -119 Hvilket et 3x3 filter blev benyttet

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                                                                                                          02511 - Niveau af dagens emne forelaeligsingA) Meget letB) LetC) PassendeD) SvaeligrtE) Meget svaeligrt

                                                                                                          23

                                                                                                          6

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                                                                                                          02512 - Niveau af dagens emne forelaeligsingA) Meget letB) LetC) PassendeD) SvaeligrtE) Meget svaeligrt

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                                                                                                          A B C D E

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                                                                                                          02511 - Mit eget udbytte af dagenA) Jeg har laeligrt meget lidtB) Lidt laeligringC) PassendeD) God laeligringE) Jeg har laeligrt meget

                                                                                                          0 0

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                                                                                                          02512 - Mit eget udbytte af dagenA) Jeg har laeligrt meget lidtB) Lidt laeligringC) PassendeD) God laeligringE) Jeg har laeligrt meget

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                                                                                                          02511 - Sidste uges oslashvelser (pixelwiseoperations)A) Meget letteB) LetteC) PassendeD) SvaeligreE) Meget svaeligre

                                                                                                          0 0

                                                                                                          1

                                                                                                          4

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                                                                                                          A B C D E

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                                                                                                          Sheet1

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                                                                                                          02512 - Sidste uges oslashvelser (pixelwiseoperations)A) Meget letteB) LetteC) PassendeD) SvaeligreE) Meget svaeligre

                                                                                                          3

                                                                                                          0

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                                                                                                          0 0

                                                                                                          A B C D E

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                                                                                                          Denne uges brug af clickersA) click click click ndash jeg bliver

                                                                                                          sindssygB) For meget clickC) PassendeD) Jeg vil gerne have lidt mereE) Jeg kan ikrsquo faring nok

                                                                                                          0 0

                                                                                                          5

                                                                                                          0

                                                                                                          6

                                                                                                          A B C D E

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                                                                                                          What can you do after today Describe the difference between point processing and neighbourhood

                                                                                                          processing Compute a rank filtered image using the min max median and

                                                                                                          difference rank filters Compute a mean filtered image Decide if median or average filtering should be used for noise removal Choose the appropriate image border handling based on a given input

                                                                                                          image Implement and apply template matching Compute the normalised cross correlation and explain why it should be

                                                                                                          used Apply given image filter kernels to images Use edge filters on images Describe finite difference approximation of image gradients Describe the concept of edge detection

                                                                                                          DTU Compute

                                                                                                          2122018Introduction to Medical Image Analysis84 DTU Compute Technical University of Denmark

                                                                                                          Oslashvelsesrapport over oslashvelse 4 - 02511 Oslashvelser taeligller cirka 30 af karakteren Skal afleveres senest den 7 marts kl 2359 Kan afleveres af 1 eller 2 personer

                                                                                                          ndash I skal skrive jeres egen oslashvelsesrapportndash Brug mindst et af jeres egne billeder

                                                                                                          Afleveres som PDF Lad vaeligre med at kopiere opgaveteksten ind i jeres

                                                                                                          opgave Put Matlab kode i et Appendix og henvis fra teksten Eksempel rapport over oslashvelse findes paring

                                                                                                          hjemmesiden under eksamen

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                                                                                                          Exercises

                                                                                                          • Introduction to Medical Image Analysis
                                                                                                          • Lecture 4 ndash Neighbourhood Processing
                                                                                                          • What can you do after today
                                                                                                          • Point processing
                                                                                                          • Point processing
                                                                                                          • Neighbourhood processing
                                                                                                          • Use of filtering
                                                                                                          • Salt and pepper noise
                                                                                                          • Salt and pepper noise
                                                                                                          • What is so special about noise
                                                                                                          • Noise ndash go away
                                                                                                          • What is the median Value
                                                                                                          • The median value
                                                                                                          • Noise away ndash the median filter
                                                                                                          • Noise removal ndash average filter
                                                                                                          • Noise removal ndash median filter
                                                                                                          • Image Filtering
                                                                                                          • Median filter
                                                                                                          • Rank filters
                                                                                                          • Median filter
                                                                                                          • Correlation
                                                                                                          • Why do we need similarity
                                                                                                          • Correlation (1D)
                                                                                                          • Correlation (1D)
                                                                                                          • Normalisation
                                                                                                          • Normalisation
                                                                                                          • Correlation on images
                                                                                                          • Correlation on images
                                                                                                          • Correlation on images
                                                                                                          • Draw your filter
                                                                                                          • Correlation on images ndash no normalisation
                                                                                                          • Correlation on images ndash no normalisation 2
                                                                                                          • Mathematics of 2D Correlation
                                                                                                          • Mathematics of 2D Correlation
                                                                                                          • Mathematics of 2D Correlation
                                                                                                          • Slide Number 40
                                                                                                          • 2D Kernel Normalisation
                                                                                                          • Correlation
                                                                                                          • Smoothing filters
                                                                                                          • Use of smoothing
                                                                                                          • Use of smoothing
                                                                                                          • Mean filter
                                                                                                          • Border handling
                                                                                                          • Border handling ndash extend the input
                                                                                                          • Correlation with zero padding
                                                                                                          • Border handling ndash extend the input
                                                                                                          • Template Matching
                                                                                                          • Template Matching
                                                                                                          • Template Matching
                                                                                                          • Template Matching
                                                                                                          • Problematic Correlation
                                                                                                          • Normalised Cross Correlation
                                                                                                          • Length of template
                                                                                                          • Length of image patch
                                                                                                          • Normalised Cross Correlation
                                                                                                          • Normalised Cross Correlation
                                                                                                          • Normalised Cross Correlation
                                                                                                          • Edges
                                                                                                          • Edges
                                                                                                          • Finite Difference
                                                                                                          • Edges
                                                                                                          • Edges in 2D
                                                                                                          • Edge filter kernel
                                                                                                          • Prewitt filter
                                                                                                          • Edge detection
                                                                                                          • Edge filtering
                                                                                                          • 02511 - Niveau af dagens emne forelaeligsing
                                                                                                          • 02512 - Niveau af dagens emne forelaeligsing
                                                                                                          • 02511 - Mit eget udbytte af dagen
                                                                                                          • 02512 - Mit eget udbytte af dagen
                                                                                                          • 02511 - Sidste uges oslashvelser (pixelwise operations)
                                                                                                          • 02512 - Sidste uges oslashvelser (pixelwise operations)
                                                                                                          • Denne uges brug af clickers
                                                                                                          • What can you do after today
                                                                                                          • Oslashvelsesrapport over oslashvelse 4 - 02511
                                                                                                          • Exercises
                                                                                                            A0
                                                                                                            B0
                                                                                                            C5
                                                                                                            D0
                                                                                                            E6
                                                                                                            A
                                                                                                            B
                                                                                                            C
                                                                                                            D
                                                                                                            E
                                                                                                            A3
                                                                                                            B0
                                                                                                            C3
                                                                                                            D0
                                                                                                            E0
                                                                                                            A
                                                                                                            B
                                                                                                            C
                                                                                                            D
                                                                                                            E
                                                                                                            A0
                                                                                                            B0
                                                                                                            C1
                                                                                                            D4
                                                                                                            E1
                                                                                                            A
                                                                                                            B
                                                                                                            C
                                                                                                            D
                                                                                                            E
                                                                                                            A2
                                                                                                            B1
                                                                                                            C3
                                                                                                            D2
                                                                                                            E0
                                                                                                            A
                                                                                                            B
                                                                                                            C
                                                                                                            D
                                                                                                            E
                                                                                                            A0
                                                                                                            B0
                                                                                                            C2
                                                                                                            D6
                                                                                                            E0
                                                                                                            A
                                                                                                            B
                                                                                                            C
                                                                                                            D
                                                                                                            E
                                                                                                            A0
                                                                                                            B0
                                                                                                            C1
                                                                                                            D0
                                                                                                            E0
                                                                                                            A
                                                                                                            B
                                                                                                            C
                                                                                                            D
                                                                                                            E
                                                                                                            A2
                                                                                                            B3
                                                                                                            C6
                                                                                                            D1
                                                                                                            E0
                                                                                                            A
                                                                                                            B
                                                                                                            C
                                                                                                            D
                                                                                                            E
                                                                                                            A0
                                                                                                            B8
                                                                                                            C1
                                                                                                            D1
                                                                                                            E0
                                                                                                            A
                                                                                                            B
                                                                                                            C
                                                                                                            D
                                                                                                            E
                                                                                                            A1
                                                                                                            B2
                                                                                                            C2
                                                                                                            D3
                                                                                                            E2
                                                                                                            A
                                                                                                            B
                                                                                                            C
                                                                                                            D
                                                                                                            E
                                                                                                            A0
                                                                                                            B13
                                                                                                            C0
                                                                                                            D0
                                                                                                            E0
                                                                                                            A
                                                                                                            B
                                                                                                            C
                                                                                                            D
                                                                                                            E
                                                                                                            A12
                                                                                                            B0
                                                                                                            C0
                                                                                                            D0
                                                                                                            E0
                                                                                                            A
                                                                                                            B
                                                                                                            C
                                                                                                            D
                                                                                                            E

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                                                                                                            Mean filterA) 166B) 113C) 12D) 51E) 245

                                                                                                            0 0 0 0

                                                                                                            A B C D E

                                                                                                            Chart1

                                                                                                            12
                                                                                                            0
                                                                                                            0
                                                                                                            0
                                                                                                            0

                                                                                                            Sheet1

                                                                                                            DTU Compute

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                                                                                                            Border handling

                                                                                                            0 2 41 2 2

                                                                                                            1 6 3

                                                                                                            1 2 12 5 3

                                                                                                            2 1 3

                                                                                                            1 3 1

                                                                                                            2 2 2

                                                                                                            0 1 3

                                                                                                            1 2 0

                                                                                                            2 1 4

                                                                                                            1 0 1

                                                                                                            Input Output

                                                                                                            No values at the border

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                                                                                                            Border handling ndash extend the input

                                                                                                            0 2 41 2 2

                                                                                                            1 6 3

                                                                                                            1 2 12 5 3

                                                                                                            2 1 3

                                                                                                            1 3 1

                                                                                                            2 2 2

                                                                                                            0 1 3

                                                                                                            1 2 0

                                                                                                            2 1 4

                                                                                                            1 0 1

                                                                                                            Input

                                                                                                            0 0 0 0 000000

                                                                                                            bull Zero padding ndash what happens

                                                                                                            bull Zero is black ndash creates dark border around the image

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                                                                                                            Correlation with zero paddingA) 5 8B) 12 16C) 13 3D) 15 21E) 17 12

                                                                                                            1 2 11 3 11 2 1

                                                                                                            0 2 41 2 2

                                                                                                            1 6 3

                                                                                                            1 2 12 5 3

                                                                                                            2 1 3

                                                                                                            1 3 1

                                                                                                            2 2 2

                                                                                                            0 1 3

                                                                                                            1 2 0

                                                                                                            2 1 4

                                                                                                            1 0 1

                                                                                                            0

                                                                                                            13

                                                                                                            0 0 0

                                                                                                            A B C D E

                                                                                                            Chart1

                                                                                                            0
                                                                                                            13
                                                                                                            0
                                                                                                            0
                                                                                                            0

                                                                                                            Sheet1

                                                                                                            DTU Compute

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                                                                                                            Border handling ndash extend the input

                                                                                                            0 2 41 2 2

                                                                                                            1 6 3

                                                                                                            1 2 12 5 3

                                                                                                            2 1 3

                                                                                                            1 3 1

                                                                                                            2 2 2

                                                                                                            0 1 3

                                                                                                            1 2 0

                                                                                                            2 1 4

                                                                                                            1 0 1

                                                                                                            Input

                                                                                                            1 2 0 1 311211

                                                                                                            bull Reflection

                                                                                                            bull Normally better than zero padding

                                                                                                            DTU Compute

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                                                                                                            Template Matching Template

                                                                                                            ndash Skabelon paring dansk Locates objects in images

                                                                                                            Input

                                                                                                            Template

                                                                                                            Output Correlation image

                                                                                                            DTU Compute

                                                                                                            2122018Introduction to Medical Image Analysis55 DTU Compute Technical University of Denmark

                                                                                                            Template Matching The correlation between the template and the input

                                                                                                            image is computed for each pixel

                                                                                                            Input

                                                                                                            Template

                                                                                                            Output Correlation image

                                                                                                            DTU Compute

                                                                                                            2122018Introduction to Medical Image Analysis56 DTU Compute Technical University of Denmark

                                                                                                            Template Matching The pixel with the highest value is found in the

                                                                                                            output imagendash Here is the highest correlation

                                                                                                            Input

                                                                                                            Template

                                                                                                            Output Correlation image

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                                                                                                            Template Matching This corresponds to the found pattern in the input

                                                                                                            image

                                                                                                            Input

                                                                                                            Template

                                                                                                            Output Correlation image

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                                                                                                            Problematic Correlation Correlation matching has problem with light areas ndash

                                                                                                            why

                                                                                                            Input (f)

                                                                                                            Template (h)

                                                                                                            Output Correlation imageFake max

                                                                                                            Real max

                                                                                                            Very High119892119892 119909119909119910119910 = 119895119895=minus119877119877

                                                                                                            119877119877

                                                                                                            119894119894=minus119877119877

                                                                                                            119877119877

                                                                                                            ℎ(119894119894 119895119895) 119891119891(119909119909 + 119894119894119910119910 + 119895119895)

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                                                                                                            Normalised Cross Correlation

                                                                                                            Input (f)

                                                                                                            Template (h)

                                                                                                            Output Correlation image

                                                                                                            Real max

                                                                                                            NCC x y =Correlation

                                                                                                            Length of image patch sdot Length of template

                                                                                                            DTU Compute

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                                                                                                            Length of template Vector length

                                                                                                            ndash Put all pixel values into a vectorndash Compute the length of this vector

                                                                                                            Describes the intensity of the templatendash Bright template has a large lengthndash Dark template has a small length

                                                                                                            Template (h)

                                                                                                            Length of template = 119895119895=minus119877119877

                                                                                                            119877119877

                                                                                                            119894119894=minus119877119877

                                                                                                            119877119877

                                                                                                            ℎ(119894119894 119895119895) ℎ(119894119894 119895119895)

                                                                                                            DTU Compute

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                                                                                                            Length of image patch Vector length based on pixel values in image patch Describes the intensity of the image patch

                                                                                                            Template (h)

                                                                                                            Input (f) with patch

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                                                                                                            Normalised Cross Correlation The length of the image patch and the length of

                                                                                                            template normalise the NCC If the image is very bright the NCC will be ldquopulled

                                                                                                            downrdquo

                                                                                                            NCC x y =Correlation

                                                                                                            Length of image patch sdot Length of template

                                                                                                            DTU Compute

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                                                                                                            Normalised Cross Correlation NCC will be between

                                                                                                            ndash 0 No similarity between template and image patchndash 1 Template and image patch are identical

                                                                                                            Input (f)

                                                                                                            Template (h)

                                                                                                            Output Correlation image

                                                                                                            Real max

                                                                                                            NCC x y =Correlation

                                                                                                            Length of image patch sdot Length of template

                                                                                                            DTU Compute

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                                                                                                            Normalised Cross Correlation

                                                                                                            A) 010B) 033C) 083D) 062E) 098

                                                                                                            Der udfoslashres template matching med og normalized crosscorrelation (NCC) beregnes Hvad bliver NNC i den markerede pixel

                                                                                                            1

                                                                                                            2 2

                                                                                                            3

                                                                                                            2

                                                                                                            A B C D E

                                                                                                            Chart1

                                                                                                            1
                                                                                                            2
                                                                                                            2
                                                                                                            3
                                                                                                            2

                                                                                                            Sheet1

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                                                                                                            Edges An edge is where there is a

                                                                                                            high change in gray level values

                                                                                                            Objects are often separated from the background by edgesGray level profile

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                                                                                                            Edges The profile as a function f(d) What value is high when there

                                                                                                            is an edgendash The slope of fndash The slope of the tangent at d

                                                                                                            f(d)

                                                                                                            119891119891prime(119889119889)

                                                                                                            DTU Compute

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                                                                                                            Finite Difference Definition of slope

                                                                                                            Approximation

                                                                                                            Simpler approximationh = 1

                                                                                                            119891119891prime 119889119889 = limℎrarr0

                                                                                                            119891119891 119889119889 + ℎ minus 119891119891(119889119889)ℎ

                                                                                                            119891119891prime 119889119889 asymp119891119891 119889119889 + ℎ minus 119891119891(119889119889)

                                                                                                            ℎ

                                                                                                            119891119891prime 119889119889 asymp 119891119891 119889119889 + 1 minus 119891119891(119889119889)

                                                                                                            DTU Compute

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                                                                                                            Edges Discrete approximation of frsquo(d) Can be implemented as a filter

                                                                                                            -1 0 1

                                                                                                            f(d-2) f(d-1) f(d) f(d+1) f(d+2) f(d+3)

                                                                                                            f(d)

                                                                                                            119891119891prime 119889119889 asymp 119891119891 119889119889 + 1 minus 119891119891(119889119889)

                                                                                                            DTU Compute

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                                                                                                            Edges in 2D Changes in gray level values

                                                                                                            ndash Image gradientndash Gradient is the 2D derivative of a 2D function f(xy)ndash Equal to the slope of the imagendash A steep slope is equal to an edge

                                                                                                            120571120571119891119891 119909119909119910119910 = 119866(119892119892119909119909119892119892119910119910)

                                                                                                            DTU Compute

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                                                                                                            Edge filter kernel The Prewitt filter is a typical

                                                                                                            edge filter Output image has high

                                                                                                            values where there are edges

                                                                                                            -1 0 1

                                                                                                            -1 0 1

                                                                                                            -1 0 1Vertical Prewitt filter

                                                                                                            DTU Compute

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                                                                                                            Prewitt filter

                                                                                                            Original Prewitt Prewitt

                                                                                                            Hot colormapSmooth 15x15

                                                                                                            Smooth 15x15

                                                                                                            Prewitt

                                                                                                            DTU Compute

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                                                                                                            Edge detection Edge filter

                                                                                                            ndash Prewitt for example Thresholding

                                                                                                            ndash Separate edges from non-edges

                                                                                                            Output is binary imagendash Edges are white

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                                                                                                            Edge filtering

                                                                                                            A) MeanB) Horizontal SobelC) Vertical PrewittD) Horisontal PrewittE) Median

                                                                                                            Der udfoslashres en filtrering (correlation) med et filter paring billedet Der bruges ikke coefficient normalization Den filtrerede vaeligrdi i den markerede pixel bliver -119 Hvilket et 3x3 filter blev benyttet

                                                                                                            0

                                                                                                            8

                                                                                                            1 10

                                                                                                            A B C D E

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                                                                                                            0

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                                                                                                            02511 - Niveau af dagens emne forelaeligsingA) Meget letB) LetC) PassendeD) SvaeligrtE) Meget svaeligrt

                                                                                                            23

                                                                                                            6

                                                                                                            10

                                                                                                            A B C D E

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                                                                                                            Sheet1

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                                                                                                            02512 - Niveau af dagens emne forelaeligsingA) Meget letB) LetC) PassendeD) SvaeligrtE) Meget svaeligrt

                                                                                                            0 0

                                                                                                            1

                                                                                                            0 0

                                                                                                            A B C D E

                                                                                                            Chart1

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                                                                                                            0
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                                                                                                            0

                                                                                                            Sheet1

                                                                                                            DTU Compute

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                                                                                                            02511 - Mit eget udbytte af dagenA) Jeg har laeligrt meget lidtB) Lidt laeligringC) PassendeD) God laeligringE) Jeg har laeligrt meget

                                                                                                            0 0

                                                                                                            2

                                                                                                            6

                                                                                                            0

                                                                                                            A B C D E

                                                                                                            Chart1

                                                                                                            0
                                                                                                            0
                                                                                                            2
                                                                                                            6
                                                                                                            0

                                                                                                            Sheet1

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                                                                                                            02512 - Mit eget udbytte af dagenA) Jeg har laeligrt meget lidtB) Lidt laeligringC) PassendeD) God laeligringE) Jeg har laeligrt meget

                                                                                                            2

                                                                                                            1

                                                                                                            3

                                                                                                            2

                                                                                                            0

                                                                                                            A B C D E

                                                                                                            Chart1

                                                                                                            2
                                                                                                            1
                                                                                                            3
                                                                                                            2
                                                                                                            0

                                                                                                            Sheet1

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                                                                                                            02511 - Sidste uges oslashvelser (pixelwiseoperations)A) Meget letteB) LetteC) PassendeD) SvaeligreE) Meget svaeligre

                                                                                                            0 0

                                                                                                            1

                                                                                                            4

                                                                                                            1

                                                                                                            A B C D E

                                                                                                            Chart1

                                                                                                            0
                                                                                                            0
                                                                                                            1
                                                                                                            4
                                                                                                            1

                                                                                                            Sheet1

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                                                                                                            02512 - Sidste uges oslashvelser (pixelwiseoperations)A) Meget letteB) LetteC) PassendeD) SvaeligreE) Meget svaeligre

                                                                                                            3

                                                                                                            0

                                                                                                            3

                                                                                                            0 0

                                                                                                            A B C D E

                                                                                                            Chart1

                                                                                                            3
                                                                                                            0
                                                                                                            3
                                                                                                            0
                                                                                                            0

                                                                                                            Sheet1

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                                                                                                            Denne uges brug af clickersA) click click click ndash jeg bliver

                                                                                                            sindssygB) For meget clickC) PassendeD) Jeg vil gerne have lidt mereE) Jeg kan ikrsquo faring nok

                                                                                                            0 0

                                                                                                            5

                                                                                                            0

                                                                                                            6

                                                                                                            A B C D E

                                                                                                            Chart1

                                                                                                            0
                                                                                                            0
                                                                                                            5
                                                                                                            0
                                                                                                            6

                                                                                                            Sheet1

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                                                                                                            What can you do after today Describe the difference between point processing and neighbourhood

                                                                                                            processing Compute a rank filtered image using the min max median and

                                                                                                            difference rank filters Compute a mean filtered image Decide if median or average filtering should be used for noise removal Choose the appropriate image border handling based on a given input

                                                                                                            image Implement and apply template matching Compute the normalised cross correlation and explain why it should be

                                                                                                            used Apply given image filter kernels to images Use edge filters on images Describe finite difference approximation of image gradients Describe the concept of edge detection

                                                                                                            DTU Compute

                                                                                                            2122018Introduction to Medical Image Analysis84 DTU Compute Technical University of Denmark

                                                                                                            Oslashvelsesrapport over oslashvelse 4 - 02511 Oslashvelser taeligller cirka 30 af karakteren Skal afleveres senest den 7 marts kl 2359 Kan afleveres af 1 eller 2 personer

                                                                                                            ndash I skal skrive jeres egen oslashvelsesrapportndash Brug mindst et af jeres egne billeder

                                                                                                            Afleveres som PDF Lad vaeligre med at kopiere opgaveteksten ind i jeres

                                                                                                            opgave Put Matlab kode i et Appendix og henvis fra teksten Eksempel rapport over oslashvelse findes paring

                                                                                                            hjemmesiden under eksamen

                                                                                                            DTU Compute

                                                                                                            2122018Introduction to Medical Image Analysis85 DTU Compute Technical University of Denmark

                                                                                                            Exercises

                                                                                                            • Introduction to Medical Image Analysis
                                                                                                            • Lecture 4 ndash Neighbourhood Processing
                                                                                                            • What can you do after today
                                                                                                            • Point processing
                                                                                                            • Point processing
                                                                                                            • Neighbourhood processing
                                                                                                            • Use of filtering
                                                                                                            • Salt and pepper noise
                                                                                                            • Salt and pepper noise
                                                                                                            • What is so special about noise
                                                                                                            • Noise ndash go away
                                                                                                            • What is the median Value
                                                                                                            • The median value
                                                                                                            • Noise away ndash the median filter
                                                                                                            • Noise removal ndash average filter
                                                                                                            • Noise removal ndash median filter
                                                                                                            • Image Filtering
                                                                                                            • Median filter
                                                                                                            • Rank filters
                                                                                                            • Median filter
                                                                                                            • Correlation
                                                                                                            • Why do we need similarity
                                                                                                            • Correlation (1D)
                                                                                                            • Correlation (1D)
                                                                                                            • Normalisation
                                                                                                            • Normalisation
                                                                                                            • Correlation on images
                                                                                                            • Correlation on images
                                                                                                            • Correlation on images
                                                                                                            • Draw your filter
                                                                                                            • Correlation on images ndash no normalisation
                                                                                                            • Correlation on images ndash no normalisation 2
                                                                                                            • Mathematics of 2D Correlation
                                                                                                            • Mathematics of 2D Correlation
                                                                                                            • Mathematics of 2D Correlation
                                                                                                            • Slide Number 40
                                                                                                            • 2D Kernel Normalisation
                                                                                                            • Correlation
                                                                                                            • Smoothing filters
                                                                                                            • Use of smoothing
                                                                                                            • Use of smoothing
                                                                                                            • Mean filter
                                                                                                            • Border handling
                                                                                                            • Border handling ndash extend the input
                                                                                                            • Correlation with zero padding
                                                                                                            • Border handling ndash extend the input
                                                                                                            • Template Matching
                                                                                                            • Template Matching
                                                                                                            • Template Matching
                                                                                                            • Template Matching
                                                                                                            • Problematic Correlation
                                                                                                            • Normalised Cross Correlation
                                                                                                            • Length of template
                                                                                                            • Length of image patch
                                                                                                            • Normalised Cross Correlation
                                                                                                            • Normalised Cross Correlation
                                                                                                            • Normalised Cross Correlation
                                                                                                            • Edges
                                                                                                            • Edges
                                                                                                            • Finite Difference
                                                                                                            • Edges
                                                                                                            • Edges in 2D
                                                                                                            • Edge filter kernel
                                                                                                            • Prewitt filter
                                                                                                            • Edge detection
                                                                                                            • Edge filtering
                                                                                                            • 02511 - Niveau af dagens emne forelaeligsing
                                                                                                            • 02512 - Niveau af dagens emne forelaeligsing
                                                                                                            • 02511 - Mit eget udbytte af dagen
                                                                                                            • 02512 - Mit eget udbytte af dagen
                                                                                                            • 02511 - Sidste uges oslashvelser (pixelwise operations)
                                                                                                            • 02512 - Sidste uges oslashvelser (pixelwise operations)
                                                                                                            • Denne uges brug af clickers
                                                                                                            • What can you do after today
                                                                                                            • Oslashvelsesrapport over oslashvelse 4 - 02511
                                                                                                            • Exercises
                                                                                                              A0
                                                                                                              B0
                                                                                                              C5
                                                                                                              D0
                                                                                                              E6
                                                                                                              A
                                                                                                              B
                                                                                                              C
                                                                                                              D
                                                                                                              E
                                                                                                              A3
                                                                                                              B0
                                                                                                              C3
                                                                                                              D0
                                                                                                              E0
                                                                                                              A
                                                                                                              B
                                                                                                              C
                                                                                                              D
                                                                                                              E
                                                                                                              A0
                                                                                                              B0
                                                                                                              C1
                                                                                                              D4
                                                                                                              E1
                                                                                                              A
                                                                                                              B
                                                                                                              C
                                                                                                              D
                                                                                                              E
                                                                                                              A2
                                                                                                              B1
                                                                                                              C3
                                                                                                              D2
                                                                                                              E0
                                                                                                              A
                                                                                                              B
                                                                                                              C
                                                                                                              D
                                                                                                              E
                                                                                                              A0
                                                                                                              B0
                                                                                                              C2
                                                                                                              D6
                                                                                                              E0
                                                                                                              A
                                                                                                              B
                                                                                                              C
                                                                                                              D
                                                                                                              E
                                                                                                              A0
                                                                                                              B0
                                                                                                              C1
                                                                                                              D0
                                                                                                              E0
                                                                                                              A
                                                                                                              B
                                                                                                              C
                                                                                                              D
                                                                                                              E
                                                                                                              A2
                                                                                                              B3
                                                                                                              C6
                                                                                                              D1
                                                                                                              E0
                                                                                                              A
                                                                                                              B
                                                                                                              C
                                                                                                              D
                                                                                                              E
                                                                                                              A0
                                                                                                              B8
                                                                                                              C1
                                                                                                              D1
                                                                                                              E0
                                                                                                              A
                                                                                                              B
                                                                                                              C
                                                                                                              D
                                                                                                              E
                                                                                                              A1
                                                                                                              B2
                                                                                                              C2
                                                                                                              D3
                                                                                                              E2
                                                                                                              A
                                                                                                              B
                                                                                                              C
                                                                                                              D
                                                                                                              E
                                                                                                              A0
                                                                                                              B13
                                                                                                              C0
                                                                                                              D0
                                                                                                              E0
                                                                                                              A
                                                                                                              B
                                                                                                              C
                                                                                                              D
                                                                                                              E
                                                                                                              A12
                                                                                                              B0
                                                                                                              C0
                                                                                                              D0
                                                                                                              E0
                                                                                                              A
                                                                                                              B
                                                                                                              C
                                                                                                              D
                                                                                                              E

                                                                                                              Chart1

                                                                                                              12
                                                                                                              0
                                                                                                              0
                                                                                                              0
                                                                                                              0

                                                                                                              Sheet1

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                                                                                                              Border handling

                                                                                                              0 2 41 2 2

                                                                                                              1 6 3

                                                                                                              1 2 12 5 3

                                                                                                              2 1 3

                                                                                                              1 3 1

                                                                                                              2 2 2

                                                                                                              0 1 3

                                                                                                              1 2 0

                                                                                                              2 1 4

                                                                                                              1 0 1

                                                                                                              Input Output

                                                                                                              No values at the border

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                                                                                                              Border handling ndash extend the input

                                                                                                              0 2 41 2 2

                                                                                                              1 6 3

                                                                                                              1 2 12 5 3

                                                                                                              2 1 3

                                                                                                              1 3 1

                                                                                                              2 2 2

                                                                                                              0 1 3

                                                                                                              1 2 0

                                                                                                              2 1 4

                                                                                                              1 0 1

                                                                                                              Input

                                                                                                              0 0 0 0 000000

                                                                                                              bull Zero padding ndash what happens

                                                                                                              bull Zero is black ndash creates dark border around the image

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                                                                                                              Correlation with zero paddingA) 5 8B) 12 16C) 13 3D) 15 21E) 17 12

                                                                                                              1 2 11 3 11 2 1

                                                                                                              0 2 41 2 2

                                                                                                              1 6 3

                                                                                                              1 2 12 5 3

                                                                                                              2 1 3

                                                                                                              1 3 1

                                                                                                              2 2 2

                                                                                                              0 1 3

                                                                                                              1 2 0

                                                                                                              2 1 4

                                                                                                              1 0 1

                                                                                                              0

                                                                                                              13

                                                                                                              0 0 0

                                                                                                              A B C D E

                                                                                                              Chart1

                                                                                                              0
                                                                                                              13
                                                                                                              0
                                                                                                              0
                                                                                                              0

                                                                                                              Sheet1

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                                                                                                              Border handling ndash extend the input

                                                                                                              0 2 41 2 2

                                                                                                              1 6 3

                                                                                                              1 2 12 5 3

                                                                                                              2 1 3

                                                                                                              1 3 1

                                                                                                              2 2 2

                                                                                                              0 1 3

                                                                                                              1 2 0

                                                                                                              2 1 4

                                                                                                              1 0 1

                                                                                                              Input

                                                                                                              1 2 0 1 311211

                                                                                                              bull Reflection

                                                                                                              bull Normally better than zero padding

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                                                                                                              Template Matching Template

                                                                                                              ndash Skabelon paring dansk Locates objects in images

                                                                                                              Input

                                                                                                              Template

                                                                                                              Output Correlation image

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                                                                                                              Template Matching The correlation between the template and the input

                                                                                                              image is computed for each pixel

                                                                                                              Input

                                                                                                              Template

                                                                                                              Output Correlation image

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                                                                                                              2122018Introduction to Medical Image Analysis56 DTU Compute Technical University of Denmark

                                                                                                              Template Matching The pixel with the highest value is found in the

                                                                                                              output imagendash Here is the highest correlation

                                                                                                              Input

                                                                                                              Template

                                                                                                              Output Correlation image

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                                                                                                              Template Matching This corresponds to the found pattern in the input

                                                                                                              image

                                                                                                              Input

                                                                                                              Template

                                                                                                              Output Correlation image

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                                                                                                              Problematic Correlation Correlation matching has problem with light areas ndash

                                                                                                              why

                                                                                                              Input (f)

                                                                                                              Template (h)

                                                                                                              Output Correlation imageFake max

                                                                                                              Real max

                                                                                                              Very High119892119892 119909119909119910119910 = 119895119895=minus119877119877

                                                                                                              119877119877

                                                                                                              119894119894=minus119877119877

                                                                                                              119877119877

                                                                                                              ℎ(119894119894 119895119895) 119891119891(119909119909 + 119894119894119910119910 + 119895119895)

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                                                                                                              Normalised Cross Correlation

                                                                                                              Input (f)

                                                                                                              Template (h)

                                                                                                              Output Correlation image

                                                                                                              Real max

                                                                                                              NCC x y =Correlation

                                                                                                              Length of image patch sdot Length of template

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                                                                                                              Length of template Vector length

                                                                                                              ndash Put all pixel values into a vectorndash Compute the length of this vector

                                                                                                              Describes the intensity of the templatendash Bright template has a large lengthndash Dark template has a small length

                                                                                                              Template (h)

                                                                                                              Length of template = 119895119895=minus119877119877

                                                                                                              119877119877

                                                                                                              119894119894=minus119877119877

                                                                                                              119877119877

                                                                                                              ℎ(119894119894 119895119895) ℎ(119894119894 119895119895)

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                                                                                                              Length of image patch Vector length based on pixel values in image patch Describes the intensity of the image patch

                                                                                                              Template (h)

                                                                                                              Input (f) with patch

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                                                                                                              Normalised Cross Correlation The length of the image patch and the length of

                                                                                                              template normalise the NCC If the image is very bright the NCC will be ldquopulled

                                                                                                              downrdquo

                                                                                                              NCC x y =Correlation

                                                                                                              Length of image patch sdot Length of template

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                                                                                                              Normalised Cross Correlation NCC will be between

                                                                                                              ndash 0 No similarity between template and image patchndash 1 Template and image patch are identical

                                                                                                              Input (f)

                                                                                                              Template (h)

                                                                                                              Output Correlation image

                                                                                                              Real max

                                                                                                              NCC x y =Correlation

                                                                                                              Length of image patch sdot Length of template

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                                                                                                              Normalised Cross Correlation

                                                                                                              A) 010B) 033C) 083D) 062E) 098

                                                                                                              Der udfoslashres template matching med og normalized crosscorrelation (NCC) beregnes Hvad bliver NNC i den markerede pixel

                                                                                                              1

                                                                                                              2 2

                                                                                                              3

                                                                                                              2

                                                                                                              A B C D E

                                                                                                              Chart1

                                                                                                              1
                                                                                                              2
                                                                                                              2
                                                                                                              3
                                                                                                              2

                                                                                                              Sheet1

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                                                                                                              Edges An edge is where there is a

                                                                                                              high change in gray level values

                                                                                                              Objects are often separated from the background by edgesGray level profile

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                                                                                                              Edges The profile as a function f(d) What value is high when there

                                                                                                              is an edgendash The slope of fndash The slope of the tangent at d

                                                                                                              f(d)

                                                                                                              119891119891prime(119889119889)

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                                                                                                              Finite Difference Definition of slope

                                                                                                              Approximation

                                                                                                              Simpler approximationh = 1

                                                                                                              119891119891prime 119889119889 = limℎrarr0

                                                                                                              119891119891 119889119889 + ℎ minus 119891119891(119889119889)ℎ

                                                                                                              119891119891prime 119889119889 asymp119891119891 119889119889 + ℎ minus 119891119891(119889119889)

                                                                                                              ℎ

                                                                                                              119891119891prime 119889119889 asymp 119891119891 119889119889 + 1 minus 119891119891(119889119889)

                                                                                                              DTU Compute

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                                                                                                              Edges Discrete approximation of frsquo(d) Can be implemented as a filter

                                                                                                              -1 0 1

                                                                                                              f(d-2) f(d-1) f(d) f(d+1) f(d+2) f(d+3)

                                                                                                              f(d)

                                                                                                              119891119891prime 119889119889 asymp 119891119891 119889119889 + 1 minus 119891119891(119889119889)

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                                                                                                              Edges in 2D Changes in gray level values

                                                                                                              ndash Image gradientndash Gradient is the 2D derivative of a 2D function f(xy)ndash Equal to the slope of the imagendash A steep slope is equal to an edge

                                                                                                              120571120571119891119891 119909119909119910119910 = 119866(119892119892119909119909119892119892119910119910)

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                                                                                                              Edge filter kernel The Prewitt filter is a typical

                                                                                                              edge filter Output image has high

                                                                                                              values where there are edges

                                                                                                              -1 0 1

                                                                                                              -1 0 1

                                                                                                              -1 0 1Vertical Prewitt filter

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                                                                                                              Prewitt filter

                                                                                                              Original Prewitt Prewitt

                                                                                                              Hot colormapSmooth 15x15

                                                                                                              Smooth 15x15

                                                                                                              Prewitt

                                                                                                              DTU Compute

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                                                                                                              Edge detection Edge filter

                                                                                                              ndash Prewitt for example Thresholding

                                                                                                              ndash Separate edges from non-edges

                                                                                                              Output is binary imagendash Edges are white

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                                                                                                              Edge filtering

                                                                                                              A) MeanB) Horizontal SobelC) Vertical PrewittD) Horisontal PrewittE) Median

                                                                                                              Der udfoslashres en filtrering (correlation) med et filter paring billedet Der bruges ikke coefficient normalization Den filtrerede vaeligrdi i den markerede pixel bliver -119 Hvilket et 3x3 filter blev benyttet

                                                                                                              0

                                                                                                              8

                                                                                                              1 10

                                                                                                              A B C D E

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                                                                                                              02511 - Niveau af dagens emne forelaeligsingA) Meget letB) LetC) PassendeD) SvaeligrtE) Meget svaeligrt

                                                                                                              23

                                                                                                              6

                                                                                                              10

                                                                                                              A B C D E

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                                                                                                              02512 - Niveau af dagens emne forelaeligsingA) Meget letB) LetC) PassendeD) SvaeligrtE) Meget svaeligrt

                                                                                                              0 0

                                                                                                              1

                                                                                                              0 0

                                                                                                              A B C D E

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                                                                                                              0
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                                                                                                              0

                                                                                                              Sheet1

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                                                                                                              02511 - Mit eget udbytte af dagenA) Jeg har laeligrt meget lidtB) Lidt laeligringC) PassendeD) God laeligringE) Jeg har laeligrt meget

                                                                                                              0 0

                                                                                                              2

                                                                                                              6

                                                                                                              0

                                                                                                              A B C D E

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                                                                                                              0

                                                                                                              Sheet1

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                                                                                                              02512 - Mit eget udbytte af dagenA) Jeg har laeligrt meget lidtB) Lidt laeligringC) PassendeD) God laeligringE) Jeg har laeligrt meget

                                                                                                              2

                                                                                                              1

                                                                                                              3

                                                                                                              2

                                                                                                              0

                                                                                                              A B C D E

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                                                                                                              Sheet1

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                                                                                                              02511 - Sidste uges oslashvelser (pixelwiseoperations)A) Meget letteB) LetteC) PassendeD) SvaeligreE) Meget svaeligre

                                                                                                              0 0

                                                                                                              1

                                                                                                              4

                                                                                                              1

                                                                                                              A B C D E

                                                                                                              Chart1

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                                                                                                              0
                                                                                                              1
                                                                                                              4
                                                                                                              1

                                                                                                              Sheet1

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                                                                                                              02512 - Sidste uges oslashvelser (pixelwiseoperations)A) Meget letteB) LetteC) PassendeD) SvaeligreE) Meget svaeligre

                                                                                                              3

                                                                                                              0

                                                                                                              3

                                                                                                              0 0

                                                                                                              A B C D E

                                                                                                              Chart1

                                                                                                              3
                                                                                                              0
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                                                                                                              0
                                                                                                              0

                                                                                                              Sheet1

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                                                                                                              2122018Introduction to Medical Image Analysis82 DTU Compute Technical University of Denmark

                                                                                                              Denne uges brug af clickersA) click click click ndash jeg bliver

                                                                                                              sindssygB) For meget clickC) PassendeD) Jeg vil gerne have lidt mereE) Jeg kan ikrsquo faring nok

                                                                                                              0 0

                                                                                                              5

                                                                                                              0

                                                                                                              6

                                                                                                              A B C D E

                                                                                                              Chart1

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                                                                                                              5
                                                                                                              0
                                                                                                              6

                                                                                                              Sheet1

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                                                                                                              What can you do after today Describe the difference between point processing and neighbourhood

                                                                                                              processing Compute a rank filtered image using the min max median and

                                                                                                              difference rank filters Compute a mean filtered image Decide if median or average filtering should be used for noise removal Choose the appropriate image border handling based on a given input

                                                                                                              image Implement and apply template matching Compute the normalised cross correlation and explain why it should be

                                                                                                              used Apply given image filter kernels to images Use edge filters on images Describe finite difference approximation of image gradients Describe the concept of edge detection

                                                                                                              DTU Compute

                                                                                                              2122018Introduction to Medical Image Analysis84 DTU Compute Technical University of Denmark

                                                                                                              Oslashvelsesrapport over oslashvelse 4 - 02511 Oslashvelser taeligller cirka 30 af karakteren Skal afleveres senest den 7 marts kl 2359 Kan afleveres af 1 eller 2 personer

                                                                                                              ndash I skal skrive jeres egen oslashvelsesrapportndash Brug mindst et af jeres egne billeder

                                                                                                              Afleveres som PDF Lad vaeligre med at kopiere opgaveteksten ind i jeres

                                                                                                              opgave Put Matlab kode i et Appendix og henvis fra teksten Eksempel rapport over oslashvelse findes paring

                                                                                                              hjemmesiden under eksamen

                                                                                                              DTU Compute

                                                                                                              2122018Introduction to Medical Image Analysis85 DTU Compute Technical University of Denmark

                                                                                                              Exercises

                                                                                                              • Introduction to Medical Image Analysis
                                                                                                              • Lecture 4 ndash Neighbourhood Processing
                                                                                                              • What can you do after today
                                                                                                              • Point processing
                                                                                                              • Point processing
                                                                                                              • Neighbourhood processing
                                                                                                              • Use of filtering
                                                                                                              • Salt and pepper noise
                                                                                                              • Salt and pepper noise
                                                                                                              • What is so special about noise
                                                                                                              • Noise ndash go away
                                                                                                              • What is the median Value
                                                                                                              • The median value
                                                                                                              • Noise away ndash the median filter
                                                                                                              • Noise removal ndash average filter
                                                                                                              • Noise removal ndash median filter
                                                                                                              • Image Filtering
                                                                                                              • Median filter
                                                                                                              • Rank filters
                                                                                                              • Median filter
                                                                                                              • Correlation
                                                                                                              • Why do we need similarity
                                                                                                              • Correlation (1D)
                                                                                                              • Correlation (1D)
                                                                                                              • Normalisation
                                                                                                              • Normalisation
                                                                                                              • Correlation on images
                                                                                                              • Correlation on images
                                                                                                              • Correlation on images
                                                                                                              • Draw your filter
                                                                                                              • Correlation on images ndash no normalisation
                                                                                                              • Correlation on images ndash no normalisation 2
                                                                                                              • Mathematics of 2D Correlation
                                                                                                              • Mathematics of 2D Correlation
                                                                                                              • Mathematics of 2D Correlation
                                                                                                              • Slide Number 40
                                                                                                              • 2D Kernel Normalisation
                                                                                                              • Correlation
                                                                                                              • Smoothing filters
                                                                                                              • Use of smoothing
                                                                                                              • Use of smoothing
                                                                                                              • Mean filter
                                                                                                              • Border handling
                                                                                                              • Border handling ndash extend the input
                                                                                                              • Correlation with zero padding
                                                                                                              • Border handling ndash extend the input
                                                                                                              • Template Matching
                                                                                                              • Template Matching
                                                                                                              • Template Matching
                                                                                                              • Template Matching
                                                                                                              • Problematic Correlation
                                                                                                              • Normalised Cross Correlation
                                                                                                              • Length of template
                                                                                                              • Length of image patch
                                                                                                              • Normalised Cross Correlation
                                                                                                              • Normalised Cross Correlation
                                                                                                              • Normalised Cross Correlation
                                                                                                              • Edges
                                                                                                              • Edges
                                                                                                              • Finite Difference
                                                                                                              • Edges
                                                                                                              • Edges in 2D
                                                                                                              • Edge filter kernel
                                                                                                              • Prewitt filter
                                                                                                              • Edge detection
                                                                                                              • Edge filtering
                                                                                                              • 02511 - Niveau af dagens emne forelaeligsing
                                                                                                              • 02512 - Niveau af dagens emne forelaeligsing
                                                                                                              • 02511 - Mit eget udbytte af dagen
                                                                                                              • 02512 - Mit eget udbytte af dagen
                                                                                                              • 02511 - Sidste uges oslashvelser (pixelwise operations)
                                                                                                              • 02512 - Sidste uges oslashvelser (pixelwise operations)
                                                                                                              • Denne uges brug af clickers
                                                                                                              • What can you do after today
                                                                                                              • Oslashvelsesrapport over oslashvelse 4 - 02511
                                                                                                              • Exercises
                                                                                                                A0
                                                                                                                B0
                                                                                                                C5
                                                                                                                D0
                                                                                                                E6
                                                                                                                A
                                                                                                                B
                                                                                                                C
                                                                                                                D
                                                                                                                E
                                                                                                                A3
                                                                                                                B0
                                                                                                                C3
                                                                                                                D0
                                                                                                                E0
                                                                                                                A
                                                                                                                B
                                                                                                                C
                                                                                                                D
                                                                                                                E
                                                                                                                A0
                                                                                                                B0
                                                                                                                C1
                                                                                                                D4
                                                                                                                E1
                                                                                                                A
                                                                                                                B
                                                                                                                C
                                                                                                                D
                                                                                                                E
                                                                                                                A2
                                                                                                                B1
                                                                                                                C3
                                                                                                                D2
                                                                                                                E0
                                                                                                                A
                                                                                                                B
                                                                                                                C
                                                                                                                D
                                                                                                                E
                                                                                                                A0
                                                                                                                B0
                                                                                                                C2
                                                                                                                D6
                                                                                                                E0
                                                                                                                A
                                                                                                                B
                                                                                                                C
                                                                                                                D
                                                                                                                E
                                                                                                                A0
                                                                                                                B0
                                                                                                                C1
                                                                                                                D0
                                                                                                                E0
                                                                                                                A
                                                                                                                B
                                                                                                                C
                                                                                                                D
                                                                                                                E
                                                                                                                A2
                                                                                                                B3
                                                                                                                C6
                                                                                                                D1
                                                                                                                E0
                                                                                                                A
                                                                                                                B
                                                                                                                C
                                                                                                                D
                                                                                                                E
                                                                                                                A0
                                                                                                                B8
                                                                                                                C1
                                                                                                                D1
                                                                                                                E0
                                                                                                                A
                                                                                                                B
                                                                                                                C
                                                                                                                D
                                                                                                                E
                                                                                                                A1
                                                                                                                B2
                                                                                                                C2
                                                                                                                D3
                                                                                                                E2
                                                                                                                A
                                                                                                                B
                                                                                                                C
                                                                                                                D
                                                                                                                E
                                                                                                                A0
                                                                                                                B13
                                                                                                                C0
                                                                                                                D0
                                                                                                                E0
                                                                                                                A
                                                                                                                B
                                                                                                                C
                                                                                                                D
                                                                                                                E
                                                                                                                A12
                                                                                                                B0
                                                                                                                C0
                                                                                                                D0
                                                                                                                E0
                                                                                                                A
                                                                                                                B
                                                                                                                C
                                                                                                                D
                                                                                                                E

                                                                                                                Sheet1

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                                                                                                                Border handling

                                                                                                                0 2 41 2 2

                                                                                                                1 6 3

                                                                                                                1 2 12 5 3

                                                                                                                2 1 3

                                                                                                                1 3 1

                                                                                                                2 2 2

                                                                                                                0 1 3

                                                                                                                1 2 0

                                                                                                                2 1 4

                                                                                                                1 0 1

                                                                                                                Input Output

                                                                                                                No values at the border

                                                                                                                DTU Compute

                                                                                                                2122018Introduction to Medical Image Analysis50 DTU Compute Technical University of Denmark

                                                                                                                Border handling ndash extend the input

                                                                                                                0 2 41 2 2

                                                                                                                1 6 3

                                                                                                                1 2 12 5 3

                                                                                                                2 1 3

                                                                                                                1 3 1

                                                                                                                2 2 2

                                                                                                                0 1 3

                                                                                                                1 2 0

                                                                                                                2 1 4

                                                                                                                1 0 1

                                                                                                                Input

                                                                                                                0 0 0 0 000000

                                                                                                                bull Zero padding ndash what happens

                                                                                                                bull Zero is black ndash creates dark border around the image

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                                                                                                                Correlation with zero paddingA) 5 8B) 12 16C) 13 3D) 15 21E) 17 12

                                                                                                                1 2 11 3 11 2 1

                                                                                                                0 2 41 2 2

                                                                                                                1 6 3

                                                                                                                1 2 12 5 3

                                                                                                                2 1 3

                                                                                                                1 3 1

                                                                                                                2 2 2

                                                                                                                0 1 3

                                                                                                                1 2 0

                                                                                                                2 1 4

                                                                                                                1 0 1

                                                                                                                0

                                                                                                                13

                                                                                                                0 0 0

                                                                                                                A B C D E

                                                                                                                Chart1

                                                                                                                0
                                                                                                                13
                                                                                                                0
                                                                                                                0
                                                                                                                0

                                                                                                                Sheet1

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                                                                                                                Border handling ndash extend the input

                                                                                                                0 2 41 2 2

                                                                                                                1 6 3

                                                                                                                1 2 12 5 3

                                                                                                                2 1 3

                                                                                                                1 3 1

                                                                                                                2 2 2

                                                                                                                0 1 3

                                                                                                                1 2 0

                                                                                                                2 1 4

                                                                                                                1 0 1

                                                                                                                Input

                                                                                                                1 2 0 1 311211

                                                                                                                bull Reflection

                                                                                                                bull Normally better than zero padding

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                                                                                                                Template Matching Template

                                                                                                                ndash Skabelon paring dansk Locates objects in images

                                                                                                                Input

                                                                                                                Template

                                                                                                                Output Correlation image

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                                                                                                                2122018Introduction to Medical Image Analysis55 DTU Compute Technical University of Denmark

                                                                                                                Template Matching The correlation between the template and the input

                                                                                                                image is computed for each pixel

                                                                                                                Input

                                                                                                                Template

                                                                                                                Output Correlation image

                                                                                                                DTU Compute

                                                                                                                2122018Introduction to Medical Image Analysis56 DTU Compute Technical University of Denmark

                                                                                                                Template Matching The pixel with the highest value is found in the

                                                                                                                output imagendash Here is the highest correlation

                                                                                                                Input

                                                                                                                Template

                                                                                                                Output Correlation image

                                                                                                                DTU Compute

                                                                                                                2122018Introduction to Medical Image Analysis57 DTU Compute Technical University of Denmark

                                                                                                                Template Matching This corresponds to the found pattern in the input

                                                                                                                image

                                                                                                                Input

                                                                                                                Template

                                                                                                                Output Correlation image

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                                                                                                                Problematic Correlation Correlation matching has problem with light areas ndash

                                                                                                                why

                                                                                                                Input (f)

                                                                                                                Template (h)

                                                                                                                Output Correlation imageFake max

                                                                                                                Real max

                                                                                                                Very High119892119892 119909119909119910119910 = 119895119895=minus119877119877

                                                                                                                119877119877

                                                                                                                119894119894=minus119877119877

                                                                                                                119877119877

                                                                                                                ℎ(119894119894 119895119895) 119891119891(119909119909 + 119894119894119910119910 + 119895119895)

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                                                                                                                Normalised Cross Correlation

                                                                                                                Input (f)

                                                                                                                Template (h)

                                                                                                                Output Correlation image

                                                                                                                Real max

                                                                                                                NCC x y =Correlation

                                                                                                                Length of image patch sdot Length of template

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                                                                                                                Length of template Vector length

                                                                                                                ndash Put all pixel values into a vectorndash Compute the length of this vector

                                                                                                                Describes the intensity of the templatendash Bright template has a large lengthndash Dark template has a small length

                                                                                                                Template (h)

                                                                                                                Length of template = 119895119895=minus119877119877

                                                                                                                119877119877

                                                                                                                119894119894=minus119877119877

                                                                                                                119877119877

                                                                                                                ℎ(119894119894 119895119895) ℎ(119894119894 119895119895)

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                                                                                                                Length of image patch Vector length based on pixel values in image patch Describes the intensity of the image patch

                                                                                                                Template (h)

                                                                                                                Input (f) with patch

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                                                                                                                Normalised Cross Correlation The length of the image patch and the length of

                                                                                                                template normalise the NCC If the image is very bright the NCC will be ldquopulled

                                                                                                                downrdquo

                                                                                                                NCC x y =Correlation

                                                                                                                Length of image patch sdot Length of template

                                                                                                                DTU Compute

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                                                                                                                Normalised Cross Correlation NCC will be between

                                                                                                                ndash 0 No similarity between template and image patchndash 1 Template and image patch are identical

                                                                                                                Input (f)

                                                                                                                Template (h)

                                                                                                                Output Correlation image

                                                                                                                Real max

                                                                                                                NCC x y =Correlation

                                                                                                                Length of image patch sdot Length of template

                                                                                                                DTU Compute

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                                                                                                                Normalised Cross Correlation

                                                                                                                A) 010B) 033C) 083D) 062E) 098

                                                                                                                Der udfoslashres template matching med og normalized crosscorrelation (NCC) beregnes Hvad bliver NNC i den markerede pixel

                                                                                                                1

                                                                                                                2 2

                                                                                                                3

                                                                                                                2

                                                                                                                A B C D E

                                                                                                                Chart1

                                                                                                                1
                                                                                                                2
                                                                                                                2
                                                                                                                3
                                                                                                                2

                                                                                                                Sheet1

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                                                                                                                Edges An edge is where there is a

                                                                                                                high change in gray level values

                                                                                                                Objects are often separated from the background by edgesGray level profile

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                                                                                                                Edges The profile as a function f(d) What value is high when there

                                                                                                                is an edgendash The slope of fndash The slope of the tangent at d

                                                                                                                f(d)

                                                                                                                119891119891prime(119889119889)

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                                                                                                                Finite Difference Definition of slope

                                                                                                                Approximation

                                                                                                                Simpler approximationh = 1

                                                                                                                119891119891prime 119889119889 = limℎrarr0

                                                                                                                119891119891 119889119889 + ℎ minus 119891119891(119889119889)ℎ

                                                                                                                119891119891prime 119889119889 asymp119891119891 119889119889 + ℎ minus 119891119891(119889119889)

                                                                                                                ℎ

                                                                                                                119891119891prime 119889119889 asymp 119891119891 119889119889 + 1 minus 119891119891(119889119889)

                                                                                                                DTU Compute

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                                                                                                                Edges Discrete approximation of frsquo(d) Can be implemented as a filter

                                                                                                                -1 0 1

                                                                                                                f(d-2) f(d-1) f(d) f(d+1) f(d+2) f(d+3)

                                                                                                                f(d)

                                                                                                                119891119891prime 119889119889 asymp 119891119891 119889119889 + 1 minus 119891119891(119889119889)

                                                                                                                DTU Compute

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                                                                                                                Edges in 2D Changes in gray level values

                                                                                                                ndash Image gradientndash Gradient is the 2D derivative of a 2D function f(xy)ndash Equal to the slope of the imagendash A steep slope is equal to an edge

                                                                                                                120571120571119891119891 119909119909119910119910 = 119866(119892119892119909119909119892119892119910119910)

                                                                                                                DTU Compute

                                                                                                                2122018Introduction to Medical Image Analysis71 DTU Compute Technical University of Denmark

                                                                                                                Edge filter kernel The Prewitt filter is a typical

                                                                                                                edge filter Output image has high

                                                                                                                values where there are edges

                                                                                                                -1 0 1

                                                                                                                -1 0 1

                                                                                                                -1 0 1Vertical Prewitt filter

                                                                                                                DTU Compute

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                                                                                                                Prewitt filter

                                                                                                                Original Prewitt Prewitt

                                                                                                                Hot colormapSmooth 15x15

                                                                                                                Smooth 15x15

                                                                                                                Prewitt

                                                                                                                DTU Compute

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                                                                                                                Edge detection Edge filter

                                                                                                                ndash Prewitt for example Thresholding

                                                                                                                ndash Separate edges from non-edges

                                                                                                                Output is binary imagendash Edges are white

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                                                                                                                Edge filtering

                                                                                                                A) MeanB) Horizontal SobelC) Vertical PrewittD) Horisontal PrewittE) Median

                                                                                                                Der udfoslashres en filtrering (correlation) med et filter paring billedet Der bruges ikke coefficient normalization Den filtrerede vaeligrdi i den markerede pixel bliver -119 Hvilket et 3x3 filter blev benyttet

                                                                                                                0

                                                                                                                8

                                                                                                                1 10

                                                                                                                A B C D E

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                                                                                                                02511 - Niveau af dagens emne forelaeligsingA) Meget letB) LetC) PassendeD) SvaeligrtE) Meget svaeligrt

                                                                                                                23

                                                                                                                6

                                                                                                                10

                                                                                                                A B C D E

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                                                                                                                Sheet1

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                                                                                                                02512 - Niveau af dagens emne forelaeligsingA) Meget letB) LetC) PassendeD) SvaeligrtE) Meget svaeligrt

                                                                                                                0 0

                                                                                                                1

                                                                                                                0 0

                                                                                                                A B C D E

                                                                                                                Chart1

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                                                                                                                0
                                                                                                                1
                                                                                                                0
                                                                                                                0

                                                                                                                Sheet1

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                                                                                                                02511 - Mit eget udbytte af dagenA) Jeg har laeligrt meget lidtB) Lidt laeligringC) PassendeD) God laeligringE) Jeg har laeligrt meget

                                                                                                                0 0

                                                                                                                2

                                                                                                                6

                                                                                                                0

                                                                                                                A B C D E

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                                                                                                                0
                                                                                                                2
                                                                                                                6
                                                                                                                0

                                                                                                                Sheet1

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                                                                                                                02512 - Mit eget udbytte af dagenA) Jeg har laeligrt meget lidtB) Lidt laeligringC) PassendeD) God laeligringE) Jeg har laeligrt meget

                                                                                                                2

                                                                                                                1

                                                                                                                3

                                                                                                                2

                                                                                                                0

                                                                                                                A B C D E

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                                                                                                                0

                                                                                                                Sheet1

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                                                                                                                02511 - Sidste uges oslashvelser (pixelwiseoperations)A) Meget letteB) LetteC) PassendeD) SvaeligreE) Meget svaeligre

                                                                                                                0 0

                                                                                                                1

                                                                                                                4

                                                                                                                1

                                                                                                                A B C D E

                                                                                                                Chart1

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                                                                                                                0
                                                                                                                1
                                                                                                                4
                                                                                                                1

                                                                                                                Sheet1

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                                                                                                                02512 - Sidste uges oslashvelser (pixelwiseoperations)A) Meget letteB) LetteC) PassendeD) SvaeligreE) Meget svaeligre

                                                                                                                3

                                                                                                                0

                                                                                                                3

                                                                                                                0 0

                                                                                                                A B C D E

                                                                                                                Chart1

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                                                                                                                0

                                                                                                                Sheet1

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                                                                                                                Denne uges brug af clickersA) click click click ndash jeg bliver

                                                                                                                sindssygB) For meget clickC) PassendeD) Jeg vil gerne have lidt mereE) Jeg kan ikrsquo faring nok

                                                                                                                0 0

                                                                                                                5

                                                                                                                0

                                                                                                                6

                                                                                                                A B C D E

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                                                                                                                6

                                                                                                                Sheet1

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                                                                                                                What can you do after today Describe the difference between point processing and neighbourhood

                                                                                                                processing Compute a rank filtered image using the min max median and

                                                                                                                difference rank filters Compute a mean filtered image Decide if median or average filtering should be used for noise removal Choose the appropriate image border handling based on a given input

                                                                                                                image Implement and apply template matching Compute the normalised cross correlation and explain why it should be

                                                                                                                used Apply given image filter kernels to images Use edge filters on images Describe finite difference approximation of image gradients Describe the concept of edge detection

                                                                                                                DTU Compute

                                                                                                                2122018Introduction to Medical Image Analysis84 DTU Compute Technical University of Denmark

                                                                                                                Oslashvelsesrapport over oslashvelse 4 - 02511 Oslashvelser taeligller cirka 30 af karakteren Skal afleveres senest den 7 marts kl 2359 Kan afleveres af 1 eller 2 personer

                                                                                                                ndash I skal skrive jeres egen oslashvelsesrapportndash Brug mindst et af jeres egne billeder

                                                                                                                Afleveres som PDF Lad vaeligre med at kopiere opgaveteksten ind i jeres

                                                                                                                opgave Put Matlab kode i et Appendix og henvis fra teksten Eksempel rapport over oslashvelse findes paring

                                                                                                                hjemmesiden under eksamen

                                                                                                                DTU Compute

                                                                                                                2122018Introduction to Medical Image Analysis85 DTU Compute Technical University of Denmark

                                                                                                                Exercises

                                                                                                                • Introduction to Medical Image Analysis
                                                                                                                • Lecture 4 ndash Neighbourhood Processing
                                                                                                                • What can you do after today
                                                                                                                • Point processing
                                                                                                                • Point processing
                                                                                                                • Neighbourhood processing
                                                                                                                • Use of filtering
                                                                                                                • Salt and pepper noise
                                                                                                                • Salt and pepper noise
                                                                                                                • What is so special about noise
                                                                                                                • Noise ndash go away
                                                                                                                • What is the median Value
                                                                                                                • The median value
                                                                                                                • Noise away ndash the median filter
                                                                                                                • Noise removal ndash average filter
                                                                                                                • Noise removal ndash median filter
                                                                                                                • Image Filtering
                                                                                                                • Median filter
                                                                                                                • Rank filters
                                                                                                                • Median filter
                                                                                                                • Correlation
                                                                                                                • Why do we need similarity
                                                                                                                • Correlation (1D)
                                                                                                                • Correlation (1D)
                                                                                                                • Normalisation
                                                                                                                • Normalisation
                                                                                                                • Correlation on images
                                                                                                                • Correlation on images
                                                                                                                • Correlation on images
                                                                                                                • Draw your filter
                                                                                                                • Correlation on images ndash no normalisation
                                                                                                                • Correlation on images ndash no normalisation 2
                                                                                                                • Mathematics of 2D Correlation
                                                                                                                • Mathematics of 2D Correlation
                                                                                                                • Mathematics of 2D Correlation
                                                                                                                • Slide Number 40
                                                                                                                • 2D Kernel Normalisation
                                                                                                                • Correlation
                                                                                                                • Smoothing filters
                                                                                                                • Use of smoothing
                                                                                                                • Use of smoothing
                                                                                                                • Mean filter
                                                                                                                • Border handling
                                                                                                                • Border handling ndash extend the input
                                                                                                                • Correlation with zero padding
                                                                                                                • Border handling ndash extend the input
                                                                                                                • Template Matching
                                                                                                                • Template Matching
                                                                                                                • Template Matching
                                                                                                                • Template Matching
                                                                                                                • Problematic Correlation
                                                                                                                • Normalised Cross Correlation
                                                                                                                • Length of template
                                                                                                                • Length of image patch
                                                                                                                • Normalised Cross Correlation
                                                                                                                • Normalised Cross Correlation
                                                                                                                • Normalised Cross Correlation
                                                                                                                • Edges
                                                                                                                • Edges
                                                                                                                • Finite Difference
                                                                                                                • Edges
                                                                                                                • Edges in 2D
                                                                                                                • Edge filter kernel
                                                                                                                • Prewitt filter
                                                                                                                • Edge detection
                                                                                                                • Edge filtering
                                                                                                                • 02511 - Niveau af dagens emne forelaeligsing
                                                                                                                • 02512 - Niveau af dagens emne forelaeligsing
                                                                                                                • 02511 - Mit eget udbytte af dagen
                                                                                                                • 02512 - Mit eget udbytte af dagen
                                                                                                                • 02511 - Sidste uges oslashvelser (pixelwise operations)
                                                                                                                • 02512 - Sidste uges oslashvelser (pixelwise operations)
                                                                                                                • Denne uges brug af clickers
                                                                                                                • What can you do after today
                                                                                                                • Oslashvelsesrapport over oslashvelse 4 - 02511
                                                                                                                • Exercises
                                                                                                                  A0
                                                                                                                  B0
                                                                                                                  C5
                                                                                                                  D0
                                                                                                                  E6
                                                                                                                  A
                                                                                                                  B
                                                                                                                  C
                                                                                                                  D
                                                                                                                  E
                                                                                                                  A3
                                                                                                                  B0
                                                                                                                  C3
                                                                                                                  D0
                                                                                                                  E0
                                                                                                                  A
                                                                                                                  B
                                                                                                                  C
                                                                                                                  D
                                                                                                                  E
                                                                                                                  A0
                                                                                                                  B0
                                                                                                                  C1
                                                                                                                  D4
                                                                                                                  E1
                                                                                                                  A
                                                                                                                  B
                                                                                                                  C
                                                                                                                  D
                                                                                                                  E
                                                                                                                  A2
                                                                                                                  B1
                                                                                                                  C3
                                                                                                                  D2
                                                                                                                  E0
                                                                                                                  A
                                                                                                                  B
                                                                                                                  C
                                                                                                                  D
                                                                                                                  E
                                                                                                                  A0
                                                                                                                  B0
                                                                                                                  C2
                                                                                                                  D6
                                                                                                                  E0
                                                                                                                  A
                                                                                                                  B
                                                                                                                  C
                                                                                                                  D
                                                                                                                  E
                                                                                                                  A0
                                                                                                                  B0
                                                                                                                  C1
                                                                                                                  D0
                                                                                                                  E0
                                                                                                                  A
                                                                                                                  B
                                                                                                                  C
                                                                                                                  D
                                                                                                                  E
                                                                                                                  A2
                                                                                                                  B3
                                                                                                                  C6
                                                                                                                  D1
                                                                                                                  E0
                                                                                                                  A
                                                                                                                  B
                                                                                                                  C
                                                                                                                  D
                                                                                                                  E
                                                                                                                  A0
                                                                                                                  B8
                                                                                                                  C1
                                                                                                                  D1
                                                                                                                  E0
                                                                                                                  A
                                                                                                                  B
                                                                                                                  C
                                                                                                                  D
                                                                                                                  E
                                                                                                                  A1
                                                                                                                  B2
                                                                                                                  C2
                                                                                                                  D3
                                                                                                                  E2
                                                                                                                  A
                                                                                                                  B
                                                                                                                  C
                                                                                                                  D
                                                                                                                  E
                                                                                                                  A0
                                                                                                                  B13
                                                                                                                  C0
                                                                                                                  D0
                                                                                                                  E0
                                                                                                                  A
                                                                                                                  B
                                                                                                                  C
                                                                                                                  D
                                                                                                                  E
                                                                                                                  A12
                                                                                                                  B0
                                                                                                                  C0
                                                                                                                  D0
                                                                                                                  E0

                                                                                                                  DTU Compute

                                                                                                                  2122018Introduction to Medical Image Analysis49 DTU Compute Technical University of Denmark

                                                                                                                  Border handling

                                                                                                                  0 2 41 2 2

                                                                                                                  1 6 3

                                                                                                                  1 2 12 5 3

                                                                                                                  2 1 3

                                                                                                                  1 3 1

                                                                                                                  2 2 2

                                                                                                                  0 1 3

                                                                                                                  1 2 0

                                                                                                                  2 1 4

                                                                                                                  1 0 1

                                                                                                                  Input Output

                                                                                                                  No values at the border

                                                                                                                  DTU Compute

                                                                                                                  2122018Introduction to Medical Image Analysis50 DTU Compute Technical University of Denmark

                                                                                                                  Border handling ndash extend the input

                                                                                                                  0 2 41 2 2

                                                                                                                  1 6 3

                                                                                                                  1 2 12 5 3

                                                                                                                  2 1 3

                                                                                                                  1 3 1

                                                                                                                  2 2 2

                                                                                                                  0 1 3

                                                                                                                  1 2 0

                                                                                                                  2 1 4

                                                                                                                  1 0 1

                                                                                                                  Input

                                                                                                                  0 0 0 0 000000

                                                                                                                  bull Zero padding ndash what happens

                                                                                                                  bull Zero is black ndash creates dark border around the image

                                                                                                                  DTU Compute

                                                                                                                  2122018Introduction to Medical Image Analysis51 DTU Compute Technical University of Denmark

                                                                                                                  Correlation with zero paddingA) 5 8B) 12 16C) 13 3D) 15 21E) 17 12

                                                                                                                  1 2 11 3 11 2 1

                                                                                                                  0 2 41 2 2

                                                                                                                  1 6 3

                                                                                                                  1 2 12 5 3

                                                                                                                  2 1 3

                                                                                                                  1 3 1

                                                                                                                  2 2 2

                                                                                                                  0 1 3

                                                                                                                  1 2 0

                                                                                                                  2 1 4

                                                                                                                  1 0 1

                                                                                                                  0

                                                                                                                  13

                                                                                                                  0 0 0

                                                                                                                  A B C D E

                                                                                                                  Chart1

                                                                                                                  0
                                                                                                                  13
                                                                                                                  0
                                                                                                                  0
                                                                                                                  0

                                                                                                                  Sheet1

                                                                                                                  DTU Compute

                                                                                                                  2122018Introduction to Medical Image Analysis53 DTU Compute Technical University of Denmark

                                                                                                                  Border handling ndash extend the input

                                                                                                                  0 2 41 2 2

                                                                                                                  1 6 3

                                                                                                                  1 2 12 5 3

                                                                                                                  2 1 3

                                                                                                                  1 3 1

                                                                                                                  2 2 2

                                                                                                                  0 1 3

                                                                                                                  1 2 0

                                                                                                                  2 1 4

                                                                                                                  1 0 1

                                                                                                                  Input

                                                                                                                  1 2 0 1 311211

                                                                                                                  bull Reflection

                                                                                                                  bull Normally better than zero padding

                                                                                                                  DTU Compute

                                                                                                                  2122018Introduction to Medical Image Analysis54 DTU Compute Technical University of Denmark

                                                                                                                  Template Matching Template

                                                                                                                  ndash Skabelon paring dansk Locates objects in images

                                                                                                                  Input

                                                                                                                  Template

                                                                                                                  Output Correlation image

                                                                                                                  DTU Compute

                                                                                                                  2122018Introduction to Medical Image Analysis55 DTU Compute Technical University of Denmark

                                                                                                                  Template Matching The correlation between the template and the input

                                                                                                                  image is computed for each pixel

                                                                                                                  Input

                                                                                                                  Template

                                                                                                                  Output Correlation image

                                                                                                                  DTU Compute

                                                                                                                  2122018Introduction to Medical Image Analysis56 DTU Compute Technical University of Denmark

                                                                                                                  Template Matching The pixel with the highest value is found in the

                                                                                                                  output imagendash Here is the highest correlation

                                                                                                                  Input

                                                                                                                  Template

                                                                                                                  Output Correlation image

                                                                                                                  DTU Compute

                                                                                                                  2122018Introduction to Medical Image Analysis57 DTU Compute Technical University of Denmark

                                                                                                                  Template Matching This corresponds to the found pattern in the input

                                                                                                                  image

                                                                                                                  Input

                                                                                                                  Template

                                                                                                                  Output Correlation image

                                                                                                                  DTU Compute

                                                                                                                  2122018Introduction to Medical Image Analysis58 DTU Compute Technical University of Denmark

                                                                                                                  Problematic Correlation Correlation matching has problem with light areas ndash

                                                                                                                  why

                                                                                                                  Input (f)

                                                                                                                  Template (h)

                                                                                                                  Output Correlation imageFake max

                                                                                                                  Real max

                                                                                                                  Very High119892119892 119909119909119910119910 = 119895119895=minus119877119877

                                                                                                                  119877119877

                                                                                                                  119894119894=minus119877119877

                                                                                                                  119877119877

                                                                                                                  ℎ(119894119894 119895119895) 119891119891(119909119909 + 119894119894119910119910 + 119895119895)

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                                                                                                                  Normalised Cross Correlation

                                                                                                                  Input (f)

                                                                                                                  Template (h)

                                                                                                                  Output Correlation image

                                                                                                                  Real max

                                                                                                                  NCC x y =Correlation

                                                                                                                  Length of image patch sdot Length of template

                                                                                                                  DTU Compute

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                                                                                                                  Length of template Vector length

                                                                                                                  ndash Put all pixel values into a vectorndash Compute the length of this vector

                                                                                                                  Describes the intensity of the templatendash Bright template has a large lengthndash Dark template has a small length

                                                                                                                  Template (h)

                                                                                                                  Length of template = 119895119895=minus119877119877

                                                                                                                  119877119877

                                                                                                                  119894119894=minus119877119877

                                                                                                                  119877119877

                                                                                                                  ℎ(119894119894 119895119895) ℎ(119894119894 119895119895)

                                                                                                                  DTU Compute

                                                                                                                  2122018Introduction to Medical Image Analysis61 DTU Compute Technical University of Denmark

                                                                                                                  Length of image patch Vector length based on pixel values in image patch Describes the intensity of the image patch

                                                                                                                  Template (h)

                                                                                                                  Input (f) with patch

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                                                                                                                  2122018Introduction to Medical Image Analysis62 DTU Compute Technical University of Denmark

                                                                                                                  Normalised Cross Correlation The length of the image patch and the length of

                                                                                                                  template normalise the NCC If the image is very bright the NCC will be ldquopulled

                                                                                                                  downrdquo

                                                                                                                  NCC x y =Correlation

                                                                                                                  Length of image patch sdot Length of template

                                                                                                                  DTU Compute

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                                                                                                                  Normalised Cross Correlation NCC will be between

                                                                                                                  ndash 0 No similarity between template and image patchndash 1 Template and image patch are identical

                                                                                                                  Input (f)

                                                                                                                  Template (h)

                                                                                                                  Output Correlation image

                                                                                                                  Real max

                                                                                                                  NCC x y =Correlation

                                                                                                                  Length of image patch sdot Length of template

                                                                                                                  DTU Compute

                                                                                                                  2122018Introduction to Medical Image Analysis64 DTU Compute Technical University of Denmark

                                                                                                                  Normalised Cross Correlation

                                                                                                                  A) 010B) 033C) 083D) 062E) 098

                                                                                                                  Der udfoslashres template matching med og normalized crosscorrelation (NCC) beregnes Hvad bliver NNC i den markerede pixel

                                                                                                                  1

                                                                                                                  2 2

                                                                                                                  3

                                                                                                                  2

                                                                                                                  A B C D E

                                                                                                                  Chart1

                                                                                                                  1
                                                                                                                  2
                                                                                                                  2
                                                                                                                  3
                                                                                                                  2

                                                                                                                  Sheet1

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                                                                                                                  Edges An edge is where there is a

                                                                                                                  high change in gray level values

                                                                                                                  Objects are often separated from the background by edgesGray level profile

                                                                                                                  DTU Compute

                                                                                                                  2122018Introduction to Medical Image Analysis67 DTU Compute Technical University of Denmark

                                                                                                                  Edges The profile as a function f(d) What value is high when there

                                                                                                                  is an edgendash The slope of fndash The slope of the tangent at d

                                                                                                                  f(d)

                                                                                                                  119891119891prime(119889119889)

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                                                                                                                  Finite Difference Definition of slope

                                                                                                                  Approximation

                                                                                                                  Simpler approximationh = 1

                                                                                                                  119891119891prime 119889119889 = limℎrarr0

                                                                                                                  119891119891 119889119889 + ℎ minus 119891119891(119889119889)ℎ

                                                                                                                  119891119891prime 119889119889 asymp119891119891 119889119889 + ℎ minus 119891119891(119889119889)

                                                                                                                  ℎ

                                                                                                                  119891119891prime 119889119889 asymp 119891119891 119889119889 + 1 minus 119891119891(119889119889)

                                                                                                                  DTU Compute

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                                                                                                                  Edges Discrete approximation of frsquo(d) Can be implemented as a filter

                                                                                                                  -1 0 1

                                                                                                                  f(d-2) f(d-1) f(d) f(d+1) f(d+2) f(d+3)

                                                                                                                  f(d)

                                                                                                                  119891119891prime 119889119889 asymp 119891119891 119889119889 + 1 minus 119891119891(119889119889)

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                                                                                                                  Edges in 2D Changes in gray level values

                                                                                                                  ndash Image gradientndash Gradient is the 2D derivative of a 2D function f(xy)ndash Equal to the slope of the imagendash A steep slope is equal to an edge

                                                                                                                  120571120571119891119891 119909119909119910119910 = 119866(119892119892119909119909119892119892119910119910)

                                                                                                                  DTU Compute

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                                                                                                                  Edge filter kernel The Prewitt filter is a typical

                                                                                                                  edge filter Output image has high

                                                                                                                  values where there are edges

                                                                                                                  -1 0 1

                                                                                                                  -1 0 1

                                                                                                                  -1 0 1Vertical Prewitt filter

                                                                                                                  DTU Compute

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                                                                                                                  Prewitt filter

                                                                                                                  Original Prewitt Prewitt

                                                                                                                  Hot colormapSmooth 15x15

                                                                                                                  Smooth 15x15

                                                                                                                  Prewitt

                                                                                                                  DTU Compute

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                                                                                                                  Edge detection Edge filter

                                                                                                                  ndash Prewitt for example Thresholding

                                                                                                                  ndash Separate edges from non-edges

                                                                                                                  Output is binary imagendash Edges are white

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                                                                                                                  Edge filtering

                                                                                                                  A) MeanB) Horizontal SobelC) Vertical PrewittD) Horisontal PrewittE) Median

                                                                                                                  Der udfoslashres en filtrering (correlation) med et filter paring billedet Der bruges ikke coefficient normalization Den filtrerede vaeligrdi i den markerede pixel bliver -119 Hvilket et 3x3 filter blev benyttet

                                                                                                                  0

                                                                                                                  8

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                                                                                                                  02511 - Niveau af dagens emne forelaeligsingA) Meget letB) LetC) PassendeD) SvaeligrtE) Meget svaeligrt

                                                                                                                  23

                                                                                                                  6

                                                                                                                  10

                                                                                                                  A B C D E

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                                                                                                                  02512 - Niveau af dagens emne forelaeligsingA) Meget letB) LetC) PassendeD) SvaeligrtE) Meget svaeligrt

                                                                                                                  0 0

                                                                                                                  1

                                                                                                                  0 0

                                                                                                                  A B C D E

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                                                                                                                  0

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                                                                                                                  02511 - Mit eget udbytte af dagenA) Jeg har laeligrt meget lidtB) Lidt laeligringC) PassendeD) God laeligringE) Jeg har laeligrt meget

                                                                                                                  0 0

                                                                                                                  2

                                                                                                                  6

                                                                                                                  0

                                                                                                                  A B C D E

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                                                                                                                  0

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                                                                                                                  02512 - Mit eget udbytte af dagenA) Jeg har laeligrt meget lidtB) Lidt laeligringC) PassendeD) God laeligringE) Jeg har laeligrt meget

                                                                                                                  2

                                                                                                                  1

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                                                                                                                  2

                                                                                                                  0

                                                                                                                  A B C D E

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                                                                                                                  02511 - Sidste uges oslashvelser (pixelwiseoperations)A) Meget letteB) LetteC) PassendeD) SvaeligreE) Meget svaeligre

                                                                                                                  0 0

                                                                                                                  1

                                                                                                                  4

                                                                                                                  1

                                                                                                                  A B C D E

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                                                                                                                  02512 - Sidste uges oslashvelser (pixelwiseoperations)A) Meget letteB) LetteC) PassendeD) SvaeligreE) Meget svaeligre

                                                                                                                  3

                                                                                                                  0

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                                                                                                                  0 0

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                                                                                                                  0

                                                                                                                  Sheet1

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                                                                                                                  Denne uges brug af clickersA) click click click ndash jeg bliver

                                                                                                                  sindssygB) For meget clickC) PassendeD) Jeg vil gerne have lidt mereE) Jeg kan ikrsquo faring nok

                                                                                                                  0 0

                                                                                                                  5

                                                                                                                  0

                                                                                                                  6

                                                                                                                  A B C D E

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                                                                                                                  6

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                                                                                                                  What can you do after today Describe the difference between point processing and neighbourhood

                                                                                                                  processing Compute a rank filtered image using the min max median and

                                                                                                                  difference rank filters Compute a mean filtered image Decide if median or average filtering should be used for noise removal Choose the appropriate image border handling based on a given input

                                                                                                                  image Implement and apply template matching Compute the normalised cross correlation and explain why it should be

                                                                                                                  used Apply given image filter kernels to images Use edge filters on images Describe finite difference approximation of image gradients Describe the concept of edge detection

                                                                                                                  DTU Compute

                                                                                                                  2122018Introduction to Medical Image Analysis84 DTU Compute Technical University of Denmark

                                                                                                                  Oslashvelsesrapport over oslashvelse 4 - 02511 Oslashvelser taeligller cirka 30 af karakteren Skal afleveres senest den 7 marts kl 2359 Kan afleveres af 1 eller 2 personer

                                                                                                                  ndash I skal skrive jeres egen oslashvelsesrapportndash Brug mindst et af jeres egne billeder

                                                                                                                  Afleveres som PDF Lad vaeligre med at kopiere opgaveteksten ind i jeres

                                                                                                                  opgave Put Matlab kode i et Appendix og henvis fra teksten Eksempel rapport over oslashvelse findes paring

                                                                                                                  hjemmesiden under eksamen

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                                                                                                                  Exercises

                                                                                                                  • Introduction to Medical Image Analysis
                                                                                                                  • Lecture 4 ndash Neighbourhood Processing
                                                                                                                  • What can you do after today
                                                                                                                  • Point processing
                                                                                                                  • Point processing
                                                                                                                  • Neighbourhood processing
                                                                                                                  • Use of filtering
                                                                                                                  • Salt and pepper noise
                                                                                                                  • Salt and pepper noise
                                                                                                                  • What is so special about noise
                                                                                                                  • Noise ndash go away
                                                                                                                  • What is the median Value
                                                                                                                  • The median value
                                                                                                                  • Noise away ndash the median filter
                                                                                                                  • Noise removal ndash average filter
                                                                                                                  • Noise removal ndash median filter
                                                                                                                  • Image Filtering
                                                                                                                  • Median filter
                                                                                                                  • Rank filters
                                                                                                                  • Median filter
                                                                                                                  • Correlation
                                                                                                                  • Why do we need similarity
                                                                                                                  • Correlation (1D)
                                                                                                                  • Correlation (1D)
                                                                                                                  • Normalisation
                                                                                                                  • Normalisation
                                                                                                                  • Correlation on images
                                                                                                                  • Correlation on images
                                                                                                                  • Correlation on images
                                                                                                                  • Draw your filter
                                                                                                                  • Correlation on images ndash no normalisation
                                                                                                                  • Correlation on images ndash no normalisation 2
                                                                                                                  • Mathematics of 2D Correlation
                                                                                                                  • Mathematics of 2D Correlation
                                                                                                                  • Mathematics of 2D Correlation
                                                                                                                  • Slide Number 40
                                                                                                                  • 2D Kernel Normalisation
                                                                                                                  • Correlation
                                                                                                                  • Smoothing filters
                                                                                                                  • Use of smoothing
                                                                                                                  • Use of smoothing
                                                                                                                  • Mean filter
                                                                                                                  • Border handling
                                                                                                                  • Border handling ndash extend the input
                                                                                                                  • Correlation with zero padding
                                                                                                                  • Border handling ndash extend the input
                                                                                                                  • Template Matching
                                                                                                                  • Template Matching
                                                                                                                  • Template Matching
                                                                                                                  • Template Matching
                                                                                                                  • Problematic Correlation
                                                                                                                  • Normalised Cross Correlation
                                                                                                                  • Length of template
                                                                                                                  • Length of image patch
                                                                                                                  • Normalised Cross Correlation
                                                                                                                  • Normalised Cross Correlation
                                                                                                                  • Normalised Cross Correlation
                                                                                                                  • Edges
                                                                                                                  • Edges
                                                                                                                  • Finite Difference
                                                                                                                  • Edges
                                                                                                                  • Edges in 2D
                                                                                                                  • Edge filter kernel
                                                                                                                  • Prewitt filter
                                                                                                                  • Edge detection
                                                                                                                  • Edge filtering
                                                                                                                  • 02511 - Niveau af dagens emne forelaeligsing
                                                                                                                  • 02512 - Niveau af dagens emne forelaeligsing
                                                                                                                  • 02511 - Mit eget udbytte af dagen
                                                                                                                  • 02512 - Mit eget udbytte af dagen
                                                                                                                  • 02511 - Sidste uges oslashvelser (pixelwise operations)
                                                                                                                  • 02512 - Sidste uges oslashvelser (pixelwise operations)
                                                                                                                  • Denne uges brug af clickers
                                                                                                                  • What can you do after today
                                                                                                                  • Oslashvelsesrapport over oslashvelse 4 - 02511
                                                                                                                  • Exercises
                                                                                                                    A0
                                                                                                                    B0
                                                                                                                    C5
                                                                                                                    D0
                                                                                                                    E6
                                                                                                                    A
                                                                                                                    B
                                                                                                                    C
                                                                                                                    D
                                                                                                                    E
                                                                                                                    A3
                                                                                                                    B0
                                                                                                                    C3
                                                                                                                    D0
                                                                                                                    E0
                                                                                                                    A
                                                                                                                    B
                                                                                                                    C
                                                                                                                    D
                                                                                                                    E
                                                                                                                    A0
                                                                                                                    B0
                                                                                                                    C1
                                                                                                                    D4
                                                                                                                    E1
                                                                                                                    A
                                                                                                                    B
                                                                                                                    C
                                                                                                                    D
                                                                                                                    E
                                                                                                                    A2
                                                                                                                    B1
                                                                                                                    C3
                                                                                                                    D2
                                                                                                                    E0
                                                                                                                    A
                                                                                                                    B
                                                                                                                    C
                                                                                                                    D
                                                                                                                    E
                                                                                                                    A0
                                                                                                                    B0
                                                                                                                    C2
                                                                                                                    D6
                                                                                                                    E0
                                                                                                                    A
                                                                                                                    B
                                                                                                                    C
                                                                                                                    D
                                                                                                                    E
                                                                                                                    A0
                                                                                                                    B0
                                                                                                                    C1
                                                                                                                    D0
                                                                                                                    E0
                                                                                                                    A
                                                                                                                    B
                                                                                                                    C
                                                                                                                    D
                                                                                                                    E
                                                                                                                    A2
                                                                                                                    B3
                                                                                                                    C6
                                                                                                                    D1
                                                                                                                    E0
                                                                                                                    A
                                                                                                                    B
                                                                                                                    C
                                                                                                                    D
                                                                                                                    E
                                                                                                                    A0
                                                                                                                    B8
                                                                                                                    C1
                                                                                                                    D1
                                                                                                                    E0
                                                                                                                    A
                                                                                                                    B
                                                                                                                    C
                                                                                                                    D
                                                                                                                    E
                                                                                                                    A1
                                                                                                                    B2
                                                                                                                    C2
                                                                                                                    D3
                                                                                                                    E2
                                                                                                                    A
                                                                                                                    B
                                                                                                                    C
                                                                                                                    D
                                                                                                                    E
                                                                                                                    A0
                                                                                                                    B13
                                                                                                                    C0
                                                                                                                    D0
                                                                                                                    E0
                                                                                                                    A
                                                                                                                    B
                                                                                                                    C
                                                                                                                    D
                                                                                                                    E

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                                                                                                                    2122018Introduction to Medical Image Analysis50 DTU Compute Technical University of Denmark

                                                                                                                    Border handling ndash extend the input

                                                                                                                    0 2 41 2 2

                                                                                                                    1 6 3

                                                                                                                    1 2 12 5 3

                                                                                                                    2 1 3

                                                                                                                    1 3 1

                                                                                                                    2 2 2

                                                                                                                    0 1 3

                                                                                                                    1 2 0

                                                                                                                    2 1 4

                                                                                                                    1 0 1

                                                                                                                    Input

                                                                                                                    0 0 0 0 000000

                                                                                                                    bull Zero padding ndash what happens

                                                                                                                    bull Zero is black ndash creates dark border around the image

                                                                                                                    DTU Compute

                                                                                                                    2122018Introduction to Medical Image Analysis51 DTU Compute Technical University of Denmark

                                                                                                                    Correlation with zero paddingA) 5 8B) 12 16C) 13 3D) 15 21E) 17 12

                                                                                                                    1 2 11 3 11 2 1

                                                                                                                    0 2 41 2 2

                                                                                                                    1 6 3

                                                                                                                    1 2 12 5 3

                                                                                                                    2 1 3

                                                                                                                    1 3 1

                                                                                                                    2 2 2

                                                                                                                    0 1 3

                                                                                                                    1 2 0

                                                                                                                    2 1 4

                                                                                                                    1 0 1

                                                                                                                    0

                                                                                                                    13

                                                                                                                    0 0 0

                                                                                                                    A B C D E

                                                                                                                    Chart1

                                                                                                                    0
                                                                                                                    13
                                                                                                                    0
                                                                                                                    0
                                                                                                                    0

                                                                                                                    Sheet1

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                                                                                                                    Border handling ndash extend the input

                                                                                                                    0 2 41 2 2

                                                                                                                    1 6 3

                                                                                                                    1 2 12 5 3

                                                                                                                    2 1 3

                                                                                                                    1 3 1

                                                                                                                    2 2 2

                                                                                                                    0 1 3

                                                                                                                    1 2 0

                                                                                                                    2 1 4

                                                                                                                    1 0 1

                                                                                                                    Input

                                                                                                                    1 2 0 1 311211

                                                                                                                    bull Reflection

                                                                                                                    bull Normally better than zero padding

                                                                                                                    DTU Compute

                                                                                                                    2122018Introduction to Medical Image Analysis54 DTU Compute Technical University of Denmark

                                                                                                                    Template Matching Template

                                                                                                                    ndash Skabelon paring dansk Locates objects in images

                                                                                                                    Input

                                                                                                                    Template

                                                                                                                    Output Correlation image

                                                                                                                    DTU Compute

                                                                                                                    2122018Introduction to Medical Image Analysis55 DTU Compute Technical University of Denmark

                                                                                                                    Template Matching The correlation between the template and the input

                                                                                                                    image is computed for each pixel

                                                                                                                    Input

                                                                                                                    Template

                                                                                                                    Output Correlation image

                                                                                                                    DTU Compute

                                                                                                                    2122018Introduction to Medical Image Analysis56 DTU Compute Technical University of Denmark

                                                                                                                    Template Matching The pixel with the highest value is found in the

                                                                                                                    output imagendash Here is the highest correlation

                                                                                                                    Input

                                                                                                                    Template

                                                                                                                    Output Correlation image

                                                                                                                    DTU Compute

                                                                                                                    2122018Introduction to Medical Image Analysis57 DTU Compute Technical University of Denmark

                                                                                                                    Template Matching This corresponds to the found pattern in the input

                                                                                                                    image

                                                                                                                    Input

                                                                                                                    Template

                                                                                                                    Output Correlation image

                                                                                                                    DTU Compute

                                                                                                                    2122018Introduction to Medical Image Analysis58 DTU Compute Technical University of Denmark

                                                                                                                    Problematic Correlation Correlation matching has problem with light areas ndash

                                                                                                                    why

                                                                                                                    Input (f)

                                                                                                                    Template (h)

                                                                                                                    Output Correlation imageFake max

                                                                                                                    Real max

                                                                                                                    Very High119892119892 119909119909119910119910 = 119895119895=minus119877119877

                                                                                                                    119877119877

                                                                                                                    119894119894=minus119877119877

                                                                                                                    119877119877

                                                                                                                    ℎ(119894119894 119895119895) 119891119891(119909119909 + 119894119894119910119910 + 119895119895)

                                                                                                                    DTU Compute

                                                                                                                    2122018Introduction to Medical Image Analysis59 DTU Compute Technical University of Denmark

                                                                                                                    Normalised Cross Correlation

                                                                                                                    Input (f)

                                                                                                                    Template (h)

                                                                                                                    Output Correlation image

                                                                                                                    Real max

                                                                                                                    NCC x y =Correlation

                                                                                                                    Length of image patch sdot Length of template

                                                                                                                    DTU Compute

                                                                                                                    2122018Introduction to Medical Image Analysis60 DTU Compute Technical University of Denmark

                                                                                                                    Length of template Vector length

                                                                                                                    ndash Put all pixel values into a vectorndash Compute the length of this vector

                                                                                                                    Describes the intensity of the templatendash Bright template has a large lengthndash Dark template has a small length

                                                                                                                    Template (h)

                                                                                                                    Length of template = 119895119895=minus119877119877

                                                                                                                    119877119877

                                                                                                                    119894119894=minus119877119877

                                                                                                                    119877119877

                                                                                                                    ℎ(119894119894 119895119895) ℎ(119894119894 119895119895)

                                                                                                                    DTU Compute

                                                                                                                    2122018Introduction to Medical Image Analysis61 DTU Compute Technical University of Denmark

                                                                                                                    Length of image patch Vector length based on pixel values in image patch Describes the intensity of the image patch

                                                                                                                    Template (h)

                                                                                                                    Input (f) with patch

                                                                                                                    DTU Compute

                                                                                                                    2122018Introduction to Medical Image Analysis62 DTU Compute Technical University of Denmark

                                                                                                                    Normalised Cross Correlation The length of the image patch and the length of

                                                                                                                    template normalise the NCC If the image is very bright the NCC will be ldquopulled

                                                                                                                    downrdquo

                                                                                                                    NCC x y =Correlation

                                                                                                                    Length of image patch sdot Length of template

                                                                                                                    DTU Compute

                                                                                                                    2122018Introduction to Medical Image Analysis63 DTU Compute Technical University of Denmark

                                                                                                                    Normalised Cross Correlation NCC will be between

                                                                                                                    ndash 0 No similarity between template and image patchndash 1 Template and image patch are identical

                                                                                                                    Input (f)

                                                                                                                    Template (h)

                                                                                                                    Output Correlation image

                                                                                                                    Real max

                                                                                                                    NCC x y =Correlation

                                                                                                                    Length of image patch sdot Length of template

                                                                                                                    DTU Compute

                                                                                                                    2122018Introduction to Medical Image Analysis64 DTU Compute Technical University of Denmark

                                                                                                                    Normalised Cross Correlation

                                                                                                                    A) 010B) 033C) 083D) 062E) 098

                                                                                                                    Der udfoslashres template matching med og normalized crosscorrelation (NCC) beregnes Hvad bliver NNC i den markerede pixel

                                                                                                                    1

                                                                                                                    2 2

                                                                                                                    3

                                                                                                                    2

                                                                                                                    A B C D E

                                                                                                                    Chart1

                                                                                                                    1
                                                                                                                    2
                                                                                                                    2
                                                                                                                    3
                                                                                                                    2

                                                                                                                    Sheet1

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                                                                                                                    Edges An edge is where there is a

                                                                                                                    high change in gray level values

                                                                                                                    Objects are often separated from the background by edgesGray level profile

                                                                                                                    DTU Compute

                                                                                                                    2122018Introduction to Medical Image Analysis67 DTU Compute Technical University of Denmark

                                                                                                                    Edges The profile as a function f(d) What value is high when there

                                                                                                                    is an edgendash The slope of fndash The slope of the tangent at d

                                                                                                                    f(d)

                                                                                                                    119891119891prime(119889119889)

                                                                                                                    DTU Compute

                                                                                                                    2122018Introduction to Medical Image Analysis68 DTU Compute Technical University of Denmark

                                                                                                                    Finite Difference Definition of slope

                                                                                                                    Approximation

                                                                                                                    Simpler approximationh = 1

                                                                                                                    119891119891prime 119889119889 = limℎrarr0

                                                                                                                    119891119891 119889119889 + ℎ minus 119891119891(119889119889)ℎ

                                                                                                                    119891119891prime 119889119889 asymp119891119891 119889119889 + ℎ minus 119891119891(119889119889)

                                                                                                                    ℎ

                                                                                                                    119891119891prime 119889119889 asymp 119891119891 119889119889 + 1 minus 119891119891(119889119889)

                                                                                                                    DTU Compute

                                                                                                                    2122018Introduction to Medical Image Analysis69 DTU Compute Technical University of Denmark

                                                                                                                    Edges Discrete approximation of frsquo(d) Can be implemented as a filter

                                                                                                                    -1 0 1

                                                                                                                    f(d-2) f(d-1) f(d) f(d+1) f(d+2) f(d+3)

                                                                                                                    f(d)

                                                                                                                    119891119891prime 119889119889 asymp 119891119891 119889119889 + 1 minus 119891119891(119889119889)

                                                                                                                    DTU Compute

                                                                                                                    2122018Introduction to Medical Image Analysis70 DTU Compute Technical University of Denmark

                                                                                                                    Edges in 2D Changes in gray level values

                                                                                                                    ndash Image gradientndash Gradient is the 2D derivative of a 2D function f(xy)ndash Equal to the slope of the imagendash A steep slope is equal to an edge

                                                                                                                    120571120571119891119891 119909119909119910119910 = 119866(119892119892119909119909119892119892119910119910)

                                                                                                                    DTU Compute

                                                                                                                    2122018Introduction to Medical Image Analysis71 DTU Compute Technical University of Denmark

                                                                                                                    Edge filter kernel The Prewitt filter is a typical

                                                                                                                    edge filter Output image has high

                                                                                                                    values where there are edges

                                                                                                                    -1 0 1

                                                                                                                    -1 0 1

                                                                                                                    -1 0 1Vertical Prewitt filter

                                                                                                                    DTU Compute

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                                                                                                                    Prewitt filter

                                                                                                                    Original Prewitt Prewitt

                                                                                                                    Hot colormapSmooth 15x15

                                                                                                                    Smooth 15x15

                                                                                                                    Prewitt

                                                                                                                    DTU Compute

                                                                                                                    2122018Introduction to Medical Image Analysis73 DTU Compute Technical University of Denmark

                                                                                                                    Edge detection Edge filter

                                                                                                                    ndash Prewitt for example Thresholding

                                                                                                                    ndash Separate edges from non-edges

                                                                                                                    Output is binary imagendash Edges are white

                                                                                                                    DTU Compute

                                                                                                                    2122018Introduction to Medical Image Analysis74 DTU Compute Technical University of Denmark

                                                                                                                    Edge filtering

                                                                                                                    A) MeanB) Horizontal SobelC) Vertical PrewittD) Horisontal PrewittE) Median

                                                                                                                    Der udfoslashres en filtrering (correlation) med et filter paring billedet Der bruges ikke coefficient normalization Den filtrerede vaeligrdi i den markerede pixel bliver -119 Hvilket et 3x3 filter blev benyttet

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                                                                                                                    02511 - Niveau af dagens emne forelaeligsingA) Meget letB) LetC) PassendeD) SvaeligrtE) Meget svaeligrt

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                                                                                                                    02512 - Niveau af dagens emne forelaeligsingA) Meget letB) LetC) PassendeD) SvaeligrtE) Meget svaeligrt

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                                                                                                                    02511 - Mit eget udbytte af dagenA) Jeg har laeligrt meget lidtB) Lidt laeligringC) PassendeD) God laeligringE) Jeg har laeligrt meget

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                                                                                                                    02512 - Mit eget udbytte af dagenA) Jeg har laeligrt meget lidtB) Lidt laeligringC) PassendeD) God laeligringE) Jeg har laeligrt meget

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                                                                                                                    02511 - Sidste uges oslashvelser (pixelwiseoperations)A) Meget letteB) LetteC) PassendeD) SvaeligreE) Meget svaeligre

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                                                                                                                    02512 - Sidste uges oslashvelser (pixelwiseoperations)A) Meget letteB) LetteC) PassendeD) SvaeligreE) Meget svaeligre

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                                                                                                                    2122018Introduction to Medical Image Analysis82 DTU Compute Technical University of Denmark

                                                                                                                    Denne uges brug af clickersA) click click click ndash jeg bliver

                                                                                                                    sindssygB) For meget clickC) PassendeD) Jeg vil gerne have lidt mereE) Jeg kan ikrsquo faring nok

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                                                                                                                    What can you do after today Describe the difference between point processing and neighbourhood

                                                                                                                    processing Compute a rank filtered image using the min max median and

                                                                                                                    difference rank filters Compute a mean filtered image Decide if median or average filtering should be used for noise removal Choose the appropriate image border handling based on a given input

                                                                                                                    image Implement and apply template matching Compute the normalised cross correlation and explain why it should be

                                                                                                                    used Apply given image filter kernels to images Use edge filters on images Describe finite difference approximation of image gradients Describe the concept of edge detection

                                                                                                                    DTU Compute

                                                                                                                    2122018Introduction to Medical Image Analysis84 DTU Compute Technical University of Denmark

                                                                                                                    Oslashvelsesrapport over oslashvelse 4 - 02511 Oslashvelser taeligller cirka 30 af karakteren Skal afleveres senest den 7 marts kl 2359 Kan afleveres af 1 eller 2 personer

                                                                                                                    ndash I skal skrive jeres egen oslashvelsesrapportndash Brug mindst et af jeres egne billeder

                                                                                                                    Afleveres som PDF Lad vaeligre med at kopiere opgaveteksten ind i jeres

                                                                                                                    opgave Put Matlab kode i et Appendix og henvis fra teksten Eksempel rapport over oslashvelse findes paring

                                                                                                                    hjemmesiden under eksamen

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                                                                                                                    2122018Introduction to Medical Image Analysis85 DTU Compute Technical University of Denmark

                                                                                                                    Exercises

                                                                                                                    • Introduction to Medical Image Analysis
                                                                                                                    • Lecture 4 ndash Neighbourhood Processing
                                                                                                                    • What can you do after today
                                                                                                                    • Point processing
                                                                                                                    • Point processing
                                                                                                                    • Neighbourhood processing
                                                                                                                    • Use of filtering
                                                                                                                    • Salt and pepper noise
                                                                                                                    • Salt and pepper noise
                                                                                                                    • What is so special about noise
                                                                                                                    • Noise ndash go away
                                                                                                                    • What is the median Value
                                                                                                                    • The median value
                                                                                                                    • Noise away ndash the median filter
                                                                                                                    • Noise removal ndash average filter
                                                                                                                    • Noise removal ndash median filter
                                                                                                                    • Image Filtering
                                                                                                                    • Median filter
                                                                                                                    • Rank filters
                                                                                                                    • Median filter
                                                                                                                    • Correlation
                                                                                                                    • Why do we need similarity
                                                                                                                    • Correlation (1D)
                                                                                                                    • Correlation (1D)
                                                                                                                    • Normalisation
                                                                                                                    • Normalisation
                                                                                                                    • Correlation on images
                                                                                                                    • Correlation on images
                                                                                                                    • Correlation on images
                                                                                                                    • Draw your filter
                                                                                                                    • Correlation on images ndash no normalisation
                                                                                                                    • Correlation on images ndash no normalisation 2
                                                                                                                    • Mathematics of 2D Correlation
                                                                                                                    • Mathematics of 2D Correlation
                                                                                                                    • Mathematics of 2D Correlation
                                                                                                                    • Slide Number 40
                                                                                                                    • 2D Kernel Normalisation
                                                                                                                    • Correlation
                                                                                                                    • Smoothing filters
                                                                                                                    • Use of smoothing
                                                                                                                    • Use of smoothing
                                                                                                                    • Mean filter
                                                                                                                    • Border handling
                                                                                                                    • Border handling ndash extend the input
                                                                                                                    • Correlation with zero padding
                                                                                                                    • Border handling ndash extend the input
                                                                                                                    • Template Matching
                                                                                                                    • Template Matching
                                                                                                                    • Template Matching
                                                                                                                    • Template Matching
                                                                                                                    • Problematic Correlation
                                                                                                                    • Normalised Cross Correlation
                                                                                                                    • Length of template
                                                                                                                    • Length of image patch
                                                                                                                    • Normalised Cross Correlation
                                                                                                                    • Normalised Cross Correlation
                                                                                                                    • Normalised Cross Correlation
                                                                                                                    • Edges
                                                                                                                    • Edges
                                                                                                                    • Finite Difference
                                                                                                                    • Edges
                                                                                                                    • Edges in 2D
                                                                                                                    • Edge filter kernel
                                                                                                                    • Prewitt filter
                                                                                                                    • Edge detection
                                                                                                                    • Edge filtering
                                                                                                                    • 02511 - Niveau af dagens emne forelaeligsing
                                                                                                                    • 02512 - Niveau af dagens emne forelaeligsing
                                                                                                                    • 02511 - Mit eget udbytte af dagen
                                                                                                                    • 02512 - Mit eget udbytte af dagen
                                                                                                                    • 02511 - Sidste uges oslashvelser (pixelwise operations)
                                                                                                                    • 02512 - Sidste uges oslashvelser (pixelwise operations)
                                                                                                                    • Denne uges brug af clickers
                                                                                                                    • What can you do after today
                                                                                                                    • Oslashvelsesrapport over oslashvelse 4 - 02511
                                                                                                                    • Exercises
                                                                                                                      A0
                                                                                                                      B0
                                                                                                                      C5
                                                                                                                      D0
                                                                                                                      E6
                                                                                                                      A
                                                                                                                      B
                                                                                                                      C
                                                                                                                      D
                                                                                                                      E
                                                                                                                      A3
                                                                                                                      B0
                                                                                                                      C3
                                                                                                                      D0
                                                                                                                      E0
                                                                                                                      A
                                                                                                                      B
                                                                                                                      C
                                                                                                                      D
                                                                                                                      E
                                                                                                                      A0
                                                                                                                      B0
                                                                                                                      C1
                                                                                                                      D4
                                                                                                                      E1
                                                                                                                      A
                                                                                                                      B
                                                                                                                      C
                                                                                                                      D
                                                                                                                      E
                                                                                                                      A2
                                                                                                                      B1
                                                                                                                      C3
                                                                                                                      D2
                                                                                                                      E0
                                                                                                                      A
                                                                                                                      B
                                                                                                                      C
                                                                                                                      D
                                                                                                                      E
                                                                                                                      A0
                                                                                                                      B0
                                                                                                                      C2
                                                                                                                      D6
                                                                                                                      E0
                                                                                                                      A
                                                                                                                      B
                                                                                                                      C
                                                                                                                      D
                                                                                                                      E
                                                                                                                      A0
                                                                                                                      B0
                                                                                                                      C1
                                                                                                                      D0
                                                                                                                      E0
                                                                                                                      A
                                                                                                                      B
                                                                                                                      C
                                                                                                                      D
                                                                                                                      E
                                                                                                                      A2
                                                                                                                      B3
                                                                                                                      C6
                                                                                                                      D1
                                                                                                                      E0
                                                                                                                      A
                                                                                                                      B
                                                                                                                      C
                                                                                                                      D
                                                                                                                      E
                                                                                                                      A0
                                                                                                                      B8
                                                                                                                      C1
                                                                                                                      D1
                                                                                                                      E0
                                                                                                                      A
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                                                                                                                      C
                                                                                                                      D
                                                                                                                      E
                                                                                                                      A1
                                                                                                                      B2
                                                                                                                      C2
                                                                                                                      D3
                                                                                                                      E2
                                                                                                                      A
                                                                                                                      B
                                                                                                                      C
                                                                                                                      D
                                                                                                                      E
                                                                                                                      A0
                                                                                                                      B13
                                                                                                                      C0
                                                                                                                      D0
                                                                                                                      E0
                                                                                                                      A
                                                                                                                      B
                                                                                                                      C
                                                                                                                      D
                                                                                                                      E

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                                                                                                                      2122018Introduction to Medical Image Analysis51 DTU Compute Technical University of Denmark

                                                                                                                      Correlation with zero paddingA) 5 8B) 12 16C) 13 3D) 15 21E) 17 12

                                                                                                                      1 2 11 3 11 2 1

                                                                                                                      0 2 41 2 2

                                                                                                                      1 6 3

                                                                                                                      1 2 12 5 3

                                                                                                                      2 1 3

                                                                                                                      1 3 1

                                                                                                                      2 2 2

                                                                                                                      0 1 3

                                                                                                                      1 2 0

                                                                                                                      2 1 4

                                                                                                                      1 0 1

                                                                                                                      0

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                                                                                                                      Border handling ndash extend the input

                                                                                                                      0 2 41 2 2

                                                                                                                      1 6 3

                                                                                                                      1 2 12 5 3

                                                                                                                      2 1 3

                                                                                                                      1 3 1

                                                                                                                      2 2 2

                                                                                                                      0 1 3

                                                                                                                      1 2 0

                                                                                                                      2 1 4

                                                                                                                      1 0 1

                                                                                                                      Input

                                                                                                                      1 2 0 1 311211

                                                                                                                      bull Reflection

                                                                                                                      bull Normally better than zero padding

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                                                                                                                      Template Matching Template

                                                                                                                      ndash Skabelon paring dansk Locates objects in images

                                                                                                                      Input

                                                                                                                      Template

                                                                                                                      Output Correlation image

                                                                                                                      DTU Compute

                                                                                                                      2122018Introduction to Medical Image Analysis55 DTU Compute Technical University of Denmark

                                                                                                                      Template Matching The correlation between the template and the input

                                                                                                                      image is computed for each pixel

                                                                                                                      Input

                                                                                                                      Template

                                                                                                                      Output Correlation image

                                                                                                                      DTU Compute

                                                                                                                      2122018Introduction to Medical Image Analysis56 DTU Compute Technical University of Denmark

                                                                                                                      Template Matching The pixel with the highest value is found in the

                                                                                                                      output imagendash Here is the highest correlation

                                                                                                                      Input

                                                                                                                      Template

                                                                                                                      Output Correlation image

                                                                                                                      DTU Compute

                                                                                                                      2122018Introduction to Medical Image Analysis57 DTU Compute Technical University of Denmark

                                                                                                                      Template Matching This corresponds to the found pattern in the input

                                                                                                                      image

                                                                                                                      Input

                                                                                                                      Template

                                                                                                                      Output Correlation image

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                                                                                                                      2122018Introduction to Medical Image Analysis58 DTU Compute Technical University of Denmark

                                                                                                                      Problematic Correlation Correlation matching has problem with light areas ndash

                                                                                                                      why

                                                                                                                      Input (f)

                                                                                                                      Template (h)

                                                                                                                      Output Correlation imageFake max

                                                                                                                      Real max

                                                                                                                      Very High119892119892 119909119909119910119910 = 119895119895=minus119877119877

                                                                                                                      119877119877

                                                                                                                      119894119894=minus119877119877

                                                                                                                      119877119877

                                                                                                                      ℎ(119894119894 119895119895) 119891119891(119909119909 + 119894119894119910119910 + 119895119895)

                                                                                                                      DTU Compute

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                                                                                                                      Normalised Cross Correlation

                                                                                                                      Input (f)

                                                                                                                      Template (h)

                                                                                                                      Output Correlation image

                                                                                                                      Real max

                                                                                                                      NCC x y =Correlation

                                                                                                                      Length of image patch sdot Length of template

                                                                                                                      DTU Compute

                                                                                                                      2122018Introduction to Medical Image Analysis60 DTU Compute Technical University of Denmark

                                                                                                                      Length of template Vector length

                                                                                                                      ndash Put all pixel values into a vectorndash Compute the length of this vector

                                                                                                                      Describes the intensity of the templatendash Bright template has a large lengthndash Dark template has a small length

                                                                                                                      Template (h)

                                                                                                                      Length of template = 119895119895=minus119877119877

                                                                                                                      119877119877

                                                                                                                      119894119894=minus119877119877

                                                                                                                      119877119877

                                                                                                                      ℎ(119894119894 119895119895) ℎ(119894119894 119895119895)

                                                                                                                      DTU Compute

                                                                                                                      2122018Introduction to Medical Image Analysis61 DTU Compute Technical University of Denmark

                                                                                                                      Length of image patch Vector length based on pixel values in image patch Describes the intensity of the image patch

                                                                                                                      Template (h)

                                                                                                                      Input (f) with patch

                                                                                                                      DTU Compute

                                                                                                                      2122018Introduction to Medical Image Analysis62 DTU Compute Technical University of Denmark

                                                                                                                      Normalised Cross Correlation The length of the image patch and the length of

                                                                                                                      template normalise the NCC If the image is very bright the NCC will be ldquopulled

                                                                                                                      downrdquo

                                                                                                                      NCC x y =Correlation

                                                                                                                      Length of image patch sdot Length of template

                                                                                                                      DTU Compute

                                                                                                                      2122018Introduction to Medical Image Analysis63 DTU Compute Technical University of Denmark

                                                                                                                      Normalised Cross Correlation NCC will be between

                                                                                                                      ndash 0 No similarity between template and image patchndash 1 Template and image patch are identical

                                                                                                                      Input (f)

                                                                                                                      Template (h)

                                                                                                                      Output Correlation image

                                                                                                                      Real max

                                                                                                                      NCC x y =Correlation

                                                                                                                      Length of image patch sdot Length of template

                                                                                                                      DTU Compute

                                                                                                                      2122018Introduction to Medical Image Analysis64 DTU Compute Technical University of Denmark

                                                                                                                      Normalised Cross Correlation

                                                                                                                      A) 010B) 033C) 083D) 062E) 098

                                                                                                                      Der udfoslashres template matching med og normalized crosscorrelation (NCC) beregnes Hvad bliver NNC i den markerede pixel

                                                                                                                      1

                                                                                                                      2 2

                                                                                                                      3

                                                                                                                      2

                                                                                                                      A B C D E

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                                                                                                                      1
                                                                                                                      2
                                                                                                                      2
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                                                                                                                      Edges An edge is where there is a

                                                                                                                      high change in gray level values

                                                                                                                      Objects are often separated from the background by edgesGray level profile

                                                                                                                      DTU Compute

                                                                                                                      2122018Introduction to Medical Image Analysis67 DTU Compute Technical University of Denmark

                                                                                                                      Edges The profile as a function f(d) What value is high when there

                                                                                                                      is an edgendash The slope of fndash The slope of the tangent at d

                                                                                                                      f(d)

                                                                                                                      119891119891prime(119889119889)

                                                                                                                      DTU Compute

                                                                                                                      2122018Introduction to Medical Image Analysis68 DTU Compute Technical University of Denmark

                                                                                                                      Finite Difference Definition of slope

                                                                                                                      Approximation

                                                                                                                      Simpler approximationh = 1

                                                                                                                      119891119891prime 119889119889 = limℎrarr0

                                                                                                                      119891119891 119889119889 + ℎ minus 119891119891(119889119889)ℎ

                                                                                                                      119891119891prime 119889119889 asymp119891119891 119889119889 + ℎ minus 119891119891(119889119889)

                                                                                                                      ℎ

                                                                                                                      119891119891prime 119889119889 asymp 119891119891 119889119889 + 1 minus 119891119891(119889119889)

                                                                                                                      DTU Compute

                                                                                                                      2122018Introduction to Medical Image Analysis69 DTU Compute Technical University of Denmark

                                                                                                                      Edges Discrete approximation of frsquo(d) Can be implemented as a filter

                                                                                                                      -1 0 1

                                                                                                                      f(d-2) f(d-1) f(d) f(d+1) f(d+2) f(d+3)

                                                                                                                      f(d)

                                                                                                                      119891119891prime 119889119889 asymp 119891119891 119889119889 + 1 minus 119891119891(119889119889)

                                                                                                                      DTU Compute

                                                                                                                      2122018Introduction to Medical Image Analysis70 DTU Compute Technical University of Denmark

                                                                                                                      Edges in 2D Changes in gray level values

                                                                                                                      ndash Image gradientndash Gradient is the 2D derivative of a 2D function f(xy)ndash Equal to the slope of the imagendash A steep slope is equal to an edge

                                                                                                                      120571120571119891119891 119909119909119910119910 = 119866(119892119892119909119909119892119892119910119910)

                                                                                                                      DTU Compute

                                                                                                                      2122018Introduction to Medical Image Analysis71 DTU Compute Technical University of Denmark

                                                                                                                      Edge filter kernel The Prewitt filter is a typical

                                                                                                                      edge filter Output image has high

                                                                                                                      values where there are edges

                                                                                                                      -1 0 1

                                                                                                                      -1 0 1

                                                                                                                      -1 0 1Vertical Prewitt filter

                                                                                                                      DTU Compute

                                                                                                                      2122018Introduction to Medical Image Analysis72 DTU Compute Technical University of Denmark

                                                                                                                      Prewitt filter

                                                                                                                      Original Prewitt Prewitt

                                                                                                                      Hot colormapSmooth 15x15

                                                                                                                      Smooth 15x15

                                                                                                                      Prewitt

                                                                                                                      DTU Compute

                                                                                                                      2122018Introduction to Medical Image Analysis73 DTU Compute Technical University of Denmark

                                                                                                                      Edge detection Edge filter

                                                                                                                      ndash Prewitt for example Thresholding

                                                                                                                      ndash Separate edges from non-edges

                                                                                                                      Output is binary imagendash Edges are white

                                                                                                                      DTU Compute

                                                                                                                      2122018Introduction to Medical Image Analysis74 DTU Compute Technical University of Denmark

                                                                                                                      Edge filtering

                                                                                                                      A) MeanB) Horizontal SobelC) Vertical PrewittD) Horisontal PrewittE) Median

                                                                                                                      Der udfoslashres en filtrering (correlation) med et filter paring billedet Der bruges ikke coefficient normalization Den filtrerede vaeligrdi i den markerede pixel bliver -119 Hvilket et 3x3 filter blev benyttet

                                                                                                                      0

                                                                                                                      8

                                                                                                                      1 10

                                                                                                                      A B C D E

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                                                                                                                      02511 - Niveau af dagens emne forelaeligsingA) Meget letB) LetC) PassendeD) SvaeligrtE) Meget svaeligrt

                                                                                                                      23

                                                                                                                      6

                                                                                                                      10

                                                                                                                      A B C D E

                                                                                                                      Chart1

                                                                                                                      2
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                                                                                                                      6
                                                                                                                      1
                                                                                                                      0

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                                                                                                                      2122018Introduction to Medical Image Analysis77 DTU Compute Technical University of Denmark

                                                                                                                      02512 - Niveau af dagens emne forelaeligsingA) Meget letB) LetC) PassendeD) SvaeligrtE) Meget svaeligrt

                                                                                                                      0 0

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                                                                                                                      02511 - Mit eget udbytte af dagenA) Jeg har laeligrt meget lidtB) Lidt laeligringC) PassendeD) God laeligringE) Jeg har laeligrt meget

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                                                                                                                      02512 - Mit eget udbytte af dagenA) Jeg har laeligrt meget lidtB) Lidt laeligringC) PassendeD) God laeligringE) Jeg har laeligrt meget

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                                                                                                                      02511 - Sidste uges oslashvelser (pixelwiseoperations)A) Meget letteB) LetteC) PassendeD) SvaeligreE) Meget svaeligre

                                                                                                                      0 0

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                                                                                                                      02512 - Sidste uges oslashvelser (pixelwiseoperations)A) Meget letteB) LetteC) PassendeD) SvaeligreE) Meget svaeligre

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                                                                                                                      2122018Introduction to Medical Image Analysis82 DTU Compute Technical University of Denmark

                                                                                                                      Denne uges brug af clickersA) click click click ndash jeg bliver

                                                                                                                      sindssygB) For meget clickC) PassendeD) Jeg vil gerne have lidt mereE) Jeg kan ikrsquo faring nok

                                                                                                                      0 0

                                                                                                                      5

                                                                                                                      0

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                                                                                                                      2122018Introduction to Medical Image Analysis83 DTU Compute Technical University of Denmark

                                                                                                                      What can you do after today Describe the difference between point processing and neighbourhood

                                                                                                                      processing Compute a rank filtered image using the min max median and

                                                                                                                      difference rank filters Compute a mean filtered image Decide if median or average filtering should be used for noise removal Choose the appropriate image border handling based on a given input

                                                                                                                      image Implement and apply template matching Compute the normalised cross correlation and explain why it should be

                                                                                                                      used Apply given image filter kernels to images Use edge filters on images Describe finite difference approximation of image gradients Describe the concept of edge detection

                                                                                                                      DTU Compute

                                                                                                                      2122018Introduction to Medical Image Analysis84 DTU Compute Technical University of Denmark

                                                                                                                      Oslashvelsesrapport over oslashvelse 4 - 02511 Oslashvelser taeligller cirka 30 af karakteren Skal afleveres senest den 7 marts kl 2359 Kan afleveres af 1 eller 2 personer

                                                                                                                      ndash I skal skrive jeres egen oslashvelsesrapportndash Brug mindst et af jeres egne billeder

                                                                                                                      Afleveres som PDF Lad vaeligre med at kopiere opgaveteksten ind i jeres

                                                                                                                      opgave Put Matlab kode i et Appendix og henvis fra teksten Eksempel rapport over oslashvelse findes paring

                                                                                                                      hjemmesiden under eksamen

                                                                                                                      DTU Compute

                                                                                                                      2122018Introduction to Medical Image Analysis85 DTU Compute Technical University of Denmark

                                                                                                                      Exercises

                                                                                                                      • Introduction to Medical Image Analysis
                                                                                                                      • Lecture 4 ndash Neighbourhood Processing
                                                                                                                      • What can you do after today
                                                                                                                      • Point processing
                                                                                                                      • Point processing
                                                                                                                      • Neighbourhood processing
                                                                                                                      • Use of filtering
                                                                                                                      • Salt and pepper noise
                                                                                                                      • Salt and pepper noise
                                                                                                                      • What is so special about noise
                                                                                                                      • Noise ndash go away
                                                                                                                      • What is the median Value
                                                                                                                      • The median value
                                                                                                                      • Noise away ndash the median filter
                                                                                                                      • Noise removal ndash average filter
                                                                                                                      • Noise removal ndash median filter
                                                                                                                      • Image Filtering
                                                                                                                      • Median filter
                                                                                                                      • Rank filters
                                                                                                                      • Median filter
                                                                                                                      • Correlation
                                                                                                                      • Why do we need similarity
                                                                                                                      • Correlation (1D)
                                                                                                                      • Correlation (1D)
                                                                                                                      • Normalisation
                                                                                                                      • Normalisation
                                                                                                                      • Correlation on images
                                                                                                                      • Correlation on images
                                                                                                                      • Correlation on images
                                                                                                                      • Draw your filter
                                                                                                                      • Correlation on images ndash no normalisation
                                                                                                                      • Correlation on images ndash no normalisation 2
                                                                                                                      • Mathematics of 2D Correlation
                                                                                                                      • Mathematics of 2D Correlation
                                                                                                                      • Mathematics of 2D Correlation
                                                                                                                      • Slide Number 40
                                                                                                                      • 2D Kernel Normalisation
                                                                                                                      • Correlation
                                                                                                                      • Smoothing filters
                                                                                                                      • Use of smoothing
                                                                                                                      • Use of smoothing
                                                                                                                      • Mean filter
                                                                                                                      • Border handling
                                                                                                                      • Border handling ndash extend the input
                                                                                                                      • Correlation with zero padding
                                                                                                                      • Border handling ndash extend the input
                                                                                                                      • Template Matching
                                                                                                                      • Template Matching
                                                                                                                      • Template Matching
                                                                                                                      • Template Matching
                                                                                                                      • Problematic Correlation
                                                                                                                      • Normalised Cross Correlation
                                                                                                                      • Length of template
                                                                                                                      • Length of image patch
                                                                                                                      • Normalised Cross Correlation
                                                                                                                      • Normalised Cross Correlation
                                                                                                                      • Normalised Cross Correlation
                                                                                                                      • Edges
                                                                                                                      • Edges
                                                                                                                      • Finite Difference
                                                                                                                      • Edges
                                                                                                                      • Edges in 2D
                                                                                                                      • Edge filter kernel
                                                                                                                      • Prewitt filter
                                                                                                                      • Edge detection
                                                                                                                      • Edge filtering
                                                                                                                      • 02511 - Niveau af dagens emne forelaeligsing
                                                                                                                      • 02512 - Niveau af dagens emne forelaeligsing
                                                                                                                      • 02511 - Mit eget udbytte af dagen
                                                                                                                      • 02512 - Mit eget udbytte af dagen
                                                                                                                      • 02511 - Sidste uges oslashvelser (pixelwise operations)
                                                                                                                      • 02512 - Sidste uges oslashvelser (pixelwise operations)
                                                                                                                      • Denne uges brug af clickers
                                                                                                                      • What can you do after today
                                                                                                                      • Oslashvelsesrapport over oslashvelse 4 - 02511
                                                                                                                      • Exercises
                                                                                                                        A0
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                                                                                                                        2122018Introduction to Medical Image Analysis53 DTU Compute Technical University of Denmark

                                                                                                                        Border handling ndash extend the input

                                                                                                                        0 2 41 2 2

                                                                                                                        1 6 3

                                                                                                                        1 2 12 5 3

                                                                                                                        2 1 3

                                                                                                                        1 3 1

                                                                                                                        2 2 2

                                                                                                                        0 1 3

                                                                                                                        1 2 0

                                                                                                                        2 1 4

                                                                                                                        1 0 1

                                                                                                                        Input

                                                                                                                        1 2 0 1 311211

                                                                                                                        bull Reflection

                                                                                                                        bull Normally better than zero padding

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                                                                                                                        2122018Introduction to Medical Image Analysis54 DTU Compute Technical University of Denmark

                                                                                                                        Template Matching Template

                                                                                                                        ndash Skabelon paring dansk Locates objects in images

                                                                                                                        Input

                                                                                                                        Template

                                                                                                                        Output Correlation image

                                                                                                                        DTU Compute

                                                                                                                        2122018Introduction to Medical Image Analysis55 DTU Compute Technical University of Denmark

                                                                                                                        Template Matching The correlation between the template and the input

                                                                                                                        image is computed for each pixel

                                                                                                                        Input

                                                                                                                        Template

                                                                                                                        Output Correlation image

                                                                                                                        DTU Compute

                                                                                                                        2122018Introduction to Medical Image Analysis56 DTU Compute Technical University of Denmark

                                                                                                                        Template Matching The pixel with the highest value is found in the

                                                                                                                        output imagendash Here is the highest correlation

                                                                                                                        Input

                                                                                                                        Template

                                                                                                                        Output Correlation image

                                                                                                                        DTU Compute

                                                                                                                        2122018Introduction to Medical Image Analysis57 DTU Compute Technical University of Denmark

                                                                                                                        Template Matching This corresponds to the found pattern in the input

                                                                                                                        image

                                                                                                                        Input

                                                                                                                        Template

                                                                                                                        Output Correlation image

                                                                                                                        DTU Compute

                                                                                                                        2122018Introduction to Medical Image Analysis58 DTU Compute Technical University of Denmark

                                                                                                                        Problematic Correlation Correlation matching has problem with light areas ndash

                                                                                                                        why

                                                                                                                        Input (f)

                                                                                                                        Template (h)

                                                                                                                        Output Correlation imageFake max

                                                                                                                        Real max

                                                                                                                        Very High119892119892 119909119909119910119910 = 119895119895=minus119877119877

                                                                                                                        119877119877

                                                                                                                        119894119894=minus119877119877

                                                                                                                        119877119877

                                                                                                                        ℎ(119894119894 119895119895) 119891119891(119909119909 + 119894119894119910119910 + 119895119895)

                                                                                                                        DTU Compute

                                                                                                                        2122018Introduction to Medical Image Analysis59 DTU Compute Technical University of Denmark

                                                                                                                        Normalised Cross Correlation

                                                                                                                        Input (f)

                                                                                                                        Template (h)

                                                                                                                        Output Correlation image

                                                                                                                        Real max

                                                                                                                        NCC x y =Correlation

                                                                                                                        Length of image patch sdot Length of template

                                                                                                                        DTU Compute

                                                                                                                        2122018Introduction to Medical Image Analysis60 DTU Compute Technical University of Denmark

                                                                                                                        Length of template Vector length

                                                                                                                        ndash Put all pixel values into a vectorndash Compute the length of this vector

                                                                                                                        Describes the intensity of the templatendash Bright template has a large lengthndash Dark template has a small length

                                                                                                                        Template (h)

                                                                                                                        Length of template = 119895119895=minus119877119877

                                                                                                                        119877119877

                                                                                                                        119894119894=minus119877119877

                                                                                                                        119877119877

                                                                                                                        ℎ(119894119894 119895119895) ℎ(119894119894 119895119895)

                                                                                                                        DTU Compute

                                                                                                                        2122018Introduction to Medical Image Analysis61 DTU Compute Technical University of Denmark

                                                                                                                        Length of image patch Vector length based on pixel values in image patch Describes the intensity of the image patch

                                                                                                                        Template (h)

                                                                                                                        Input (f) with patch

                                                                                                                        DTU Compute

                                                                                                                        2122018Introduction to Medical Image Analysis62 DTU Compute Technical University of Denmark

                                                                                                                        Normalised Cross Correlation The length of the image patch and the length of

                                                                                                                        template normalise the NCC If the image is very bright the NCC will be ldquopulled

                                                                                                                        downrdquo

                                                                                                                        NCC x y =Correlation

                                                                                                                        Length of image patch sdot Length of template

                                                                                                                        DTU Compute

                                                                                                                        2122018Introduction to Medical Image Analysis63 DTU Compute Technical University of Denmark

                                                                                                                        Normalised Cross Correlation NCC will be between

                                                                                                                        ndash 0 No similarity between template and image patchndash 1 Template and image patch are identical

                                                                                                                        Input (f)

                                                                                                                        Template (h)

                                                                                                                        Output Correlation image

                                                                                                                        Real max

                                                                                                                        NCC x y =Correlation

                                                                                                                        Length of image patch sdot Length of template

                                                                                                                        DTU Compute

                                                                                                                        2122018Introduction to Medical Image Analysis64 DTU Compute Technical University of Denmark

                                                                                                                        Normalised Cross Correlation

                                                                                                                        A) 010B) 033C) 083D) 062E) 098

                                                                                                                        Der udfoslashres template matching med og normalized crosscorrelation (NCC) beregnes Hvad bliver NNC i den markerede pixel

                                                                                                                        1

                                                                                                                        2 2

                                                                                                                        3

                                                                                                                        2

                                                                                                                        A B C D E

                                                                                                                        Chart1

                                                                                                                        1
                                                                                                                        2
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                                                                                                                        2122018Introduction to Medical Image Analysis66 DTU Compute Technical University of Denmark

                                                                                                                        Edges An edge is where there is a

                                                                                                                        high change in gray level values

                                                                                                                        Objects are often separated from the background by edgesGray level profile

                                                                                                                        DTU Compute

                                                                                                                        2122018Introduction to Medical Image Analysis67 DTU Compute Technical University of Denmark

                                                                                                                        Edges The profile as a function f(d) What value is high when there

                                                                                                                        is an edgendash The slope of fndash The slope of the tangent at d

                                                                                                                        f(d)

                                                                                                                        119891119891prime(119889119889)

                                                                                                                        DTU Compute

                                                                                                                        2122018Introduction to Medical Image Analysis68 DTU Compute Technical University of Denmark

                                                                                                                        Finite Difference Definition of slope

                                                                                                                        Approximation

                                                                                                                        Simpler approximationh = 1

                                                                                                                        119891119891prime 119889119889 = limℎrarr0

                                                                                                                        119891119891 119889119889 + ℎ minus 119891119891(119889119889)ℎ

                                                                                                                        119891119891prime 119889119889 asymp119891119891 119889119889 + ℎ minus 119891119891(119889119889)

                                                                                                                        ℎ

                                                                                                                        119891119891prime 119889119889 asymp 119891119891 119889119889 + 1 minus 119891119891(119889119889)

                                                                                                                        DTU Compute

                                                                                                                        2122018Introduction to Medical Image Analysis69 DTU Compute Technical University of Denmark

                                                                                                                        Edges Discrete approximation of frsquo(d) Can be implemented as a filter

                                                                                                                        -1 0 1

                                                                                                                        f(d-2) f(d-1) f(d) f(d+1) f(d+2) f(d+3)

                                                                                                                        f(d)

                                                                                                                        119891119891prime 119889119889 asymp 119891119891 119889119889 + 1 minus 119891119891(119889119889)

                                                                                                                        DTU Compute

                                                                                                                        2122018Introduction to Medical Image Analysis70 DTU Compute Technical University of Denmark

                                                                                                                        Edges in 2D Changes in gray level values

                                                                                                                        ndash Image gradientndash Gradient is the 2D derivative of a 2D function f(xy)ndash Equal to the slope of the imagendash A steep slope is equal to an edge

                                                                                                                        120571120571119891119891 119909119909119910119910 = 119866(119892119892119909119909119892119892119910119910)

                                                                                                                        DTU Compute

                                                                                                                        2122018Introduction to Medical Image Analysis71 DTU Compute Technical University of Denmark

                                                                                                                        Edge filter kernel The Prewitt filter is a typical

                                                                                                                        edge filter Output image has high

                                                                                                                        values where there are edges

                                                                                                                        -1 0 1

                                                                                                                        -1 0 1

                                                                                                                        -1 0 1Vertical Prewitt filter

                                                                                                                        DTU Compute

                                                                                                                        2122018Introduction to Medical Image Analysis72 DTU Compute Technical University of Denmark

                                                                                                                        Prewitt filter

                                                                                                                        Original Prewitt Prewitt

                                                                                                                        Hot colormapSmooth 15x15

                                                                                                                        Smooth 15x15

                                                                                                                        Prewitt

                                                                                                                        DTU Compute

                                                                                                                        2122018Introduction to Medical Image Analysis73 DTU Compute Technical University of Denmark

                                                                                                                        Edge detection Edge filter

                                                                                                                        ndash Prewitt for example Thresholding

                                                                                                                        ndash Separate edges from non-edges

                                                                                                                        Output is binary imagendash Edges are white

                                                                                                                        DTU Compute

                                                                                                                        2122018Introduction to Medical Image Analysis74 DTU Compute Technical University of Denmark

                                                                                                                        Edge filtering

                                                                                                                        A) MeanB) Horizontal SobelC) Vertical PrewittD) Horisontal PrewittE) Median

                                                                                                                        Der udfoslashres en filtrering (correlation) med et filter paring billedet Der bruges ikke coefficient normalization Den filtrerede vaeligrdi i den markerede pixel bliver -119 Hvilket et 3x3 filter blev benyttet

                                                                                                                        0

                                                                                                                        8

                                                                                                                        1 10

                                                                                                                        A B C D E

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                                                                                                                        0

                                                                                                                        Sheet1

                                                                                                                        DTU Compute

                                                                                                                        2122018Introduction to Medical Image Analysis76 DTU Compute Technical University of Denmark

                                                                                                                        02511 - Niveau af dagens emne forelaeligsingA) Meget letB) LetC) PassendeD) SvaeligrtE) Meget svaeligrt

                                                                                                                        23

                                                                                                                        6

                                                                                                                        10

                                                                                                                        A B C D E

                                                                                                                        Chart1

                                                                                                                        2
                                                                                                                        3
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                                                                                                                        1
                                                                                                                        0

                                                                                                                        Sheet1

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                                                                                                                        2122018Introduction to Medical Image Analysis77 DTU Compute Technical University of Denmark

                                                                                                                        02512 - Niveau af dagens emne forelaeligsingA) Meget letB) LetC) PassendeD) SvaeligrtE) Meget svaeligrt

                                                                                                                        0 0

                                                                                                                        1

                                                                                                                        0 0

                                                                                                                        A B C D E

                                                                                                                        Chart1

                                                                                                                        0
                                                                                                                        0
                                                                                                                        1
                                                                                                                        0
                                                                                                                        0

                                                                                                                        Sheet1

                                                                                                                        DTU Compute

                                                                                                                        2122018Introduction to Medical Image Analysis78 DTU Compute Technical University of Denmark

                                                                                                                        02511 - Mit eget udbytte af dagenA) Jeg har laeligrt meget lidtB) Lidt laeligringC) PassendeD) God laeligringE) Jeg har laeligrt meget

                                                                                                                        0 0

                                                                                                                        2

                                                                                                                        6

                                                                                                                        0

                                                                                                                        A B C D E

                                                                                                                        Chart1

                                                                                                                        0
                                                                                                                        0
                                                                                                                        2
                                                                                                                        6
                                                                                                                        0

                                                                                                                        Sheet1

                                                                                                                        DTU Compute

                                                                                                                        2122018Introduction to Medical Image Analysis79 DTU Compute Technical University of Denmark

                                                                                                                        02512 - Mit eget udbytte af dagenA) Jeg har laeligrt meget lidtB) Lidt laeligringC) PassendeD) God laeligringE) Jeg har laeligrt meget

                                                                                                                        2

                                                                                                                        1

                                                                                                                        3

                                                                                                                        2

                                                                                                                        0

                                                                                                                        A B C D E

                                                                                                                        Chart1

                                                                                                                        2
                                                                                                                        1
                                                                                                                        3
                                                                                                                        2
                                                                                                                        0

                                                                                                                        Sheet1

                                                                                                                        DTU Compute

                                                                                                                        2122018Introduction to Medical Image Analysis80 DTU Compute Technical University of Denmark

                                                                                                                        02511 - Sidste uges oslashvelser (pixelwiseoperations)A) Meget letteB) LetteC) PassendeD) SvaeligreE) Meget svaeligre

                                                                                                                        0 0

                                                                                                                        1

                                                                                                                        4

                                                                                                                        1

                                                                                                                        A B C D E

                                                                                                                        Chart1

                                                                                                                        0
                                                                                                                        0
                                                                                                                        1
                                                                                                                        4
                                                                                                                        1

                                                                                                                        Sheet1

                                                                                                                        DTU Compute

                                                                                                                        2122018Introduction to Medical Image Analysis81 DTU Compute Technical University of Denmark

                                                                                                                        02512 - Sidste uges oslashvelser (pixelwiseoperations)A) Meget letteB) LetteC) PassendeD) SvaeligreE) Meget svaeligre

                                                                                                                        3

                                                                                                                        0

                                                                                                                        3

                                                                                                                        0 0

                                                                                                                        A B C D E

                                                                                                                        Chart1

                                                                                                                        3
                                                                                                                        0
                                                                                                                        3
                                                                                                                        0
                                                                                                                        0

                                                                                                                        Sheet1

                                                                                                                        DTU Compute

                                                                                                                        2122018Introduction to Medical Image Analysis82 DTU Compute Technical University of Denmark

                                                                                                                        Denne uges brug af clickersA) click click click ndash jeg bliver

                                                                                                                        sindssygB) For meget clickC) PassendeD) Jeg vil gerne have lidt mereE) Jeg kan ikrsquo faring nok

                                                                                                                        0 0

                                                                                                                        5

                                                                                                                        0

                                                                                                                        6

                                                                                                                        A B C D E

                                                                                                                        Chart1

                                                                                                                        0
                                                                                                                        0
                                                                                                                        5
                                                                                                                        0
                                                                                                                        6

                                                                                                                        Sheet1

                                                                                                                        DTU Compute

                                                                                                                        2122018Introduction to Medical Image Analysis83 DTU Compute Technical University of Denmark

                                                                                                                        What can you do after today Describe the difference between point processing and neighbourhood

                                                                                                                        processing Compute a rank filtered image using the min max median and

                                                                                                                        difference rank filters Compute a mean filtered image Decide if median or average filtering should be used for noise removal Choose the appropriate image border handling based on a given input

                                                                                                                        image Implement and apply template matching Compute the normalised cross correlation and explain why it should be

                                                                                                                        used Apply given image filter kernels to images Use edge filters on images Describe finite difference approximation of image gradients Describe the concept of edge detection

                                                                                                                        DTU Compute

                                                                                                                        2122018Introduction to Medical Image Analysis84 DTU Compute Technical University of Denmark

                                                                                                                        Oslashvelsesrapport over oslashvelse 4 - 02511 Oslashvelser taeligller cirka 30 af karakteren Skal afleveres senest den 7 marts kl 2359 Kan afleveres af 1 eller 2 personer

                                                                                                                        ndash I skal skrive jeres egen oslashvelsesrapportndash Brug mindst et af jeres egne billeder

                                                                                                                        Afleveres som PDF Lad vaeligre med at kopiere opgaveteksten ind i jeres

                                                                                                                        opgave Put Matlab kode i et Appendix og henvis fra teksten Eksempel rapport over oslashvelse findes paring

                                                                                                                        hjemmesiden under eksamen

                                                                                                                        DTU Compute

                                                                                                                        2122018Introduction to Medical Image Analysis85 DTU Compute Technical University of Denmark

                                                                                                                        Exercises

                                                                                                                        • Introduction to Medical Image Analysis
                                                                                                                        • Lecture 4 ndash Neighbourhood Processing
                                                                                                                        • What can you do after today
                                                                                                                        • Point processing
                                                                                                                        • Point processing
                                                                                                                        • Neighbourhood processing
                                                                                                                        • Use of filtering
                                                                                                                        • Salt and pepper noise
                                                                                                                        • Salt and pepper noise
                                                                                                                        • What is so special about noise
                                                                                                                        • Noise ndash go away
                                                                                                                        • What is the median Value
                                                                                                                        • The median value
                                                                                                                        • Noise away ndash the median filter
                                                                                                                        • Noise removal ndash average filter
                                                                                                                        • Noise removal ndash median filter
                                                                                                                        • Image Filtering
                                                                                                                        • Median filter
                                                                                                                        • Rank filters
                                                                                                                        • Median filter
                                                                                                                        • Correlation
                                                                                                                        • Why do we need similarity
                                                                                                                        • Correlation (1D)
                                                                                                                        • Correlation (1D)
                                                                                                                        • Normalisation
                                                                                                                        • Normalisation
                                                                                                                        • Correlation on images
                                                                                                                        • Correlation on images
                                                                                                                        • Correlation on images
                                                                                                                        • Draw your filter
                                                                                                                        • Correlation on images ndash no normalisation
                                                                                                                        • Correlation on images ndash no normalisation 2
                                                                                                                        • Mathematics of 2D Correlation
                                                                                                                        • Mathematics of 2D Correlation
                                                                                                                        • Mathematics of 2D Correlation
                                                                                                                        • Slide Number 40
                                                                                                                        • 2D Kernel Normalisation
                                                                                                                        • Correlation
                                                                                                                        • Smoothing filters
                                                                                                                        • Use of smoothing
                                                                                                                        • Use of smoothing
                                                                                                                        • Mean filter
                                                                                                                        • Border handling
                                                                                                                        • Border handling ndash extend the input
                                                                                                                        • Correlation with zero padding
                                                                                                                        • Border handling ndash extend the input
                                                                                                                        • Template Matching
                                                                                                                        • Template Matching
                                                                                                                        • Template Matching
                                                                                                                        • Template Matching
                                                                                                                        • Problematic Correlation
                                                                                                                        • Normalised Cross Correlation
                                                                                                                        • Length of template
                                                                                                                        • Length of image patch
                                                                                                                        • Normalised Cross Correlation
                                                                                                                        • Normalised Cross Correlation
                                                                                                                        • Normalised Cross Correlation
                                                                                                                        • Edges
                                                                                                                        • Edges
                                                                                                                        • Finite Difference
                                                                                                                        • Edges
                                                                                                                        • Edges in 2D
                                                                                                                        • Edge filter kernel
                                                                                                                        • Prewitt filter
                                                                                                                        • Edge detection
                                                                                                                        • Edge filtering
                                                                                                                        • 02511 - Niveau af dagens emne forelaeligsing
                                                                                                                        • 02512 - Niveau af dagens emne forelaeligsing
                                                                                                                        • 02511 - Mit eget udbytte af dagen
                                                                                                                        • 02512 - Mit eget udbytte af dagen
                                                                                                                        • 02511 - Sidste uges oslashvelser (pixelwise operations)
                                                                                                                        • 02512 - Sidste uges oslashvelser (pixelwise operations)
                                                                                                                        • Denne uges brug af clickers
                                                                                                                        • What can you do after today
                                                                                                                        • Oslashvelsesrapport over oslashvelse 4 - 02511
                                                                                                                        • Exercises
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                                                                                                                          Border handling ndash extend the input

                                                                                                                          0 2 41 2 2

                                                                                                                          1 6 3

                                                                                                                          1 2 12 5 3

                                                                                                                          2 1 3

                                                                                                                          1 3 1

                                                                                                                          2 2 2

                                                                                                                          0 1 3

                                                                                                                          1 2 0

                                                                                                                          2 1 4

                                                                                                                          1 0 1

                                                                                                                          Input

                                                                                                                          1 2 0 1 311211

                                                                                                                          bull Reflection

                                                                                                                          bull Normally better than zero padding

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                                                                                                                          Template Matching Template

                                                                                                                          ndash Skabelon paring dansk Locates objects in images

                                                                                                                          Input

                                                                                                                          Template

                                                                                                                          Output Correlation image

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                                                                                                                          2122018Introduction to Medical Image Analysis55 DTU Compute Technical University of Denmark

                                                                                                                          Template Matching The correlation between the template and the input

                                                                                                                          image is computed for each pixel

                                                                                                                          Input

                                                                                                                          Template

                                                                                                                          Output Correlation image

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                                                                                                                          2122018Introduction to Medical Image Analysis56 DTU Compute Technical University of Denmark

                                                                                                                          Template Matching The pixel with the highest value is found in the

                                                                                                                          output imagendash Here is the highest correlation

                                                                                                                          Input

                                                                                                                          Template

                                                                                                                          Output Correlation image

                                                                                                                          DTU Compute

                                                                                                                          2122018Introduction to Medical Image Analysis57 DTU Compute Technical University of Denmark

                                                                                                                          Template Matching This corresponds to the found pattern in the input

                                                                                                                          image

                                                                                                                          Input

                                                                                                                          Template

                                                                                                                          Output Correlation image

                                                                                                                          DTU Compute

                                                                                                                          2122018Introduction to Medical Image Analysis58 DTU Compute Technical University of Denmark

                                                                                                                          Problematic Correlation Correlation matching has problem with light areas ndash

                                                                                                                          why

                                                                                                                          Input (f)

                                                                                                                          Template (h)

                                                                                                                          Output Correlation imageFake max

                                                                                                                          Real max

                                                                                                                          Very High119892119892 119909119909119910119910 = 119895119895=minus119877119877

                                                                                                                          119877119877

                                                                                                                          119894119894=minus119877119877

                                                                                                                          119877119877

                                                                                                                          ℎ(119894119894 119895119895) 119891119891(119909119909 + 119894119894119910119910 + 119895119895)

                                                                                                                          DTU Compute

                                                                                                                          2122018Introduction to Medical Image Analysis59 DTU Compute Technical University of Denmark

                                                                                                                          Normalised Cross Correlation

                                                                                                                          Input (f)

                                                                                                                          Template (h)

                                                                                                                          Output Correlation image

                                                                                                                          Real max

                                                                                                                          NCC x y =Correlation

                                                                                                                          Length of image patch sdot Length of template

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                                                                                                                          2122018Introduction to Medical Image Analysis60 DTU Compute Technical University of Denmark

                                                                                                                          Length of template Vector length

                                                                                                                          ndash Put all pixel values into a vectorndash Compute the length of this vector

                                                                                                                          Describes the intensity of the templatendash Bright template has a large lengthndash Dark template has a small length

                                                                                                                          Template (h)

                                                                                                                          Length of template = 119895119895=minus119877119877

                                                                                                                          119877119877

                                                                                                                          119894119894=minus119877119877

                                                                                                                          119877119877

                                                                                                                          ℎ(119894119894 119895119895) ℎ(119894119894 119895119895)

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                                                                                                                          2122018Introduction to Medical Image Analysis61 DTU Compute Technical University of Denmark

                                                                                                                          Length of image patch Vector length based on pixel values in image patch Describes the intensity of the image patch

                                                                                                                          Template (h)

                                                                                                                          Input (f) with patch

                                                                                                                          DTU Compute

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                                                                                                                          Normalised Cross Correlation The length of the image patch and the length of

                                                                                                                          template normalise the NCC If the image is very bright the NCC will be ldquopulled

                                                                                                                          downrdquo

                                                                                                                          NCC x y =Correlation

                                                                                                                          Length of image patch sdot Length of template

                                                                                                                          DTU Compute

                                                                                                                          2122018Introduction to Medical Image Analysis63 DTU Compute Technical University of Denmark

                                                                                                                          Normalised Cross Correlation NCC will be between

                                                                                                                          ndash 0 No similarity between template and image patchndash 1 Template and image patch are identical

                                                                                                                          Input (f)

                                                                                                                          Template (h)

                                                                                                                          Output Correlation image

                                                                                                                          Real max

                                                                                                                          NCC x y =Correlation

                                                                                                                          Length of image patch sdot Length of template

                                                                                                                          DTU Compute

                                                                                                                          2122018Introduction to Medical Image Analysis64 DTU Compute Technical University of Denmark

                                                                                                                          Normalised Cross Correlation

                                                                                                                          A) 010B) 033C) 083D) 062E) 098

                                                                                                                          Der udfoslashres template matching med og normalized crosscorrelation (NCC) beregnes Hvad bliver NNC i den markerede pixel

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                                                                                                                          Edges An edge is where there is a

                                                                                                                          high change in gray level values

                                                                                                                          Objects are often separated from the background by edgesGray level profile

                                                                                                                          DTU Compute

                                                                                                                          2122018Introduction to Medical Image Analysis67 DTU Compute Technical University of Denmark

                                                                                                                          Edges The profile as a function f(d) What value is high when there

                                                                                                                          is an edgendash The slope of fndash The slope of the tangent at d

                                                                                                                          f(d)

                                                                                                                          119891119891prime(119889119889)

                                                                                                                          DTU Compute

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                                                                                                                          Finite Difference Definition of slope

                                                                                                                          Approximation

                                                                                                                          Simpler approximationh = 1

                                                                                                                          119891119891prime 119889119889 = limℎrarr0

                                                                                                                          119891119891 119889119889 + ℎ minus 119891119891(119889119889)ℎ

                                                                                                                          119891119891prime 119889119889 asymp119891119891 119889119889 + ℎ minus 119891119891(119889119889)

                                                                                                                          ℎ

                                                                                                                          119891119891prime 119889119889 asymp 119891119891 119889119889 + 1 minus 119891119891(119889119889)

                                                                                                                          DTU Compute

                                                                                                                          2122018Introduction to Medical Image Analysis69 DTU Compute Technical University of Denmark

                                                                                                                          Edges Discrete approximation of frsquo(d) Can be implemented as a filter

                                                                                                                          -1 0 1

                                                                                                                          f(d-2) f(d-1) f(d) f(d+1) f(d+2) f(d+3)

                                                                                                                          f(d)

                                                                                                                          119891119891prime 119889119889 asymp 119891119891 119889119889 + 1 minus 119891119891(119889119889)

                                                                                                                          DTU Compute

                                                                                                                          2122018Introduction to Medical Image Analysis70 DTU Compute Technical University of Denmark

                                                                                                                          Edges in 2D Changes in gray level values

                                                                                                                          ndash Image gradientndash Gradient is the 2D derivative of a 2D function f(xy)ndash Equal to the slope of the imagendash A steep slope is equal to an edge

                                                                                                                          120571120571119891119891 119909119909119910119910 = 119866(119892119892119909119909119892119892119910119910)

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                                                                                                                          Edge filter kernel The Prewitt filter is a typical

                                                                                                                          edge filter Output image has high

                                                                                                                          values where there are edges

                                                                                                                          -1 0 1

                                                                                                                          -1 0 1

                                                                                                                          -1 0 1Vertical Prewitt filter

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                                                                                                                          Prewitt filter

                                                                                                                          Original Prewitt Prewitt

                                                                                                                          Hot colormapSmooth 15x15

                                                                                                                          Smooth 15x15

                                                                                                                          Prewitt

                                                                                                                          DTU Compute

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                                                                                                                          Edge detection Edge filter

                                                                                                                          ndash Prewitt for example Thresholding

                                                                                                                          ndash Separate edges from non-edges

                                                                                                                          Output is binary imagendash Edges are white

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                                                                                                                          Edge filtering

                                                                                                                          A) MeanB) Horizontal SobelC) Vertical PrewittD) Horisontal PrewittE) Median

                                                                                                                          Der udfoslashres en filtrering (correlation) med et filter paring billedet Der bruges ikke coefficient normalization Den filtrerede vaeligrdi i den markerede pixel bliver -119 Hvilket et 3x3 filter blev benyttet

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                                                                                                                          02511 - Niveau af dagens emne forelaeligsingA) Meget letB) LetC) PassendeD) SvaeligrtE) Meget svaeligrt

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                                                                                                                          02512 - Niveau af dagens emne forelaeligsingA) Meget letB) LetC) PassendeD) SvaeligrtE) Meget svaeligrt

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                                                                                                                          02511 - Mit eget udbytte af dagenA) Jeg har laeligrt meget lidtB) Lidt laeligringC) PassendeD) God laeligringE) Jeg har laeligrt meget

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                                                                                                                          02512 - Mit eget udbytte af dagenA) Jeg har laeligrt meget lidtB) Lidt laeligringC) PassendeD) God laeligringE) Jeg har laeligrt meget

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                                                                                                                          02511 - Sidste uges oslashvelser (pixelwiseoperations)A) Meget letteB) LetteC) PassendeD) SvaeligreE) Meget svaeligre

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                                                                                                                          02512 - Sidste uges oslashvelser (pixelwiseoperations)A) Meget letteB) LetteC) PassendeD) SvaeligreE) Meget svaeligre

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                                                                                                                          Denne uges brug af clickersA) click click click ndash jeg bliver

                                                                                                                          sindssygB) For meget clickC) PassendeD) Jeg vil gerne have lidt mereE) Jeg kan ikrsquo faring nok

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                                                                                                                          What can you do after today Describe the difference between point processing and neighbourhood

                                                                                                                          processing Compute a rank filtered image using the min max median and

                                                                                                                          difference rank filters Compute a mean filtered image Decide if median or average filtering should be used for noise removal Choose the appropriate image border handling based on a given input

                                                                                                                          image Implement and apply template matching Compute the normalised cross correlation and explain why it should be

                                                                                                                          used Apply given image filter kernels to images Use edge filters on images Describe finite difference approximation of image gradients Describe the concept of edge detection

                                                                                                                          DTU Compute

                                                                                                                          2122018Introduction to Medical Image Analysis84 DTU Compute Technical University of Denmark

                                                                                                                          Oslashvelsesrapport over oslashvelse 4 - 02511 Oslashvelser taeligller cirka 30 af karakteren Skal afleveres senest den 7 marts kl 2359 Kan afleveres af 1 eller 2 personer

                                                                                                                          ndash I skal skrive jeres egen oslashvelsesrapportndash Brug mindst et af jeres egne billeder

                                                                                                                          Afleveres som PDF Lad vaeligre med at kopiere opgaveteksten ind i jeres

                                                                                                                          opgave Put Matlab kode i et Appendix og henvis fra teksten Eksempel rapport over oslashvelse findes paring

                                                                                                                          hjemmesiden under eksamen

                                                                                                                          DTU Compute

                                                                                                                          2122018Introduction to Medical Image Analysis85 DTU Compute Technical University of Denmark

                                                                                                                          Exercises

                                                                                                                          • Introduction to Medical Image Analysis
                                                                                                                          • Lecture 4 ndash Neighbourhood Processing
                                                                                                                          • What can you do after today
                                                                                                                          • Point processing
                                                                                                                          • Point processing
                                                                                                                          • Neighbourhood processing
                                                                                                                          • Use of filtering
                                                                                                                          • Salt and pepper noise
                                                                                                                          • Salt and pepper noise
                                                                                                                          • What is so special about noise
                                                                                                                          • Noise ndash go away
                                                                                                                          • What is the median Value
                                                                                                                          • The median value
                                                                                                                          • Noise away ndash the median filter
                                                                                                                          • Noise removal ndash average filter
                                                                                                                          • Noise removal ndash median filter
                                                                                                                          • Image Filtering
                                                                                                                          • Median filter
                                                                                                                          • Rank filters
                                                                                                                          • Median filter
                                                                                                                          • Correlation
                                                                                                                          • Why do we need similarity
                                                                                                                          • Correlation (1D)
                                                                                                                          • Correlation (1D)
                                                                                                                          • Normalisation
                                                                                                                          • Normalisation
                                                                                                                          • Correlation on images
                                                                                                                          • Correlation on images
                                                                                                                          • Correlation on images
                                                                                                                          • Draw your filter
                                                                                                                          • Correlation on images ndash no normalisation
                                                                                                                          • Correlation on images ndash no normalisation 2
                                                                                                                          • Mathematics of 2D Correlation
                                                                                                                          • Mathematics of 2D Correlation
                                                                                                                          • Mathematics of 2D Correlation
                                                                                                                          • Slide Number 40
                                                                                                                          • 2D Kernel Normalisation
                                                                                                                          • Correlation
                                                                                                                          • Smoothing filters
                                                                                                                          • Use of smoothing
                                                                                                                          • Use of smoothing
                                                                                                                          • Mean filter
                                                                                                                          • Border handling
                                                                                                                          • Border handling ndash extend the input
                                                                                                                          • Correlation with zero padding
                                                                                                                          • Border handling ndash extend the input
                                                                                                                          • Template Matching
                                                                                                                          • Template Matching
                                                                                                                          • Template Matching
                                                                                                                          • Template Matching
                                                                                                                          • Problematic Correlation
                                                                                                                          • Normalised Cross Correlation
                                                                                                                          • Length of template
                                                                                                                          • Length of image patch
                                                                                                                          • Normalised Cross Correlation
                                                                                                                          • Normalised Cross Correlation
                                                                                                                          • Normalised Cross Correlation
                                                                                                                          • Edges
                                                                                                                          • Edges
                                                                                                                          • Finite Difference
                                                                                                                          • Edges
                                                                                                                          • Edges in 2D
                                                                                                                          • Edge filter kernel
                                                                                                                          • Prewitt filter
                                                                                                                          • Edge detection
                                                                                                                          • Edge filtering
                                                                                                                          • 02511 - Niveau af dagens emne forelaeligsing
                                                                                                                          • 02512 - Niveau af dagens emne forelaeligsing
                                                                                                                          • 02511 - Mit eget udbytte af dagen
                                                                                                                          • 02512 - Mit eget udbytte af dagen
                                                                                                                          • 02511 - Sidste uges oslashvelser (pixelwise operations)
                                                                                                                          • 02512 - Sidste uges oslashvelser (pixelwise operations)
                                                                                                                          • Denne uges brug af clickers
                                                                                                                          • What can you do after today
                                                                                                                          • Oslashvelsesrapport over oslashvelse 4 - 02511
                                                                                                                          • Exercises
                                                                                                                            A0
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                                                                                                                            C5
                                                                                                                            D0
                                                                                                                            E6
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                                                                                                                            D
                                                                                                                            E
                                                                                                                            A3
                                                                                                                            B0
                                                                                                                            C3
                                                                                                                            D0
                                                                                                                            E0
                                                                                                                            A
                                                                                                                            B
                                                                                                                            C
                                                                                                                            D
                                                                                                                            E
                                                                                                                            A0
                                                                                                                            B0
                                                                                                                            C1
                                                                                                                            D4
                                                                                                                            E1
                                                                                                                            A
                                                                                                                            B
                                                                                                                            C
                                                                                                                            D
                                                                                                                            E
                                                                                                                            A2
                                                                                                                            B1
                                                                                                                            C3
                                                                                                                            D2
                                                                                                                            E0
                                                                                                                            A
                                                                                                                            B
                                                                                                                            C
                                                                                                                            D
                                                                                                                            E
                                                                                                                            A0
                                                                                                                            B0
                                                                                                                            C2
                                                                                                                            D6
                                                                                                                            E0
                                                                                                                            A
                                                                                                                            B
                                                                                                                            C
                                                                                                                            D
                                                                                                                            E
                                                                                                                            A0
                                                                                                                            B0
                                                                                                                            C1
                                                                                                                            D0
                                                                                                                            E0
                                                                                                                            A
                                                                                                                            B
                                                                                                                            C
                                                                                                                            D
                                                                                                                            E
                                                                                                                            A2
                                                                                                                            B3
                                                                                                                            C6
                                                                                                                            D1
                                                                                                                            E0
                                                                                                                            A
                                                                                                                            B
                                                                                                                            C
                                                                                                                            D
                                                                                                                            E
                                                                                                                            A0
                                                                                                                            B8
                                                                                                                            C1
                                                                                                                            D1
                                                                                                                            E0
                                                                                                                            A
                                                                                                                            B
                                                                                                                            C
                                                                                                                            D
                                                                                                                            E
                                                                                                                            A1
                                                                                                                            B2
                                                                                                                            C2
                                                                                                                            D3
                                                                                                                            E2
                                                                                                                            A
                                                                                                                            B
                                                                                                                            C
                                                                                                                            D
                                                                                                                            E
                                                                                                                            A0
                                                                                                                            B13
                                                                                                                            C0
                                                                                                                            D0
                                                                                                                            E0

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                                                                                                                            2122018Introduction to Medical Image Analysis53 DTU Compute Technical University of Denmark

                                                                                                                            Border handling ndash extend the input

                                                                                                                            0 2 41 2 2

                                                                                                                            1 6 3

                                                                                                                            1 2 12 5 3

                                                                                                                            2 1 3

                                                                                                                            1 3 1

                                                                                                                            2 2 2

                                                                                                                            0 1 3

                                                                                                                            1 2 0

                                                                                                                            2 1 4

                                                                                                                            1 0 1

                                                                                                                            Input

                                                                                                                            1 2 0 1 311211

                                                                                                                            bull Reflection

                                                                                                                            bull Normally better than zero padding

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                                                                                                                            Template Matching Template

                                                                                                                            ndash Skabelon paring dansk Locates objects in images

                                                                                                                            Input

                                                                                                                            Template

                                                                                                                            Output Correlation image

                                                                                                                            DTU Compute

                                                                                                                            2122018Introduction to Medical Image Analysis55 DTU Compute Technical University of Denmark

                                                                                                                            Template Matching The correlation between the template and the input

                                                                                                                            image is computed for each pixel

                                                                                                                            Input

                                                                                                                            Template

                                                                                                                            Output Correlation image

                                                                                                                            DTU Compute

                                                                                                                            2122018Introduction to Medical Image Analysis56 DTU Compute Technical University of Denmark

                                                                                                                            Template Matching The pixel with the highest value is found in the

                                                                                                                            output imagendash Here is the highest correlation

                                                                                                                            Input

                                                                                                                            Template

                                                                                                                            Output Correlation image

                                                                                                                            DTU Compute

                                                                                                                            2122018Introduction to Medical Image Analysis57 DTU Compute Technical University of Denmark

                                                                                                                            Template Matching This corresponds to the found pattern in the input

                                                                                                                            image

                                                                                                                            Input

                                                                                                                            Template

                                                                                                                            Output Correlation image

                                                                                                                            DTU Compute

                                                                                                                            2122018Introduction to Medical Image Analysis58 DTU Compute Technical University of Denmark

                                                                                                                            Problematic Correlation Correlation matching has problem with light areas ndash

                                                                                                                            why

                                                                                                                            Input (f)

                                                                                                                            Template (h)

                                                                                                                            Output Correlation imageFake max

                                                                                                                            Real max

                                                                                                                            Very High119892119892 119909119909119910119910 = 119895119895=minus119877119877

                                                                                                                            119877119877

                                                                                                                            119894119894=minus119877119877

                                                                                                                            119877119877

                                                                                                                            ℎ(119894119894 119895119895) 119891119891(119909119909 + 119894119894119910119910 + 119895119895)

                                                                                                                            DTU Compute

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                                                                                                                            Normalised Cross Correlation

                                                                                                                            Input (f)

                                                                                                                            Template (h)

                                                                                                                            Output Correlation image

                                                                                                                            Real max

                                                                                                                            NCC x y =Correlation

                                                                                                                            Length of image patch sdot Length of template

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                                                                                                                            2122018Introduction to Medical Image Analysis60 DTU Compute Technical University of Denmark

                                                                                                                            Length of template Vector length

                                                                                                                            ndash Put all pixel values into a vectorndash Compute the length of this vector

                                                                                                                            Describes the intensity of the templatendash Bright template has a large lengthndash Dark template has a small length

                                                                                                                            Template (h)

                                                                                                                            Length of template = 119895119895=minus119877119877

                                                                                                                            119877119877

                                                                                                                            119894119894=minus119877119877

                                                                                                                            119877119877

                                                                                                                            ℎ(119894119894 119895119895) ℎ(119894119894 119895119895)

                                                                                                                            DTU Compute

                                                                                                                            2122018Introduction to Medical Image Analysis61 DTU Compute Technical University of Denmark

                                                                                                                            Length of image patch Vector length based on pixel values in image patch Describes the intensity of the image patch

                                                                                                                            Template (h)

                                                                                                                            Input (f) with patch

                                                                                                                            DTU Compute

                                                                                                                            2122018Introduction to Medical Image Analysis62 DTU Compute Technical University of Denmark

                                                                                                                            Normalised Cross Correlation The length of the image patch and the length of

                                                                                                                            template normalise the NCC If the image is very bright the NCC will be ldquopulled

                                                                                                                            downrdquo

                                                                                                                            NCC x y =Correlation

                                                                                                                            Length of image patch sdot Length of template

                                                                                                                            DTU Compute

                                                                                                                            2122018Introduction to Medical Image Analysis63 DTU Compute Technical University of Denmark

                                                                                                                            Normalised Cross Correlation NCC will be between

                                                                                                                            ndash 0 No similarity between template and image patchndash 1 Template and image patch are identical

                                                                                                                            Input (f)

                                                                                                                            Template (h)

                                                                                                                            Output Correlation image

                                                                                                                            Real max

                                                                                                                            NCC x y =Correlation

                                                                                                                            Length of image patch sdot Length of template

                                                                                                                            DTU Compute

                                                                                                                            2122018Introduction to Medical Image Analysis64 DTU Compute Technical University of Denmark

                                                                                                                            Normalised Cross Correlation

                                                                                                                            A) 010B) 033C) 083D) 062E) 098

                                                                                                                            Der udfoslashres template matching med og normalized crosscorrelation (NCC) beregnes Hvad bliver NNC i den markerede pixel

                                                                                                                            1

                                                                                                                            2 2

                                                                                                                            3

                                                                                                                            2

                                                                                                                            A B C D E

                                                                                                                            Chart1

                                                                                                                            1
                                                                                                                            2
                                                                                                                            2
                                                                                                                            3
                                                                                                                            2

                                                                                                                            Sheet1

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                                                                                                                            Edges An edge is where there is a

                                                                                                                            high change in gray level values

                                                                                                                            Objects are often separated from the background by edgesGray level profile

                                                                                                                            DTU Compute

                                                                                                                            2122018Introduction to Medical Image Analysis67 DTU Compute Technical University of Denmark

                                                                                                                            Edges The profile as a function f(d) What value is high when there

                                                                                                                            is an edgendash The slope of fndash The slope of the tangent at d

                                                                                                                            f(d)

                                                                                                                            119891119891prime(119889119889)

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                                                                                                                            Finite Difference Definition of slope

                                                                                                                            Approximation

                                                                                                                            Simpler approximationh = 1

                                                                                                                            119891119891prime 119889119889 = limℎrarr0

                                                                                                                            119891119891 119889119889 + ℎ minus 119891119891(119889119889)ℎ

                                                                                                                            119891119891prime 119889119889 asymp119891119891 119889119889 + ℎ minus 119891119891(119889119889)

                                                                                                                            ℎ

                                                                                                                            119891119891prime 119889119889 asymp 119891119891 119889119889 + 1 minus 119891119891(119889119889)

                                                                                                                            DTU Compute

                                                                                                                            2122018Introduction to Medical Image Analysis69 DTU Compute Technical University of Denmark

                                                                                                                            Edges Discrete approximation of frsquo(d) Can be implemented as a filter

                                                                                                                            -1 0 1

                                                                                                                            f(d-2) f(d-1) f(d) f(d+1) f(d+2) f(d+3)

                                                                                                                            f(d)

                                                                                                                            119891119891prime 119889119889 asymp 119891119891 119889119889 + 1 minus 119891119891(119889119889)

                                                                                                                            DTU Compute

                                                                                                                            2122018Introduction to Medical Image Analysis70 DTU Compute Technical University of Denmark

                                                                                                                            Edges in 2D Changes in gray level values

                                                                                                                            ndash Image gradientndash Gradient is the 2D derivative of a 2D function f(xy)ndash Equal to the slope of the imagendash A steep slope is equal to an edge

                                                                                                                            120571120571119891119891 119909119909119910119910 = 119866(119892119892119909119909119892119892119910119910)

                                                                                                                            DTU Compute

                                                                                                                            2122018Introduction to Medical Image Analysis71 DTU Compute Technical University of Denmark

                                                                                                                            Edge filter kernel The Prewitt filter is a typical

                                                                                                                            edge filter Output image has high

                                                                                                                            values where there are edges

                                                                                                                            -1 0 1

                                                                                                                            -1 0 1

                                                                                                                            -1 0 1Vertical Prewitt filter

                                                                                                                            DTU Compute

                                                                                                                            2122018Introduction to Medical Image Analysis72 DTU Compute Technical University of Denmark

                                                                                                                            Prewitt filter

                                                                                                                            Original Prewitt Prewitt

                                                                                                                            Hot colormapSmooth 15x15

                                                                                                                            Smooth 15x15

                                                                                                                            Prewitt

                                                                                                                            DTU Compute

                                                                                                                            2122018Introduction to Medical Image Analysis73 DTU Compute Technical University of Denmark

                                                                                                                            Edge detection Edge filter

                                                                                                                            ndash Prewitt for example Thresholding

                                                                                                                            ndash Separate edges from non-edges

                                                                                                                            Output is binary imagendash Edges are white

                                                                                                                            DTU Compute

                                                                                                                            2122018Introduction to Medical Image Analysis74 DTU Compute Technical University of Denmark

                                                                                                                            Edge filtering

                                                                                                                            A) MeanB) Horizontal SobelC) Vertical PrewittD) Horisontal PrewittE) Median

                                                                                                                            Der udfoslashres en filtrering (correlation) med et filter paring billedet Der bruges ikke coefficient normalization Den filtrerede vaeligrdi i den markerede pixel bliver -119 Hvilket et 3x3 filter blev benyttet

                                                                                                                            0

                                                                                                                            8

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                                                                                                                            0

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                                                                                                                            02511 - Niveau af dagens emne forelaeligsingA) Meget letB) LetC) PassendeD) SvaeligrtE) Meget svaeligrt

                                                                                                                            23

                                                                                                                            6

                                                                                                                            10

                                                                                                                            A B C D E

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                                                                                                                            0

                                                                                                                            Sheet1

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                                                                                                                            02512 - Niveau af dagens emne forelaeligsingA) Meget letB) LetC) PassendeD) SvaeligrtE) Meget svaeligrt

                                                                                                                            0 0

                                                                                                                            1

                                                                                                                            0 0

                                                                                                                            A B C D E

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                                                                                                                            0
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                                                                                                                            0

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                                                                                                                            02511 - Mit eget udbytte af dagenA) Jeg har laeligrt meget lidtB) Lidt laeligringC) PassendeD) God laeligringE) Jeg har laeligrt meget

                                                                                                                            0 0

                                                                                                                            2

                                                                                                                            6

                                                                                                                            0

                                                                                                                            A B C D E

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                                                                                                                            2
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                                                                                                                            0

                                                                                                                            Sheet1

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                                                                                                                            02512 - Mit eget udbytte af dagenA) Jeg har laeligrt meget lidtB) Lidt laeligringC) PassendeD) God laeligringE) Jeg har laeligrt meget

                                                                                                                            2

                                                                                                                            1

                                                                                                                            3

                                                                                                                            2

                                                                                                                            0

                                                                                                                            A B C D E

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                                                                                                                            2
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                                                                                                                            2
                                                                                                                            0

                                                                                                                            Sheet1

                                                                                                                            DTU Compute

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                                                                                                                            02511 - Sidste uges oslashvelser (pixelwiseoperations)A) Meget letteB) LetteC) PassendeD) SvaeligreE) Meget svaeligre

                                                                                                                            0 0

                                                                                                                            1

                                                                                                                            4

                                                                                                                            1

                                                                                                                            A B C D E

                                                                                                                            Chart1

                                                                                                                            0
                                                                                                                            0
                                                                                                                            1
                                                                                                                            4
                                                                                                                            1

                                                                                                                            Sheet1

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                                                                                                                            02512 - Sidste uges oslashvelser (pixelwiseoperations)A) Meget letteB) LetteC) PassendeD) SvaeligreE) Meget svaeligre

                                                                                                                            3

                                                                                                                            0

                                                                                                                            3

                                                                                                                            0 0

                                                                                                                            A B C D E

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                                                                                                                            3
                                                                                                                            0
                                                                                                                            3
                                                                                                                            0
                                                                                                                            0

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                                                                                                                            2122018Introduction to Medical Image Analysis82 DTU Compute Technical University of Denmark

                                                                                                                            Denne uges brug af clickersA) click click click ndash jeg bliver

                                                                                                                            sindssygB) For meget clickC) PassendeD) Jeg vil gerne have lidt mereE) Jeg kan ikrsquo faring nok

                                                                                                                            0 0

                                                                                                                            5

                                                                                                                            0

                                                                                                                            6

                                                                                                                            A B C D E

                                                                                                                            Chart1

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                                                                                                                            Sheet1

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                                                                                                                            2122018Introduction to Medical Image Analysis83 DTU Compute Technical University of Denmark

                                                                                                                            What can you do after today Describe the difference between point processing and neighbourhood

                                                                                                                            processing Compute a rank filtered image using the min max median and

                                                                                                                            difference rank filters Compute a mean filtered image Decide if median or average filtering should be used for noise removal Choose the appropriate image border handling based on a given input

                                                                                                                            image Implement and apply template matching Compute the normalised cross correlation and explain why it should be

                                                                                                                            used Apply given image filter kernels to images Use edge filters on images Describe finite difference approximation of image gradients Describe the concept of edge detection

                                                                                                                            DTU Compute

                                                                                                                            2122018Introduction to Medical Image Analysis84 DTU Compute Technical University of Denmark

                                                                                                                            Oslashvelsesrapport over oslashvelse 4 - 02511 Oslashvelser taeligller cirka 30 af karakteren Skal afleveres senest den 7 marts kl 2359 Kan afleveres af 1 eller 2 personer

                                                                                                                            ndash I skal skrive jeres egen oslashvelsesrapportndash Brug mindst et af jeres egne billeder

                                                                                                                            Afleveres som PDF Lad vaeligre med at kopiere opgaveteksten ind i jeres

                                                                                                                            opgave Put Matlab kode i et Appendix og henvis fra teksten Eksempel rapport over oslashvelse findes paring

                                                                                                                            hjemmesiden under eksamen

                                                                                                                            DTU Compute

                                                                                                                            2122018Introduction to Medical Image Analysis85 DTU Compute Technical University of Denmark

                                                                                                                            Exercises

                                                                                                                            • Introduction to Medical Image Analysis
                                                                                                                            • Lecture 4 ndash Neighbourhood Processing
                                                                                                                            • What can you do after today
                                                                                                                            • Point processing
                                                                                                                            • Point processing
                                                                                                                            • Neighbourhood processing
                                                                                                                            • Use of filtering
                                                                                                                            • Salt and pepper noise
                                                                                                                            • Salt and pepper noise
                                                                                                                            • What is so special about noise
                                                                                                                            • Noise ndash go away
                                                                                                                            • What is the median Value
                                                                                                                            • The median value
                                                                                                                            • Noise away ndash the median filter
                                                                                                                            • Noise removal ndash average filter
                                                                                                                            • Noise removal ndash median filter
                                                                                                                            • Image Filtering
                                                                                                                            • Median filter
                                                                                                                            • Rank filters
                                                                                                                            • Median filter
                                                                                                                            • Correlation
                                                                                                                            • Why do we need similarity
                                                                                                                            • Correlation (1D)
                                                                                                                            • Correlation (1D)
                                                                                                                            • Normalisation
                                                                                                                            • Normalisation
                                                                                                                            • Correlation on images
                                                                                                                            • Correlation on images
                                                                                                                            • Correlation on images
                                                                                                                            • Draw your filter
                                                                                                                            • Correlation on images ndash no normalisation
                                                                                                                            • Correlation on images ndash no normalisation 2
                                                                                                                            • Mathematics of 2D Correlation
                                                                                                                            • Mathematics of 2D Correlation
                                                                                                                            • Mathematics of 2D Correlation
                                                                                                                            • Slide Number 40
                                                                                                                            • 2D Kernel Normalisation
                                                                                                                            • Correlation
                                                                                                                            • Smoothing filters
                                                                                                                            • Use of smoothing
                                                                                                                            • Use of smoothing
                                                                                                                            • Mean filter
                                                                                                                            • Border handling
                                                                                                                            • Border handling ndash extend the input
                                                                                                                            • Correlation with zero padding
                                                                                                                            • Border handling ndash extend the input
                                                                                                                            • Template Matching
                                                                                                                            • Template Matching
                                                                                                                            • Template Matching
                                                                                                                            • Template Matching
                                                                                                                            • Problematic Correlation
                                                                                                                            • Normalised Cross Correlation
                                                                                                                            • Length of template
                                                                                                                            • Length of image patch
                                                                                                                            • Normalised Cross Correlation
                                                                                                                            • Normalised Cross Correlation
                                                                                                                            • Normalised Cross Correlation
                                                                                                                            • Edges
                                                                                                                            • Edges
                                                                                                                            • Finite Difference
                                                                                                                            • Edges
                                                                                                                            • Edges in 2D
                                                                                                                            • Edge filter kernel
                                                                                                                            • Prewitt filter
                                                                                                                            • Edge detection
                                                                                                                            • Edge filtering
                                                                                                                            • 02511 - Niveau af dagens emne forelaeligsing
                                                                                                                            • 02512 - Niveau af dagens emne forelaeligsing
                                                                                                                            • 02511 - Mit eget udbytte af dagen
                                                                                                                            • 02512 - Mit eget udbytte af dagen
                                                                                                                            • 02511 - Sidste uges oslashvelser (pixelwise operations)
                                                                                                                            • 02512 - Sidste uges oslashvelser (pixelwise operations)
                                                                                                                            • Denne uges brug af clickers
                                                                                                                            • What can you do after today
                                                                                                                            • Oslashvelsesrapport over oslashvelse 4 - 02511
                                                                                                                            • Exercises
                                                                                                                              A0
                                                                                                                              B0
                                                                                                                              C5
                                                                                                                              D0
                                                                                                                              E6
                                                                                                                              A
                                                                                                                              B
                                                                                                                              C
                                                                                                                              D
                                                                                                                              E
                                                                                                                              A3
                                                                                                                              B0
                                                                                                                              C3
                                                                                                                              D0
                                                                                                                              E0
                                                                                                                              A
                                                                                                                              B
                                                                                                                              C
                                                                                                                              D
                                                                                                                              E
                                                                                                                              A0
                                                                                                                              B0
                                                                                                                              C1
                                                                                                                              D4
                                                                                                                              E1
                                                                                                                              A
                                                                                                                              B
                                                                                                                              C
                                                                                                                              D
                                                                                                                              E
                                                                                                                              A2
                                                                                                                              B1
                                                                                                                              C3
                                                                                                                              D2
                                                                                                                              E0
                                                                                                                              A
                                                                                                                              B
                                                                                                                              C
                                                                                                                              D
                                                                                                                              E
                                                                                                                              A0
                                                                                                                              B0
                                                                                                                              C2
                                                                                                                              D6
                                                                                                                              E0
                                                                                                                              A
                                                                                                                              B
                                                                                                                              C
                                                                                                                              D
                                                                                                                              E
                                                                                                                              A0
                                                                                                                              B0
                                                                                                                              C1
                                                                                                                              D0
                                                                                                                              E0
                                                                                                                              A
                                                                                                                              B
                                                                                                                              C
                                                                                                                              D
                                                                                                                              E
                                                                                                                              A2
                                                                                                                              B3
                                                                                                                              C6
                                                                                                                              D1
                                                                                                                              E0
                                                                                                                              A
                                                                                                                              B
                                                                                                                              C
                                                                                                                              D
                                                                                                                              E
                                                                                                                              A0
                                                                                                                              B8
                                                                                                                              C1
                                                                                                                              D1
                                                                                                                              E0
                                                                                                                              A
                                                                                                                              B
                                                                                                                              C
                                                                                                                              D
                                                                                                                              E
                                                                                                                              A1
                                                                                                                              B2
                                                                                                                              C2
                                                                                                                              D3
                                                                                                                              E2
                                                                                                                              A
                                                                                                                              B
                                                                                                                              C
                                                                                                                              D
                                                                                                                              E

                                                                                                                              DTU Compute

                                                                                                                              2122018Introduction to Medical Image Analysis54 DTU Compute Technical University of Denmark

                                                                                                                              Template Matching Template

                                                                                                                              ndash Skabelon paring dansk Locates objects in images

                                                                                                                              Input

                                                                                                                              Template

                                                                                                                              Output Correlation image

                                                                                                                              DTU Compute

                                                                                                                              2122018Introduction to Medical Image Analysis55 DTU Compute Technical University of Denmark

                                                                                                                              Template Matching The correlation between the template and the input

                                                                                                                              image is computed for each pixel

                                                                                                                              Input

                                                                                                                              Template

                                                                                                                              Output Correlation image

                                                                                                                              DTU Compute

                                                                                                                              2122018Introduction to Medical Image Analysis56 DTU Compute Technical University of Denmark

                                                                                                                              Template Matching The pixel with the highest value is found in the

                                                                                                                              output imagendash Here is the highest correlation

                                                                                                                              Input

                                                                                                                              Template

                                                                                                                              Output Correlation image

                                                                                                                              DTU Compute

                                                                                                                              2122018Introduction to Medical Image Analysis57 DTU Compute Technical University of Denmark

                                                                                                                              Template Matching This corresponds to the found pattern in the input

                                                                                                                              image

                                                                                                                              Input

                                                                                                                              Template

                                                                                                                              Output Correlation image

                                                                                                                              DTU Compute

                                                                                                                              2122018Introduction to Medical Image Analysis58 DTU Compute Technical University of Denmark

                                                                                                                              Problematic Correlation Correlation matching has problem with light areas ndash

                                                                                                                              why

                                                                                                                              Input (f)

                                                                                                                              Template (h)

                                                                                                                              Output Correlation imageFake max

                                                                                                                              Real max

                                                                                                                              Very High119892119892 119909119909119910119910 = 119895119895=minus119877119877

                                                                                                                              119877119877

                                                                                                                              119894119894=minus119877119877

                                                                                                                              119877119877

                                                                                                                              ℎ(119894119894 119895119895) 119891119891(119909119909 + 119894119894119910119910 + 119895119895)

                                                                                                                              DTU Compute

                                                                                                                              2122018Introduction to Medical Image Analysis59 DTU Compute Technical University of Denmark

                                                                                                                              Normalised Cross Correlation

                                                                                                                              Input (f)

                                                                                                                              Template (h)

                                                                                                                              Output Correlation image

                                                                                                                              Real max

                                                                                                                              NCC x y =Correlation

                                                                                                                              Length of image patch sdot Length of template

                                                                                                                              DTU Compute

                                                                                                                              2122018Introduction to Medical Image Analysis60 DTU Compute Technical University of Denmark

                                                                                                                              Length of template Vector length

                                                                                                                              ndash Put all pixel values into a vectorndash Compute the length of this vector

                                                                                                                              Describes the intensity of the templatendash Bright template has a large lengthndash Dark template has a small length

                                                                                                                              Template (h)

                                                                                                                              Length of template = 119895119895=minus119877119877

                                                                                                                              119877119877

                                                                                                                              119894119894=minus119877119877

                                                                                                                              119877119877

                                                                                                                              ℎ(119894119894 119895119895) ℎ(119894119894 119895119895)

                                                                                                                              DTU Compute

                                                                                                                              2122018Introduction to Medical Image Analysis61 DTU Compute Technical University of Denmark

                                                                                                                              Length of image patch Vector length based on pixel values in image patch Describes the intensity of the image patch

                                                                                                                              Template (h)

                                                                                                                              Input (f) with patch

                                                                                                                              DTU Compute

                                                                                                                              2122018Introduction to Medical Image Analysis62 DTU Compute Technical University of Denmark

                                                                                                                              Normalised Cross Correlation The length of the image patch and the length of

                                                                                                                              template normalise the NCC If the image is very bright the NCC will be ldquopulled

                                                                                                                              downrdquo

                                                                                                                              NCC x y =Correlation

                                                                                                                              Length of image patch sdot Length of template

                                                                                                                              DTU Compute

                                                                                                                              2122018Introduction to Medical Image Analysis63 DTU Compute Technical University of Denmark

                                                                                                                              Normalised Cross Correlation NCC will be between

                                                                                                                              ndash 0 No similarity between template and image patchndash 1 Template and image patch are identical

                                                                                                                              Input (f)

                                                                                                                              Template (h)

                                                                                                                              Output Correlation image

                                                                                                                              Real max

                                                                                                                              NCC x y =Correlation

                                                                                                                              Length of image patch sdot Length of template

                                                                                                                              DTU Compute

                                                                                                                              2122018Introduction to Medical Image Analysis64 DTU Compute Technical University of Denmark

                                                                                                                              Normalised Cross Correlation

                                                                                                                              A) 010B) 033C) 083D) 062E) 098

                                                                                                                              Der udfoslashres template matching med og normalized crosscorrelation (NCC) beregnes Hvad bliver NNC i den markerede pixel

                                                                                                                              1

                                                                                                                              2 2

                                                                                                                              3

                                                                                                                              2

                                                                                                                              A B C D E

                                                                                                                              Chart1

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                                                                                                                              Edges An edge is where there is a

                                                                                                                              high change in gray level values

                                                                                                                              Objects are often separated from the background by edgesGray level profile

                                                                                                                              DTU Compute

                                                                                                                              2122018Introduction to Medical Image Analysis67 DTU Compute Technical University of Denmark

                                                                                                                              Edges The profile as a function f(d) What value is high when there

                                                                                                                              is an edgendash The slope of fndash The slope of the tangent at d

                                                                                                                              f(d)

                                                                                                                              119891119891prime(119889119889)

                                                                                                                              DTU Compute

                                                                                                                              2122018Introduction to Medical Image Analysis68 DTU Compute Technical University of Denmark

                                                                                                                              Finite Difference Definition of slope

                                                                                                                              Approximation

                                                                                                                              Simpler approximationh = 1

                                                                                                                              119891119891prime 119889119889 = limℎrarr0

                                                                                                                              119891119891 119889119889 + ℎ minus 119891119891(119889119889)ℎ

                                                                                                                              119891119891prime 119889119889 asymp119891119891 119889119889 + ℎ minus 119891119891(119889119889)

                                                                                                                              ℎ

                                                                                                                              119891119891prime 119889119889 asymp 119891119891 119889119889 + 1 minus 119891119891(119889119889)

                                                                                                                              DTU Compute

                                                                                                                              2122018Introduction to Medical Image Analysis69 DTU Compute Technical University of Denmark

                                                                                                                              Edges Discrete approximation of frsquo(d) Can be implemented as a filter

                                                                                                                              -1 0 1

                                                                                                                              f(d-2) f(d-1) f(d) f(d+1) f(d+2) f(d+3)

                                                                                                                              f(d)

                                                                                                                              119891119891prime 119889119889 asymp 119891119891 119889119889 + 1 minus 119891119891(119889119889)

                                                                                                                              DTU Compute

                                                                                                                              2122018Introduction to Medical Image Analysis70 DTU Compute Technical University of Denmark

                                                                                                                              Edges in 2D Changes in gray level values

                                                                                                                              ndash Image gradientndash Gradient is the 2D derivative of a 2D function f(xy)ndash Equal to the slope of the imagendash A steep slope is equal to an edge

                                                                                                                              120571120571119891119891 119909119909119910119910 = 119866(119892119892119909119909119892119892119910119910)

                                                                                                                              DTU Compute

                                                                                                                              2122018Introduction to Medical Image Analysis71 DTU Compute Technical University of Denmark

                                                                                                                              Edge filter kernel The Prewitt filter is a typical

                                                                                                                              edge filter Output image has high

                                                                                                                              values where there are edges

                                                                                                                              -1 0 1

                                                                                                                              -1 0 1

                                                                                                                              -1 0 1Vertical Prewitt filter

                                                                                                                              DTU Compute

                                                                                                                              2122018Introduction to Medical Image Analysis72 DTU Compute Technical University of Denmark

                                                                                                                              Prewitt filter

                                                                                                                              Original Prewitt Prewitt

                                                                                                                              Hot colormapSmooth 15x15

                                                                                                                              Smooth 15x15

                                                                                                                              Prewitt

                                                                                                                              DTU Compute

                                                                                                                              2122018Introduction to Medical Image Analysis73 DTU Compute Technical University of Denmark

                                                                                                                              Edge detection Edge filter

                                                                                                                              ndash Prewitt for example Thresholding

                                                                                                                              ndash Separate edges from non-edges

                                                                                                                              Output is binary imagendash Edges are white

                                                                                                                              DTU Compute

                                                                                                                              2122018Introduction to Medical Image Analysis74 DTU Compute Technical University of Denmark

                                                                                                                              Edge filtering

                                                                                                                              A) MeanB) Horizontal SobelC) Vertical PrewittD) Horisontal PrewittE) Median

                                                                                                                              Der udfoslashres en filtrering (correlation) med et filter paring billedet Der bruges ikke coefficient normalization Den filtrerede vaeligrdi i den markerede pixel bliver -119 Hvilket et 3x3 filter blev benyttet

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                                                                                                                              02511 - Niveau af dagens emne forelaeligsingA) Meget letB) LetC) PassendeD) SvaeligrtE) Meget svaeligrt

                                                                                                                              23

                                                                                                                              6

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                                                                                                                              02512 - Niveau af dagens emne forelaeligsingA) Meget letB) LetC) PassendeD) SvaeligrtE) Meget svaeligrt

                                                                                                                              0 0

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                                                                                                                              2122018Introduction to Medical Image Analysis78 DTU Compute Technical University of Denmark

                                                                                                                              02511 - Mit eget udbytte af dagenA) Jeg har laeligrt meget lidtB) Lidt laeligringC) PassendeD) God laeligringE) Jeg har laeligrt meget

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                                                                                                                              02512 - Mit eget udbytte af dagenA) Jeg har laeligrt meget lidtB) Lidt laeligringC) PassendeD) God laeligringE) Jeg har laeligrt meget

                                                                                                                              2

                                                                                                                              1

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                                                                                                                              02511 - Sidste uges oslashvelser (pixelwiseoperations)A) Meget letteB) LetteC) PassendeD) SvaeligreE) Meget svaeligre

                                                                                                                              0 0

                                                                                                                              1

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                                                                                                                              02512 - Sidste uges oslashvelser (pixelwiseoperations)A) Meget letteB) LetteC) PassendeD) SvaeligreE) Meget svaeligre

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                                                                                                                              2122018Introduction to Medical Image Analysis82 DTU Compute Technical University of Denmark

                                                                                                                              Denne uges brug af clickersA) click click click ndash jeg bliver

                                                                                                                              sindssygB) For meget clickC) PassendeD) Jeg vil gerne have lidt mereE) Jeg kan ikrsquo faring nok

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                                                                                                                              2122018Introduction to Medical Image Analysis83 DTU Compute Technical University of Denmark

                                                                                                                              What can you do after today Describe the difference between point processing and neighbourhood

                                                                                                                              processing Compute a rank filtered image using the min max median and

                                                                                                                              difference rank filters Compute a mean filtered image Decide if median or average filtering should be used for noise removal Choose the appropriate image border handling based on a given input

                                                                                                                              image Implement and apply template matching Compute the normalised cross correlation and explain why it should be

                                                                                                                              used Apply given image filter kernels to images Use edge filters on images Describe finite difference approximation of image gradients Describe the concept of edge detection

                                                                                                                              DTU Compute

                                                                                                                              2122018Introduction to Medical Image Analysis84 DTU Compute Technical University of Denmark

                                                                                                                              Oslashvelsesrapport over oslashvelse 4 - 02511 Oslashvelser taeligller cirka 30 af karakteren Skal afleveres senest den 7 marts kl 2359 Kan afleveres af 1 eller 2 personer

                                                                                                                              ndash I skal skrive jeres egen oslashvelsesrapportndash Brug mindst et af jeres egne billeder

                                                                                                                              Afleveres som PDF Lad vaeligre med at kopiere opgaveteksten ind i jeres

                                                                                                                              opgave Put Matlab kode i et Appendix og henvis fra teksten Eksempel rapport over oslashvelse findes paring

                                                                                                                              hjemmesiden under eksamen

                                                                                                                              DTU Compute

                                                                                                                              2122018Introduction to Medical Image Analysis85 DTU Compute Technical University of Denmark

                                                                                                                              Exercises

                                                                                                                              • Introduction to Medical Image Analysis
                                                                                                                              • Lecture 4 ndash Neighbourhood Processing
                                                                                                                              • What can you do after today
                                                                                                                              • Point processing
                                                                                                                              • Point processing
                                                                                                                              • Neighbourhood processing
                                                                                                                              • Use of filtering
                                                                                                                              • Salt and pepper noise
                                                                                                                              • Salt and pepper noise
                                                                                                                              • What is so special about noise
                                                                                                                              • Noise ndash go away
                                                                                                                              • What is the median Value
                                                                                                                              • The median value
                                                                                                                              • Noise away ndash the median filter
                                                                                                                              • Noise removal ndash average filter
                                                                                                                              • Noise removal ndash median filter
                                                                                                                              • Image Filtering
                                                                                                                              • Median filter
                                                                                                                              • Rank filters
                                                                                                                              • Median filter
                                                                                                                              • Correlation
                                                                                                                              • Why do we need similarity
                                                                                                                              • Correlation (1D)
                                                                                                                              • Correlation (1D)
                                                                                                                              • Normalisation
                                                                                                                              • Normalisation
                                                                                                                              • Correlation on images
                                                                                                                              • Correlation on images
                                                                                                                              • Correlation on images
                                                                                                                              • Draw your filter
                                                                                                                              • Correlation on images ndash no normalisation
                                                                                                                              • Correlation on images ndash no normalisation 2
                                                                                                                              • Mathematics of 2D Correlation
                                                                                                                              • Mathematics of 2D Correlation
                                                                                                                              • Mathematics of 2D Correlation
                                                                                                                              • Slide Number 40
                                                                                                                              • 2D Kernel Normalisation
                                                                                                                              • Correlation
                                                                                                                              • Smoothing filters
                                                                                                                              • Use of smoothing
                                                                                                                              • Use of smoothing
                                                                                                                              • Mean filter
                                                                                                                              • Border handling
                                                                                                                              • Border handling ndash extend the input
                                                                                                                              • Correlation with zero padding
                                                                                                                              • Border handling ndash extend the input
                                                                                                                              • Template Matching
                                                                                                                              • Template Matching
                                                                                                                              • Template Matching
                                                                                                                              • Template Matching
                                                                                                                              • Problematic Correlation
                                                                                                                              • Normalised Cross Correlation
                                                                                                                              • Length of template
                                                                                                                              • Length of image patch
                                                                                                                              • Normalised Cross Correlation
                                                                                                                              • Normalised Cross Correlation
                                                                                                                              • Normalised Cross Correlation
                                                                                                                              • Edges
                                                                                                                              • Edges
                                                                                                                              • Finite Difference
                                                                                                                              • Edges
                                                                                                                              • Edges in 2D
                                                                                                                              • Edge filter kernel
                                                                                                                              • Prewitt filter
                                                                                                                              • Edge detection
                                                                                                                              • Edge filtering
                                                                                                                              • 02511 - Niveau af dagens emne forelaeligsing
                                                                                                                              • 02512 - Niveau af dagens emne forelaeligsing
                                                                                                                              • 02511 - Mit eget udbytte af dagen
                                                                                                                              • 02512 - Mit eget udbytte af dagen
                                                                                                                              • 02511 - Sidste uges oslashvelser (pixelwise operations)
                                                                                                                              • 02512 - Sidste uges oslashvelser (pixelwise operations)
                                                                                                                              • Denne uges brug af clickers
                                                                                                                              • What can you do after today
                                                                                                                              • Oslashvelsesrapport over oslashvelse 4 - 02511
                                                                                                                              • Exercises
                                                                                                                                A0
                                                                                                                                B0
                                                                                                                                C5
                                                                                                                                D0
                                                                                                                                E6
                                                                                                                                A
                                                                                                                                B
                                                                                                                                C
                                                                                                                                D
                                                                                                                                E
                                                                                                                                A3
                                                                                                                                B0
                                                                                                                                C3
                                                                                                                                D0
                                                                                                                                E0
                                                                                                                                A
                                                                                                                                B
                                                                                                                                C
                                                                                                                                D
                                                                                                                                E
                                                                                                                                A0
                                                                                                                                B0
                                                                                                                                C1
                                                                                                                                D4
                                                                                                                                E1
                                                                                                                                A
                                                                                                                                B
                                                                                                                                C
                                                                                                                                D
                                                                                                                                E
                                                                                                                                A2
                                                                                                                                B1
                                                                                                                                C3
                                                                                                                                D2
                                                                                                                                E0
                                                                                                                                A
                                                                                                                                B
                                                                                                                                C
                                                                                                                                D
                                                                                                                                E
                                                                                                                                A0
                                                                                                                                B0
                                                                                                                                C2
                                                                                                                                D6
                                                                                                                                E0
                                                                                                                                A
                                                                                                                                B
                                                                                                                                C
                                                                                                                                D
                                                                                                                                E
                                                                                                                                A0
                                                                                                                                B0
                                                                                                                                C1
                                                                                                                                D0
                                                                                                                                E0
                                                                                                                                A
                                                                                                                                B
                                                                                                                                C
                                                                                                                                D
                                                                                                                                E
                                                                                                                                A2
                                                                                                                                B3
                                                                                                                                C6
                                                                                                                                D1
                                                                                                                                E0
                                                                                                                                A
                                                                                                                                B
                                                                                                                                C
                                                                                                                                D
                                                                                                                                E
                                                                                                                                A0
                                                                                                                                B8
                                                                                                                                C1
                                                                                                                                D1
                                                                                                                                E0
                                                                                                                                A
                                                                                                                                B
                                                                                                                                C
                                                                                                                                D
                                                                                                                                E
                                                                                                                                A1
                                                                                                                                B2
                                                                                                                                C2
                                                                                                                                D3
                                                                                                                                E2
                                                                                                                                A
                                                                                                                                B
                                                                                                                                C
                                                                                                                                D
                                                                                                                                E

                                                                                                                                DTU Compute

                                                                                                                                2122018Introduction to Medical Image Analysis55 DTU Compute Technical University of Denmark

                                                                                                                                Template Matching The correlation between the template and the input

                                                                                                                                image is computed for each pixel

                                                                                                                                Input

                                                                                                                                Template

                                                                                                                                Output Correlation image

                                                                                                                                DTU Compute

                                                                                                                                2122018Introduction to Medical Image Analysis56 DTU Compute Technical University of Denmark

                                                                                                                                Template Matching The pixel with the highest value is found in the

                                                                                                                                output imagendash Here is the highest correlation

                                                                                                                                Input

                                                                                                                                Template

                                                                                                                                Output Correlation image

                                                                                                                                DTU Compute

                                                                                                                                2122018Introduction to Medical Image Analysis57 DTU Compute Technical University of Denmark

                                                                                                                                Template Matching This corresponds to the found pattern in the input

                                                                                                                                image

                                                                                                                                Input

                                                                                                                                Template

                                                                                                                                Output Correlation image

                                                                                                                                DTU Compute

                                                                                                                                2122018Introduction to Medical Image Analysis58 DTU Compute Technical University of Denmark

                                                                                                                                Problematic Correlation Correlation matching has problem with light areas ndash

                                                                                                                                why

                                                                                                                                Input (f)

                                                                                                                                Template (h)

                                                                                                                                Output Correlation imageFake max

                                                                                                                                Real max

                                                                                                                                Very High119892119892 119909119909119910119910 = 119895119895=minus119877119877

                                                                                                                                119877119877

                                                                                                                                119894119894=minus119877119877

                                                                                                                                119877119877

                                                                                                                                ℎ(119894119894 119895119895) 119891119891(119909119909 + 119894119894119910119910 + 119895119895)

                                                                                                                                DTU Compute

                                                                                                                                2122018Introduction to Medical Image Analysis59 DTU Compute Technical University of Denmark

                                                                                                                                Normalised Cross Correlation

                                                                                                                                Input (f)

                                                                                                                                Template (h)

                                                                                                                                Output Correlation image

                                                                                                                                Real max

                                                                                                                                NCC x y =Correlation

                                                                                                                                Length of image patch sdot Length of template

                                                                                                                                DTU Compute

                                                                                                                                2122018Introduction to Medical Image Analysis60 DTU Compute Technical University of Denmark

                                                                                                                                Length of template Vector length

                                                                                                                                ndash Put all pixel values into a vectorndash Compute the length of this vector

                                                                                                                                Describes the intensity of the templatendash Bright template has a large lengthndash Dark template has a small length

                                                                                                                                Template (h)

                                                                                                                                Length of template = 119895119895=minus119877119877

                                                                                                                                119877119877

                                                                                                                                119894119894=minus119877119877

                                                                                                                                119877119877

                                                                                                                                ℎ(119894119894 119895119895) ℎ(119894119894 119895119895)

                                                                                                                                DTU Compute

                                                                                                                                2122018Introduction to Medical Image Analysis61 DTU Compute Technical University of Denmark

                                                                                                                                Length of image patch Vector length based on pixel values in image patch Describes the intensity of the image patch

                                                                                                                                Template (h)

                                                                                                                                Input (f) with patch

                                                                                                                                DTU Compute

                                                                                                                                2122018Introduction to Medical Image Analysis62 DTU Compute Technical University of Denmark

                                                                                                                                Normalised Cross Correlation The length of the image patch and the length of

                                                                                                                                template normalise the NCC If the image is very bright the NCC will be ldquopulled

                                                                                                                                downrdquo

                                                                                                                                NCC x y =Correlation

                                                                                                                                Length of image patch sdot Length of template

                                                                                                                                DTU Compute

                                                                                                                                2122018Introduction to Medical Image Analysis63 DTU Compute Technical University of Denmark

                                                                                                                                Normalised Cross Correlation NCC will be between

                                                                                                                                ndash 0 No similarity between template and image patchndash 1 Template and image patch are identical

                                                                                                                                Input (f)

                                                                                                                                Template (h)

                                                                                                                                Output Correlation image

                                                                                                                                Real max

                                                                                                                                NCC x y =Correlation

                                                                                                                                Length of image patch sdot Length of template

                                                                                                                                DTU Compute

                                                                                                                                2122018Introduction to Medical Image Analysis64 DTU Compute Technical University of Denmark

                                                                                                                                Normalised Cross Correlation

                                                                                                                                A) 010B) 033C) 083D) 062E) 098

                                                                                                                                Der udfoslashres template matching med og normalized crosscorrelation (NCC) beregnes Hvad bliver NNC i den markerede pixel

                                                                                                                                1

                                                                                                                                2 2

                                                                                                                                3

                                                                                                                                2

                                                                                                                                A B C D E

                                                                                                                                Chart1

                                                                                                                                1
                                                                                                                                2
                                                                                                                                2
                                                                                                                                3
                                                                                                                                2

                                                                                                                                Sheet1

                                                                                                                                DTU Compute

                                                                                                                                2122018Introduction to Medical Image Analysis66 DTU Compute Technical University of Denmark

                                                                                                                                Edges An edge is where there is a

                                                                                                                                high change in gray level values

                                                                                                                                Objects are often separated from the background by edgesGray level profile

                                                                                                                                DTU Compute

                                                                                                                                2122018Introduction to Medical Image Analysis67 DTU Compute Technical University of Denmark

                                                                                                                                Edges The profile as a function f(d) What value is high when there

                                                                                                                                is an edgendash The slope of fndash The slope of the tangent at d

                                                                                                                                f(d)

                                                                                                                                119891119891prime(119889119889)

                                                                                                                                DTU Compute

                                                                                                                                2122018Introduction to Medical Image Analysis68 DTU Compute Technical University of Denmark

                                                                                                                                Finite Difference Definition of slope

                                                                                                                                Approximation

                                                                                                                                Simpler approximationh = 1

                                                                                                                                119891119891prime 119889119889 = limℎrarr0

                                                                                                                                119891119891 119889119889 + ℎ minus 119891119891(119889119889)ℎ

                                                                                                                                119891119891prime 119889119889 asymp119891119891 119889119889 + ℎ minus 119891119891(119889119889)

                                                                                                                                ℎ

                                                                                                                                119891119891prime 119889119889 asymp 119891119891 119889119889 + 1 minus 119891119891(119889119889)

                                                                                                                                DTU Compute

                                                                                                                                2122018Introduction to Medical Image Analysis69 DTU Compute Technical University of Denmark

                                                                                                                                Edges Discrete approximation of frsquo(d) Can be implemented as a filter

                                                                                                                                -1 0 1

                                                                                                                                f(d-2) f(d-1) f(d) f(d+1) f(d+2) f(d+3)

                                                                                                                                f(d)

                                                                                                                                119891119891prime 119889119889 asymp 119891119891 119889119889 + 1 minus 119891119891(119889119889)

                                                                                                                                DTU Compute

                                                                                                                                2122018Introduction to Medical Image Analysis70 DTU Compute Technical University of Denmark

                                                                                                                                Edges in 2D Changes in gray level values

                                                                                                                                ndash Image gradientndash Gradient is the 2D derivative of a 2D function f(xy)ndash Equal to the slope of the imagendash A steep slope is equal to an edge

                                                                                                                                120571120571119891119891 119909119909119910119910 = 119866(119892119892119909119909119892119892119910119910)

                                                                                                                                DTU Compute

                                                                                                                                2122018Introduction to Medical Image Analysis71 DTU Compute Technical University of Denmark

                                                                                                                                Edge filter kernel The Prewitt filter is a typical

                                                                                                                                edge filter Output image has high

                                                                                                                                values where there are edges

                                                                                                                                -1 0 1

                                                                                                                                -1 0 1

                                                                                                                                -1 0 1Vertical Prewitt filter

                                                                                                                                DTU Compute

                                                                                                                                2122018Introduction to Medical Image Analysis72 DTU Compute Technical University of Denmark

                                                                                                                                Prewitt filter

                                                                                                                                Original Prewitt Prewitt

                                                                                                                                Hot colormapSmooth 15x15

                                                                                                                                Smooth 15x15

                                                                                                                                Prewitt

                                                                                                                                DTU Compute

                                                                                                                                2122018Introduction to Medical Image Analysis73 DTU Compute Technical University of Denmark

                                                                                                                                Edge detection Edge filter

                                                                                                                                ndash Prewitt for example Thresholding

                                                                                                                                ndash Separate edges from non-edges

                                                                                                                                Output is binary imagendash Edges are white

                                                                                                                                DTU Compute

                                                                                                                                2122018Introduction to Medical Image Analysis74 DTU Compute Technical University of Denmark

                                                                                                                                Edge filtering

                                                                                                                                A) MeanB) Horizontal SobelC) Vertical PrewittD) Horisontal PrewittE) Median

                                                                                                                                Der udfoslashres en filtrering (correlation) med et filter paring billedet Der bruges ikke coefficient normalization Den filtrerede vaeligrdi i den markerede pixel bliver -119 Hvilket et 3x3 filter blev benyttet

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                                                                                                                                02511 - Niveau af dagens emne forelaeligsingA) Meget letB) LetC) PassendeD) SvaeligrtE) Meget svaeligrt

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                                                                                                                                02512 - Niveau af dagens emne forelaeligsingA) Meget letB) LetC) PassendeD) SvaeligrtE) Meget svaeligrt

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                                                                                                                                02511 - Mit eget udbytte af dagenA) Jeg har laeligrt meget lidtB) Lidt laeligringC) PassendeD) God laeligringE) Jeg har laeligrt meget

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                                                                                                                                02512 - Mit eget udbytte af dagenA) Jeg har laeligrt meget lidtB) Lidt laeligringC) PassendeD) God laeligringE) Jeg har laeligrt meget

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                                                                                                                                02511 - Sidste uges oslashvelser (pixelwiseoperations)A) Meget letteB) LetteC) PassendeD) SvaeligreE) Meget svaeligre

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                                                                                                                                Denne uges brug af clickersA) click click click ndash jeg bliver

                                                                                                                                sindssygB) For meget clickC) PassendeD) Jeg vil gerne have lidt mereE) Jeg kan ikrsquo faring nok

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                                                                                                                                What can you do after today Describe the difference between point processing and neighbourhood

                                                                                                                                processing Compute a rank filtered image using the min max median and

                                                                                                                                difference rank filters Compute a mean filtered image Decide if median or average filtering should be used for noise removal Choose the appropriate image border handling based on a given input

                                                                                                                                image Implement and apply template matching Compute the normalised cross correlation and explain why it should be

                                                                                                                                used Apply given image filter kernels to images Use edge filters on images Describe finite difference approximation of image gradients Describe the concept of edge detection

                                                                                                                                DTU Compute

                                                                                                                                2122018Introduction to Medical Image Analysis84 DTU Compute Technical University of Denmark

                                                                                                                                Oslashvelsesrapport over oslashvelse 4 - 02511 Oslashvelser taeligller cirka 30 af karakteren Skal afleveres senest den 7 marts kl 2359 Kan afleveres af 1 eller 2 personer

                                                                                                                                ndash I skal skrive jeres egen oslashvelsesrapportndash Brug mindst et af jeres egne billeder

                                                                                                                                Afleveres som PDF Lad vaeligre med at kopiere opgaveteksten ind i jeres

                                                                                                                                opgave Put Matlab kode i et Appendix og henvis fra teksten Eksempel rapport over oslashvelse findes paring

                                                                                                                                hjemmesiden under eksamen

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                                                                                                                                2122018Introduction to Medical Image Analysis85 DTU Compute Technical University of Denmark

                                                                                                                                Exercises

                                                                                                                                • Introduction to Medical Image Analysis
                                                                                                                                • Lecture 4 ndash Neighbourhood Processing
                                                                                                                                • What can you do after today
                                                                                                                                • Point processing
                                                                                                                                • Point processing
                                                                                                                                • Neighbourhood processing
                                                                                                                                • Use of filtering
                                                                                                                                • Salt and pepper noise
                                                                                                                                • Salt and pepper noise
                                                                                                                                • What is so special about noise
                                                                                                                                • Noise ndash go away
                                                                                                                                • What is the median Value
                                                                                                                                • The median value
                                                                                                                                • Noise away ndash the median filter
                                                                                                                                • Noise removal ndash average filter
                                                                                                                                • Noise removal ndash median filter
                                                                                                                                • Image Filtering
                                                                                                                                • Median filter
                                                                                                                                • Rank filters
                                                                                                                                • Median filter
                                                                                                                                • Correlation
                                                                                                                                • Why do we need similarity
                                                                                                                                • Correlation (1D)
                                                                                                                                • Correlation (1D)
                                                                                                                                • Normalisation
                                                                                                                                • Normalisation
                                                                                                                                • Correlation on images
                                                                                                                                • Correlation on images
                                                                                                                                • Correlation on images
                                                                                                                                • Draw your filter
                                                                                                                                • Correlation on images ndash no normalisation
                                                                                                                                • Correlation on images ndash no normalisation 2
                                                                                                                                • Mathematics of 2D Correlation
                                                                                                                                • Mathematics of 2D Correlation
                                                                                                                                • Mathematics of 2D Correlation
                                                                                                                                • Slide Number 40
                                                                                                                                • 2D Kernel Normalisation
                                                                                                                                • Correlation
                                                                                                                                • Smoothing filters
                                                                                                                                • Use of smoothing
                                                                                                                                • Use of smoothing
                                                                                                                                • Mean filter
                                                                                                                                • Border handling
                                                                                                                                • Border handling ndash extend the input
                                                                                                                                • Correlation with zero padding
                                                                                                                                • Border handling ndash extend the input
                                                                                                                                • Template Matching
                                                                                                                                • Template Matching
                                                                                                                                • Template Matching
                                                                                                                                • Template Matching
                                                                                                                                • Problematic Correlation
                                                                                                                                • Normalised Cross Correlation
                                                                                                                                • Length of template
                                                                                                                                • Length of image patch
                                                                                                                                • Normalised Cross Correlation
                                                                                                                                • Normalised Cross Correlation
                                                                                                                                • Normalised Cross Correlation
                                                                                                                                • Edges
                                                                                                                                • Edges
                                                                                                                                • Finite Difference
                                                                                                                                • Edges
                                                                                                                                • Edges in 2D
                                                                                                                                • Edge filter kernel
                                                                                                                                • Prewitt filter
                                                                                                                                • Edge detection
                                                                                                                                • Edge filtering
                                                                                                                                • 02511 - Niveau af dagens emne forelaeligsing
                                                                                                                                • 02512 - Niveau af dagens emne forelaeligsing
                                                                                                                                • 02511 - Mit eget udbytte af dagen
                                                                                                                                • 02512 - Mit eget udbytte af dagen
                                                                                                                                • 02511 - Sidste uges oslashvelser (pixelwise operations)
                                                                                                                                • 02512 - Sidste uges oslashvelser (pixelwise operations)
                                                                                                                                • Denne uges brug af clickers
                                                                                                                                • What can you do after today
                                                                                                                                • Oslashvelsesrapport over oslashvelse 4 - 02511
                                                                                                                                • Exercises
                                                                                                                                  A0
                                                                                                                                  B0
                                                                                                                                  C5
                                                                                                                                  D0
                                                                                                                                  E6
                                                                                                                                  A
                                                                                                                                  B
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                                                                                                                                  D
                                                                                                                                  E
                                                                                                                                  A3
                                                                                                                                  B0
                                                                                                                                  C3
                                                                                                                                  D0
                                                                                                                                  E0
                                                                                                                                  A
                                                                                                                                  B
                                                                                                                                  C
                                                                                                                                  D
                                                                                                                                  E
                                                                                                                                  A0
                                                                                                                                  B0
                                                                                                                                  C1
                                                                                                                                  D4
                                                                                                                                  E1
                                                                                                                                  A
                                                                                                                                  B
                                                                                                                                  C
                                                                                                                                  D
                                                                                                                                  E
                                                                                                                                  A2
                                                                                                                                  B1
                                                                                                                                  C3
                                                                                                                                  D2
                                                                                                                                  E0
                                                                                                                                  A
                                                                                                                                  B
                                                                                                                                  C
                                                                                                                                  D
                                                                                                                                  E
                                                                                                                                  A0
                                                                                                                                  B0
                                                                                                                                  C2
                                                                                                                                  D6
                                                                                                                                  E0
                                                                                                                                  A
                                                                                                                                  B
                                                                                                                                  C
                                                                                                                                  D
                                                                                                                                  E
                                                                                                                                  A0
                                                                                                                                  B0
                                                                                                                                  C1
                                                                                                                                  D0
                                                                                                                                  E0
                                                                                                                                  A
                                                                                                                                  B
                                                                                                                                  C
                                                                                                                                  D
                                                                                                                                  E
                                                                                                                                  A2
                                                                                                                                  B3
                                                                                                                                  C6
                                                                                                                                  D1
                                                                                                                                  E0
                                                                                                                                  A
                                                                                                                                  B
                                                                                                                                  C
                                                                                                                                  D
                                                                                                                                  E
                                                                                                                                  A0
                                                                                                                                  B8
                                                                                                                                  C1
                                                                                                                                  D1
                                                                                                                                  E0
                                                                                                                                  A
                                                                                                                                  B
                                                                                                                                  C
                                                                                                                                  D
                                                                                                                                  E
                                                                                                                                  A1
                                                                                                                                  B2
                                                                                                                                  C2
                                                                                                                                  D3
                                                                                                                                  E2
                                                                                                                                  A
                                                                                                                                  B
                                                                                                                                  C
                                                                                                                                  D
                                                                                                                                  E

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                                                                                                                                  2122018Introduction to Medical Image Analysis56 DTU Compute Technical University of Denmark

                                                                                                                                  Template Matching The pixel with the highest value is found in the

                                                                                                                                  output imagendash Here is the highest correlation

                                                                                                                                  Input

                                                                                                                                  Template

                                                                                                                                  Output Correlation image

                                                                                                                                  DTU Compute

                                                                                                                                  2122018Introduction to Medical Image Analysis57 DTU Compute Technical University of Denmark

                                                                                                                                  Template Matching This corresponds to the found pattern in the input

                                                                                                                                  image

                                                                                                                                  Input

                                                                                                                                  Template

                                                                                                                                  Output Correlation image

                                                                                                                                  DTU Compute

                                                                                                                                  2122018Introduction to Medical Image Analysis58 DTU Compute Technical University of Denmark

                                                                                                                                  Problematic Correlation Correlation matching has problem with light areas ndash

                                                                                                                                  why

                                                                                                                                  Input (f)

                                                                                                                                  Template (h)

                                                                                                                                  Output Correlation imageFake max

                                                                                                                                  Real max

                                                                                                                                  Very High119892119892 119909119909119910119910 = 119895119895=minus119877119877

                                                                                                                                  119877119877

                                                                                                                                  119894119894=minus119877119877

                                                                                                                                  119877119877

                                                                                                                                  ℎ(119894119894 119895119895) 119891119891(119909119909 + 119894119894119910119910 + 119895119895)

                                                                                                                                  DTU Compute

                                                                                                                                  2122018Introduction to Medical Image Analysis59 DTU Compute Technical University of Denmark

                                                                                                                                  Normalised Cross Correlation

                                                                                                                                  Input (f)

                                                                                                                                  Template (h)

                                                                                                                                  Output Correlation image

                                                                                                                                  Real max

                                                                                                                                  NCC x y =Correlation

                                                                                                                                  Length of image patch sdot Length of template

                                                                                                                                  DTU Compute

                                                                                                                                  2122018Introduction to Medical Image Analysis60 DTU Compute Technical University of Denmark

                                                                                                                                  Length of template Vector length

                                                                                                                                  ndash Put all pixel values into a vectorndash Compute the length of this vector

                                                                                                                                  Describes the intensity of the templatendash Bright template has a large lengthndash Dark template has a small length

                                                                                                                                  Template (h)

                                                                                                                                  Length of template = 119895119895=minus119877119877

                                                                                                                                  119877119877

                                                                                                                                  119894119894=minus119877119877

                                                                                                                                  119877119877

                                                                                                                                  ℎ(119894119894 119895119895) ℎ(119894119894 119895119895)

                                                                                                                                  DTU Compute

                                                                                                                                  2122018Introduction to Medical Image Analysis61 DTU Compute Technical University of Denmark

                                                                                                                                  Length of image patch Vector length based on pixel values in image patch Describes the intensity of the image patch

                                                                                                                                  Template (h)

                                                                                                                                  Input (f) with patch

                                                                                                                                  DTU Compute

                                                                                                                                  2122018Introduction to Medical Image Analysis62 DTU Compute Technical University of Denmark

                                                                                                                                  Normalised Cross Correlation The length of the image patch and the length of

                                                                                                                                  template normalise the NCC If the image is very bright the NCC will be ldquopulled

                                                                                                                                  downrdquo

                                                                                                                                  NCC x y =Correlation

                                                                                                                                  Length of image patch sdot Length of template

                                                                                                                                  DTU Compute

                                                                                                                                  2122018Introduction to Medical Image Analysis63 DTU Compute Technical University of Denmark

                                                                                                                                  Normalised Cross Correlation NCC will be between

                                                                                                                                  ndash 0 No similarity between template and image patchndash 1 Template and image patch are identical

                                                                                                                                  Input (f)

                                                                                                                                  Template (h)

                                                                                                                                  Output Correlation image

                                                                                                                                  Real max

                                                                                                                                  NCC x y =Correlation

                                                                                                                                  Length of image patch sdot Length of template

                                                                                                                                  DTU Compute

                                                                                                                                  2122018Introduction to Medical Image Analysis64 DTU Compute Technical University of Denmark

                                                                                                                                  Normalised Cross Correlation

                                                                                                                                  A) 010B) 033C) 083D) 062E) 098

                                                                                                                                  Der udfoslashres template matching med og normalized crosscorrelation (NCC) beregnes Hvad bliver NNC i den markerede pixel

                                                                                                                                  1

                                                                                                                                  2 2

                                                                                                                                  3

                                                                                                                                  2

                                                                                                                                  A B C D E

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                                                                                                                                  Edges An edge is where there is a

                                                                                                                                  high change in gray level values

                                                                                                                                  Objects are often separated from the background by edgesGray level profile

                                                                                                                                  DTU Compute

                                                                                                                                  2122018Introduction to Medical Image Analysis67 DTU Compute Technical University of Denmark

                                                                                                                                  Edges The profile as a function f(d) What value is high when there

                                                                                                                                  is an edgendash The slope of fndash The slope of the tangent at d

                                                                                                                                  f(d)

                                                                                                                                  119891119891prime(119889119889)

                                                                                                                                  DTU Compute

                                                                                                                                  2122018Introduction to Medical Image Analysis68 DTU Compute Technical University of Denmark

                                                                                                                                  Finite Difference Definition of slope

                                                                                                                                  Approximation

                                                                                                                                  Simpler approximationh = 1

                                                                                                                                  119891119891prime 119889119889 = limℎrarr0

                                                                                                                                  119891119891 119889119889 + ℎ minus 119891119891(119889119889)ℎ

                                                                                                                                  119891119891prime 119889119889 asymp119891119891 119889119889 + ℎ minus 119891119891(119889119889)

                                                                                                                                  ℎ

                                                                                                                                  119891119891prime 119889119889 asymp 119891119891 119889119889 + 1 minus 119891119891(119889119889)

                                                                                                                                  DTU Compute

                                                                                                                                  2122018Introduction to Medical Image Analysis69 DTU Compute Technical University of Denmark

                                                                                                                                  Edges Discrete approximation of frsquo(d) Can be implemented as a filter

                                                                                                                                  -1 0 1

                                                                                                                                  f(d-2) f(d-1) f(d) f(d+1) f(d+2) f(d+3)

                                                                                                                                  f(d)

                                                                                                                                  119891119891prime 119889119889 asymp 119891119891 119889119889 + 1 minus 119891119891(119889119889)

                                                                                                                                  DTU Compute

                                                                                                                                  2122018Introduction to Medical Image Analysis70 DTU Compute Technical University of Denmark

                                                                                                                                  Edges in 2D Changes in gray level values

                                                                                                                                  ndash Image gradientndash Gradient is the 2D derivative of a 2D function f(xy)ndash Equal to the slope of the imagendash A steep slope is equal to an edge

                                                                                                                                  120571120571119891119891 119909119909119910119910 = 119866(119892119892119909119909119892119892119910119910)

                                                                                                                                  DTU Compute

                                                                                                                                  2122018Introduction to Medical Image Analysis71 DTU Compute Technical University of Denmark

                                                                                                                                  Edge filter kernel The Prewitt filter is a typical

                                                                                                                                  edge filter Output image has high

                                                                                                                                  values where there are edges

                                                                                                                                  -1 0 1

                                                                                                                                  -1 0 1

                                                                                                                                  -1 0 1Vertical Prewitt filter

                                                                                                                                  DTU Compute

                                                                                                                                  2122018Introduction to Medical Image Analysis72 DTU Compute Technical University of Denmark

                                                                                                                                  Prewitt filter

                                                                                                                                  Original Prewitt Prewitt

                                                                                                                                  Hot colormapSmooth 15x15

                                                                                                                                  Smooth 15x15

                                                                                                                                  Prewitt

                                                                                                                                  DTU Compute

                                                                                                                                  2122018Introduction to Medical Image Analysis73 DTU Compute Technical University of Denmark

                                                                                                                                  Edge detection Edge filter

                                                                                                                                  ndash Prewitt for example Thresholding

                                                                                                                                  ndash Separate edges from non-edges

                                                                                                                                  Output is binary imagendash Edges are white

                                                                                                                                  DTU Compute

                                                                                                                                  2122018Introduction to Medical Image Analysis74 DTU Compute Technical University of Denmark

                                                                                                                                  Edge filtering

                                                                                                                                  A) MeanB) Horizontal SobelC) Vertical PrewittD) Horisontal PrewittE) Median

                                                                                                                                  Der udfoslashres en filtrering (correlation) med et filter paring billedet Der bruges ikke coefficient normalization Den filtrerede vaeligrdi i den markerede pixel bliver -119 Hvilket et 3x3 filter blev benyttet

                                                                                                                                  0

                                                                                                                                  8

                                                                                                                                  1 10

                                                                                                                                  A B C D E

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                                                                                                                                  02511 - Niveau af dagens emne forelaeligsingA) Meget letB) LetC) PassendeD) SvaeligrtE) Meget svaeligrt

                                                                                                                                  23

                                                                                                                                  6

                                                                                                                                  10

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                                                                                                                                  2122018Introduction to Medical Image Analysis77 DTU Compute Technical University of Denmark

                                                                                                                                  02512 - Niveau af dagens emne forelaeligsingA) Meget letB) LetC) PassendeD) SvaeligrtE) Meget svaeligrt

                                                                                                                                  0 0

                                                                                                                                  1

                                                                                                                                  0 0

                                                                                                                                  A B C D E

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                                                                                                                                  0
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                                                                                                                                  2122018Introduction to Medical Image Analysis78 DTU Compute Technical University of Denmark

                                                                                                                                  02511 - Mit eget udbytte af dagenA) Jeg har laeligrt meget lidtB) Lidt laeligringC) PassendeD) God laeligringE) Jeg har laeligrt meget

                                                                                                                                  0 0

                                                                                                                                  2

                                                                                                                                  6

                                                                                                                                  0

                                                                                                                                  A B C D E

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                                                                                                                                  2122018Introduction to Medical Image Analysis79 DTU Compute Technical University of Denmark

                                                                                                                                  02512 - Mit eget udbytte af dagenA) Jeg har laeligrt meget lidtB) Lidt laeligringC) PassendeD) God laeligringE) Jeg har laeligrt meget

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                                                                                                                                  02511 - Sidste uges oslashvelser (pixelwiseoperations)A) Meget letteB) LetteC) PassendeD) SvaeligreE) Meget svaeligre

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                                                                                                                                  2122018Introduction to Medical Image Analysis81 DTU Compute Technical University of Denmark

                                                                                                                                  02512 - Sidste uges oslashvelser (pixelwiseoperations)A) Meget letteB) LetteC) PassendeD) SvaeligreE) Meget svaeligre

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                                                                                                                                  2122018Introduction to Medical Image Analysis82 DTU Compute Technical University of Denmark

                                                                                                                                  Denne uges brug af clickersA) click click click ndash jeg bliver

                                                                                                                                  sindssygB) For meget clickC) PassendeD) Jeg vil gerne have lidt mereE) Jeg kan ikrsquo faring nok

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                                                                                                                                  2122018Introduction to Medical Image Analysis83 DTU Compute Technical University of Denmark

                                                                                                                                  What can you do after today Describe the difference between point processing and neighbourhood

                                                                                                                                  processing Compute a rank filtered image using the min max median and

                                                                                                                                  difference rank filters Compute a mean filtered image Decide if median or average filtering should be used for noise removal Choose the appropriate image border handling based on a given input

                                                                                                                                  image Implement and apply template matching Compute the normalised cross correlation and explain why it should be

                                                                                                                                  used Apply given image filter kernels to images Use edge filters on images Describe finite difference approximation of image gradients Describe the concept of edge detection

                                                                                                                                  DTU Compute

                                                                                                                                  2122018Introduction to Medical Image Analysis84 DTU Compute Technical University of Denmark

                                                                                                                                  Oslashvelsesrapport over oslashvelse 4 - 02511 Oslashvelser taeligller cirka 30 af karakteren Skal afleveres senest den 7 marts kl 2359 Kan afleveres af 1 eller 2 personer

                                                                                                                                  ndash I skal skrive jeres egen oslashvelsesrapportndash Brug mindst et af jeres egne billeder

                                                                                                                                  Afleveres som PDF Lad vaeligre med at kopiere opgaveteksten ind i jeres

                                                                                                                                  opgave Put Matlab kode i et Appendix og henvis fra teksten Eksempel rapport over oslashvelse findes paring

                                                                                                                                  hjemmesiden under eksamen

                                                                                                                                  DTU Compute

                                                                                                                                  2122018Introduction to Medical Image Analysis85 DTU Compute Technical University of Denmark

                                                                                                                                  Exercises

                                                                                                                                  • Introduction to Medical Image Analysis
                                                                                                                                  • Lecture 4 ndash Neighbourhood Processing
                                                                                                                                  • What can you do after today
                                                                                                                                  • Point processing
                                                                                                                                  • Point processing
                                                                                                                                  • Neighbourhood processing
                                                                                                                                  • Use of filtering
                                                                                                                                  • Salt and pepper noise
                                                                                                                                  • Salt and pepper noise
                                                                                                                                  • What is so special about noise
                                                                                                                                  • Noise ndash go away
                                                                                                                                  • What is the median Value
                                                                                                                                  • The median value
                                                                                                                                  • Noise away ndash the median filter
                                                                                                                                  • Noise removal ndash average filter
                                                                                                                                  • Noise removal ndash median filter
                                                                                                                                  • Image Filtering
                                                                                                                                  • Median filter
                                                                                                                                  • Rank filters
                                                                                                                                  • Median filter
                                                                                                                                  • Correlation
                                                                                                                                  • Why do we need similarity
                                                                                                                                  • Correlation (1D)
                                                                                                                                  • Correlation (1D)
                                                                                                                                  • Normalisation
                                                                                                                                  • Normalisation
                                                                                                                                  • Correlation on images
                                                                                                                                  • Correlation on images
                                                                                                                                  • Correlation on images
                                                                                                                                  • Draw your filter
                                                                                                                                  • Correlation on images ndash no normalisation
                                                                                                                                  • Correlation on images ndash no normalisation 2
                                                                                                                                  • Mathematics of 2D Correlation
                                                                                                                                  • Mathematics of 2D Correlation
                                                                                                                                  • Mathematics of 2D Correlation
                                                                                                                                  • Slide Number 40
                                                                                                                                  • 2D Kernel Normalisation
                                                                                                                                  • Correlation
                                                                                                                                  • Smoothing filters
                                                                                                                                  • Use of smoothing
                                                                                                                                  • Use of smoothing
                                                                                                                                  • Mean filter
                                                                                                                                  • Border handling
                                                                                                                                  • Border handling ndash extend the input
                                                                                                                                  • Correlation with zero padding
                                                                                                                                  • Border handling ndash extend the input
                                                                                                                                  • Template Matching
                                                                                                                                  • Template Matching
                                                                                                                                  • Template Matching
                                                                                                                                  • Template Matching
                                                                                                                                  • Problematic Correlation
                                                                                                                                  • Normalised Cross Correlation
                                                                                                                                  • Length of template
                                                                                                                                  • Length of image patch
                                                                                                                                  • Normalised Cross Correlation
                                                                                                                                  • Normalised Cross Correlation
                                                                                                                                  • Normalised Cross Correlation
                                                                                                                                  • Edges
                                                                                                                                  • Edges
                                                                                                                                  • Finite Difference
                                                                                                                                  • Edges
                                                                                                                                  • Edges in 2D
                                                                                                                                  • Edge filter kernel
                                                                                                                                  • Prewitt filter
                                                                                                                                  • Edge detection
                                                                                                                                  • Edge filtering
                                                                                                                                  • 02511 - Niveau af dagens emne forelaeligsing
                                                                                                                                  • 02512 - Niveau af dagens emne forelaeligsing
                                                                                                                                  • 02511 - Mit eget udbytte af dagen
                                                                                                                                  • 02512 - Mit eget udbytte af dagen
                                                                                                                                  • 02511 - Sidste uges oslashvelser (pixelwise operations)
                                                                                                                                  • 02512 - Sidste uges oslashvelser (pixelwise operations)
                                                                                                                                  • Denne uges brug af clickers
                                                                                                                                  • What can you do after today
                                                                                                                                  • Oslashvelsesrapport over oslashvelse 4 - 02511
                                                                                                                                  • Exercises
                                                                                                                                    A0
                                                                                                                                    B0
                                                                                                                                    C5
                                                                                                                                    D0
                                                                                                                                    E6
                                                                                                                                    A
                                                                                                                                    B
                                                                                                                                    C
                                                                                                                                    D
                                                                                                                                    E
                                                                                                                                    A3
                                                                                                                                    B0
                                                                                                                                    C3
                                                                                                                                    D0
                                                                                                                                    E0
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                                                                                                                                    B
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                                                                                                                                    D
                                                                                                                                    E
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                                                                                                                                    B0
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                                                                                                                                    D4
                                                                                                                                    E1
                                                                                                                                    A
                                                                                                                                    B
                                                                                                                                    C
                                                                                                                                    D
                                                                                                                                    E
                                                                                                                                    A2
                                                                                                                                    B1
                                                                                                                                    C3
                                                                                                                                    D2
                                                                                                                                    E0
                                                                                                                                    A
                                                                                                                                    B
                                                                                                                                    C
                                                                                                                                    D
                                                                                                                                    E
                                                                                                                                    A0
                                                                                                                                    B0
                                                                                                                                    C2
                                                                                                                                    D6
                                                                                                                                    E0
                                                                                                                                    A
                                                                                                                                    B
                                                                                                                                    C
                                                                                                                                    D
                                                                                                                                    E
                                                                                                                                    A0
                                                                                                                                    B0
                                                                                                                                    C1
                                                                                                                                    D0
                                                                                                                                    E0
                                                                                                                                    A
                                                                                                                                    B
                                                                                                                                    C
                                                                                                                                    D
                                                                                                                                    E
                                                                                                                                    A2
                                                                                                                                    B3
                                                                                                                                    C6
                                                                                                                                    D1
                                                                                                                                    E0
                                                                                                                                    A
                                                                                                                                    B
                                                                                                                                    C
                                                                                                                                    D
                                                                                                                                    E
                                                                                                                                    A0
                                                                                                                                    B8
                                                                                                                                    C1
                                                                                                                                    D1
                                                                                                                                    E0
                                                                                                                                    A
                                                                                                                                    B
                                                                                                                                    C
                                                                                                                                    D
                                                                                                                                    E
                                                                                                                                    A1
                                                                                                                                    B2
                                                                                                                                    C2
                                                                                                                                    D3
                                                                                                                                    E2
                                                                                                                                    A
                                                                                                                                    B
                                                                                                                                    C
                                                                                                                                    D
                                                                                                                                    E

                                                                                                                                    DTU Compute

                                                                                                                                    2122018Introduction to Medical Image Analysis57 DTU Compute Technical University of Denmark

                                                                                                                                    Template Matching This corresponds to the found pattern in the input

                                                                                                                                    image

                                                                                                                                    Input

                                                                                                                                    Template

                                                                                                                                    Output Correlation image

                                                                                                                                    DTU Compute

                                                                                                                                    2122018Introduction to Medical Image Analysis58 DTU Compute Technical University of Denmark

                                                                                                                                    Problematic Correlation Correlation matching has problem with light areas ndash

                                                                                                                                    why

                                                                                                                                    Input (f)

                                                                                                                                    Template (h)

                                                                                                                                    Output Correlation imageFake max

                                                                                                                                    Real max

                                                                                                                                    Very High119892119892 119909119909119910119910 = 119895119895=minus119877119877

                                                                                                                                    119877119877

                                                                                                                                    119894119894=minus119877119877

                                                                                                                                    119877119877

                                                                                                                                    ℎ(119894119894 119895119895) 119891119891(119909119909 + 119894119894119910119910 + 119895119895)

                                                                                                                                    DTU Compute

                                                                                                                                    2122018Introduction to Medical Image Analysis59 DTU Compute Technical University of Denmark

                                                                                                                                    Normalised Cross Correlation

                                                                                                                                    Input (f)

                                                                                                                                    Template (h)

                                                                                                                                    Output Correlation image

                                                                                                                                    Real max

                                                                                                                                    NCC x y =Correlation

                                                                                                                                    Length of image patch sdot Length of template

                                                                                                                                    DTU Compute

                                                                                                                                    2122018Introduction to Medical Image Analysis60 DTU Compute Technical University of Denmark

                                                                                                                                    Length of template Vector length

                                                                                                                                    ndash Put all pixel values into a vectorndash Compute the length of this vector

                                                                                                                                    Describes the intensity of the templatendash Bright template has a large lengthndash Dark template has a small length

                                                                                                                                    Template (h)

                                                                                                                                    Length of template = 119895119895=minus119877119877

                                                                                                                                    119877119877

                                                                                                                                    119894119894=minus119877119877

                                                                                                                                    119877119877

                                                                                                                                    ℎ(119894119894 119895119895) ℎ(119894119894 119895119895)

                                                                                                                                    DTU Compute

                                                                                                                                    2122018Introduction to Medical Image Analysis61 DTU Compute Technical University of Denmark

                                                                                                                                    Length of image patch Vector length based on pixel values in image patch Describes the intensity of the image patch

                                                                                                                                    Template (h)

                                                                                                                                    Input (f) with patch

                                                                                                                                    DTU Compute

                                                                                                                                    2122018Introduction to Medical Image Analysis62 DTU Compute Technical University of Denmark

                                                                                                                                    Normalised Cross Correlation The length of the image patch and the length of

                                                                                                                                    template normalise the NCC If the image is very bright the NCC will be ldquopulled

                                                                                                                                    downrdquo

                                                                                                                                    NCC x y =Correlation

                                                                                                                                    Length of image patch sdot Length of template

                                                                                                                                    DTU Compute

                                                                                                                                    2122018Introduction to Medical Image Analysis63 DTU Compute Technical University of Denmark

                                                                                                                                    Normalised Cross Correlation NCC will be between

                                                                                                                                    ndash 0 No similarity between template and image patchndash 1 Template and image patch are identical

                                                                                                                                    Input (f)

                                                                                                                                    Template (h)

                                                                                                                                    Output Correlation image

                                                                                                                                    Real max

                                                                                                                                    NCC x y =Correlation

                                                                                                                                    Length of image patch sdot Length of template

                                                                                                                                    DTU Compute

                                                                                                                                    2122018Introduction to Medical Image Analysis64 DTU Compute Technical University of Denmark

                                                                                                                                    Normalised Cross Correlation

                                                                                                                                    A) 010B) 033C) 083D) 062E) 098

                                                                                                                                    Der udfoslashres template matching med og normalized crosscorrelation (NCC) beregnes Hvad bliver NNC i den markerede pixel

                                                                                                                                    1

                                                                                                                                    2 2

                                                                                                                                    3

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                                                                                                                                    2122018Introduction to Medical Image Analysis66 DTU Compute Technical University of Denmark

                                                                                                                                    Edges An edge is where there is a

                                                                                                                                    high change in gray level values

                                                                                                                                    Objects are often separated from the background by edgesGray level profile

                                                                                                                                    DTU Compute

                                                                                                                                    2122018Introduction to Medical Image Analysis67 DTU Compute Technical University of Denmark

                                                                                                                                    Edges The profile as a function f(d) What value is high when there

                                                                                                                                    is an edgendash The slope of fndash The slope of the tangent at d

                                                                                                                                    f(d)

                                                                                                                                    119891119891prime(119889119889)

                                                                                                                                    DTU Compute

                                                                                                                                    2122018Introduction to Medical Image Analysis68 DTU Compute Technical University of Denmark

                                                                                                                                    Finite Difference Definition of slope

                                                                                                                                    Approximation

                                                                                                                                    Simpler approximationh = 1

                                                                                                                                    119891119891prime 119889119889 = limℎrarr0

                                                                                                                                    119891119891 119889119889 + ℎ minus 119891119891(119889119889)ℎ

                                                                                                                                    119891119891prime 119889119889 asymp119891119891 119889119889 + ℎ minus 119891119891(119889119889)

                                                                                                                                    ℎ

                                                                                                                                    119891119891prime 119889119889 asymp 119891119891 119889119889 + 1 minus 119891119891(119889119889)

                                                                                                                                    DTU Compute

                                                                                                                                    2122018Introduction to Medical Image Analysis69 DTU Compute Technical University of Denmark

                                                                                                                                    Edges Discrete approximation of frsquo(d) Can be implemented as a filter

                                                                                                                                    -1 0 1

                                                                                                                                    f(d-2) f(d-1) f(d) f(d+1) f(d+2) f(d+3)

                                                                                                                                    f(d)

                                                                                                                                    119891119891prime 119889119889 asymp 119891119891 119889119889 + 1 minus 119891119891(119889119889)

                                                                                                                                    DTU Compute

                                                                                                                                    2122018Introduction to Medical Image Analysis70 DTU Compute Technical University of Denmark

                                                                                                                                    Edges in 2D Changes in gray level values

                                                                                                                                    ndash Image gradientndash Gradient is the 2D derivative of a 2D function f(xy)ndash Equal to the slope of the imagendash A steep slope is equal to an edge

                                                                                                                                    120571120571119891119891 119909119909119910119910 = 119866(119892119892119909119909119892119892119910119910)

                                                                                                                                    DTU Compute

                                                                                                                                    2122018Introduction to Medical Image Analysis71 DTU Compute Technical University of Denmark

                                                                                                                                    Edge filter kernel The Prewitt filter is a typical

                                                                                                                                    edge filter Output image has high

                                                                                                                                    values where there are edges

                                                                                                                                    -1 0 1

                                                                                                                                    -1 0 1

                                                                                                                                    -1 0 1Vertical Prewitt filter

                                                                                                                                    DTU Compute

                                                                                                                                    2122018Introduction to Medical Image Analysis72 DTU Compute Technical University of Denmark

                                                                                                                                    Prewitt filter

                                                                                                                                    Original Prewitt Prewitt

                                                                                                                                    Hot colormapSmooth 15x15

                                                                                                                                    Smooth 15x15

                                                                                                                                    Prewitt

                                                                                                                                    DTU Compute

                                                                                                                                    2122018Introduction to Medical Image Analysis73 DTU Compute Technical University of Denmark

                                                                                                                                    Edge detection Edge filter

                                                                                                                                    ndash Prewitt for example Thresholding

                                                                                                                                    ndash Separate edges from non-edges

                                                                                                                                    Output is binary imagendash Edges are white

                                                                                                                                    DTU Compute

                                                                                                                                    2122018Introduction to Medical Image Analysis74 DTU Compute Technical University of Denmark

                                                                                                                                    Edge filtering

                                                                                                                                    A) MeanB) Horizontal SobelC) Vertical PrewittD) Horisontal PrewittE) Median

                                                                                                                                    Der udfoslashres en filtrering (correlation) med et filter paring billedet Der bruges ikke coefficient normalization Den filtrerede vaeligrdi i den markerede pixel bliver -119 Hvilket et 3x3 filter blev benyttet

                                                                                                                                    0

                                                                                                                                    8

                                                                                                                                    1 10

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                                                                                                                                    2122018Introduction to Medical Image Analysis76 DTU Compute Technical University of Denmark

                                                                                                                                    02511 - Niveau af dagens emne forelaeligsingA) Meget letB) LetC) PassendeD) SvaeligrtE) Meget svaeligrt

                                                                                                                                    23

                                                                                                                                    6

                                                                                                                                    10

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                                                                                                                                    2122018Introduction to Medical Image Analysis77 DTU Compute Technical University of Denmark

                                                                                                                                    02512 - Niveau af dagens emne forelaeligsingA) Meget letB) LetC) PassendeD) SvaeligrtE) Meget svaeligrt

                                                                                                                                    0 0

                                                                                                                                    1

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                                                                                                                                    2122018Introduction to Medical Image Analysis78 DTU Compute Technical University of Denmark

                                                                                                                                    02511 - Mit eget udbytte af dagenA) Jeg har laeligrt meget lidtB) Lidt laeligringC) PassendeD) God laeligringE) Jeg har laeligrt meget

                                                                                                                                    0 0

                                                                                                                                    2

                                                                                                                                    6

                                                                                                                                    0

                                                                                                                                    A B C D E

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                                                                                                                                    2122018Introduction to Medical Image Analysis79 DTU Compute Technical University of Denmark

                                                                                                                                    02512 - Mit eget udbytte af dagenA) Jeg har laeligrt meget lidtB) Lidt laeligringC) PassendeD) God laeligringE) Jeg har laeligrt meget

                                                                                                                                    2

                                                                                                                                    1

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                                                                                                                                    2

                                                                                                                                    0

                                                                                                                                    A B C D E

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                                                                                                                                    2
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                                                                                                                                    DTU Compute

                                                                                                                                    2122018Introduction to Medical Image Analysis80 DTU Compute Technical University of Denmark

                                                                                                                                    02511 - Sidste uges oslashvelser (pixelwiseoperations)A) Meget letteB) LetteC) PassendeD) SvaeligreE) Meget svaeligre

                                                                                                                                    0 0

                                                                                                                                    1

                                                                                                                                    4

                                                                                                                                    1

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                                                                                                                                    2122018Introduction to Medical Image Analysis81 DTU Compute Technical University of Denmark

                                                                                                                                    02512 - Sidste uges oslashvelser (pixelwiseoperations)A) Meget letteB) LetteC) PassendeD) SvaeligreE) Meget svaeligre

                                                                                                                                    3

                                                                                                                                    0

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                                                                                                                                    DTU Compute

                                                                                                                                    2122018Introduction to Medical Image Analysis82 DTU Compute Technical University of Denmark

                                                                                                                                    Denne uges brug af clickersA) click click click ndash jeg bliver

                                                                                                                                    sindssygB) For meget clickC) PassendeD) Jeg vil gerne have lidt mereE) Jeg kan ikrsquo faring nok

                                                                                                                                    0 0

                                                                                                                                    5

                                                                                                                                    0

                                                                                                                                    6

                                                                                                                                    A B C D E

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                                                                                                                                    DTU Compute

                                                                                                                                    2122018Introduction to Medical Image Analysis83 DTU Compute Technical University of Denmark

                                                                                                                                    What can you do after today Describe the difference between point processing and neighbourhood

                                                                                                                                    processing Compute a rank filtered image using the min max median and

                                                                                                                                    difference rank filters Compute a mean filtered image Decide if median or average filtering should be used for noise removal Choose the appropriate image border handling based on a given input

                                                                                                                                    image Implement and apply template matching Compute the normalised cross correlation and explain why it should be

                                                                                                                                    used Apply given image filter kernels to images Use edge filters on images Describe finite difference approximation of image gradients Describe the concept of edge detection

                                                                                                                                    DTU Compute

                                                                                                                                    2122018Introduction to Medical Image Analysis84 DTU Compute Technical University of Denmark

                                                                                                                                    Oslashvelsesrapport over oslashvelse 4 - 02511 Oslashvelser taeligller cirka 30 af karakteren Skal afleveres senest den 7 marts kl 2359 Kan afleveres af 1 eller 2 personer

                                                                                                                                    ndash I skal skrive jeres egen oslashvelsesrapportndash Brug mindst et af jeres egne billeder

                                                                                                                                    Afleveres som PDF Lad vaeligre med at kopiere opgaveteksten ind i jeres

                                                                                                                                    opgave Put Matlab kode i et Appendix og henvis fra teksten Eksempel rapport over oslashvelse findes paring

                                                                                                                                    hjemmesiden under eksamen

                                                                                                                                    DTU Compute

                                                                                                                                    2122018Introduction to Medical Image Analysis85 DTU Compute Technical University of Denmark

                                                                                                                                    Exercises

                                                                                                                                    • Introduction to Medical Image Analysis
                                                                                                                                    • Lecture 4 ndash Neighbourhood Processing
                                                                                                                                    • What can you do after today
                                                                                                                                    • Point processing
                                                                                                                                    • Point processing
                                                                                                                                    • Neighbourhood processing
                                                                                                                                    • Use of filtering
                                                                                                                                    • Salt and pepper noise
                                                                                                                                    • Salt and pepper noise
                                                                                                                                    • What is so special about noise
                                                                                                                                    • Noise ndash go away
                                                                                                                                    • What is the median Value
                                                                                                                                    • The median value
                                                                                                                                    • Noise away ndash the median filter
                                                                                                                                    • Noise removal ndash average filter
                                                                                                                                    • Noise removal ndash median filter
                                                                                                                                    • Image Filtering
                                                                                                                                    • Median filter
                                                                                                                                    • Rank filters
                                                                                                                                    • Median filter
                                                                                                                                    • Correlation
                                                                                                                                    • Why do we need similarity
                                                                                                                                    • Correlation (1D)
                                                                                                                                    • Correlation (1D)
                                                                                                                                    • Normalisation
                                                                                                                                    • Normalisation
                                                                                                                                    • Correlation on images
                                                                                                                                    • Correlation on images
                                                                                                                                    • Correlation on images
                                                                                                                                    • Draw your filter
                                                                                                                                    • Correlation on images ndash no normalisation
                                                                                                                                    • Correlation on images ndash no normalisation 2
                                                                                                                                    • Mathematics of 2D Correlation
                                                                                                                                    • Mathematics of 2D Correlation
                                                                                                                                    • Mathematics of 2D Correlation
                                                                                                                                    • Slide Number 40
                                                                                                                                    • 2D Kernel Normalisation
                                                                                                                                    • Correlation
                                                                                                                                    • Smoothing filters
                                                                                                                                    • Use of smoothing
                                                                                                                                    • Use of smoothing
                                                                                                                                    • Mean filter
                                                                                                                                    • Border handling
                                                                                                                                    • Border handling ndash extend the input
                                                                                                                                    • Correlation with zero padding
                                                                                                                                    • Border handling ndash extend the input
                                                                                                                                    • Template Matching
                                                                                                                                    • Template Matching
                                                                                                                                    • Template Matching
                                                                                                                                    • Template Matching
                                                                                                                                    • Problematic Correlation
                                                                                                                                    • Normalised Cross Correlation
                                                                                                                                    • Length of template
                                                                                                                                    • Length of image patch
                                                                                                                                    • Normalised Cross Correlation
                                                                                                                                    • Normalised Cross Correlation
                                                                                                                                    • Normalised Cross Correlation
                                                                                                                                    • Edges
                                                                                                                                    • Edges
                                                                                                                                    • Finite Difference
                                                                                                                                    • Edges
                                                                                                                                    • Edges in 2D
                                                                                                                                    • Edge filter kernel
                                                                                                                                    • Prewitt filter
                                                                                                                                    • Edge detection
                                                                                                                                    • Edge filtering
                                                                                                                                    • 02511 - Niveau af dagens emne forelaeligsing
                                                                                                                                    • 02512 - Niveau af dagens emne forelaeligsing
                                                                                                                                    • 02511 - Mit eget udbytte af dagen
                                                                                                                                    • 02512 - Mit eget udbytte af dagen
                                                                                                                                    • 02511 - Sidste uges oslashvelser (pixelwise operations)
                                                                                                                                    • 02512 - Sidste uges oslashvelser (pixelwise operations)
                                                                                                                                    • Denne uges brug af clickers
                                                                                                                                    • What can you do after today
                                                                                                                                    • Oslashvelsesrapport over oslashvelse 4 - 02511
                                                                                                                                    • Exercises
                                                                                                                                      A0
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                                                                                                                                      E
                                                                                                                                      A1
                                                                                                                                      B2
                                                                                                                                      C2
                                                                                                                                      D3
                                                                                                                                      E2
                                                                                                                                      A
                                                                                                                                      B
                                                                                                                                      C
                                                                                                                                      D
                                                                                                                                      E

                                                                                                                                      DTU Compute

                                                                                                                                      2122018Introduction to Medical Image Analysis58 DTU Compute Technical University of Denmark

                                                                                                                                      Problematic Correlation Correlation matching has problem with light areas ndash

                                                                                                                                      why

                                                                                                                                      Input (f)

                                                                                                                                      Template (h)

                                                                                                                                      Output Correlation imageFake max

                                                                                                                                      Real max

                                                                                                                                      Very High119892119892 119909119909119910119910 = 119895119895=minus119877119877

                                                                                                                                      119877119877

                                                                                                                                      119894119894=minus119877119877

                                                                                                                                      119877119877

                                                                                                                                      ℎ(119894119894 119895119895) 119891119891(119909119909 + 119894119894119910119910 + 119895119895)

                                                                                                                                      DTU Compute

                                                                                                                                      2122018Introduction to Medical Image Analysis59 DTU Compute Technical University of Denmark

                                                                                                                                      Normalised Cross Correlation

                                                                                                                                      Input (f)

                                                                                                                                      Template (h)

                                                                                                                                      Output Correlation image

                                                                                                                                      Real max

                                                                                                                                      NCC x y =Correlation

                                                                                                                                      Length of image patch sdot Length of template

                                                                                                                                      DTU Compute

                                                                                                                                      2122018Introduction to Medical Image Analysis60 DTU Compute Technical University of Denmark

                                                                                                                                      Length of template Vector length

                                                                                                                                      ndash Put all pixel values into a vectorndash Compute the length of this vector

                                                                                                                                      Describes the intensity of the templatendash Bright template has a large lengthndash Dark template has a small length

                                                                                                                                      Template (h)

                                                                                                                                      Length of template = 119895119895=minus119877119877

                                                                                                                                      119877119877

                                                                                                                                      119894119894=minus119877119877

                                                                                                                                      119877119877

                                                                                                                                      ℎ(119894119894 119895119895) ℎ(119894119894 119895119895)

                                                                                                                                      DTU Compute

                                                                                                                                      2122018Introduction to Medical Image Analysis61 DTU Compute Technical University of Denmark

                                                                                                                                      Length of image patch Vector length based on pixel values in image patch Describes the intensity of the image patch

                                                                                                                                      Template (h)

                                                                                                                                      Input (f) with patch

                                                                                                                                      DTU Compute

                                                                                                                                      2122018Introduction to Medical Image Analysis62 DTU Compute Technical University of Denmark

                                                                                                                                      Normalised Cross Correlation The length of the image patch and the length of

                                                                                                                                      template normalise the NCC If the image is very bright the NCC will be ldquopulled

                                                                                                                                      downrdquo

                                                                                                                                      NCC x y =Correlation

                                                                                                                                      Length of image patch sdot Length of template

                                                                                                                                      DTU Compute

                                                                                                                                      2122018Introduction to Medical Image Analysis63 DTU Compute Technical University of Denmark

                                                                                                                                      Normalised Cross Correlation NCC will be between

                                                                                                                                      ndash 0 No similarity between template and image patchndash 1 Template and image patch are identical

                                                                                                                                      Input (f)

                                                                                                                                      Template (h)

                                                                                                                                      Output Correlation image

                                                                                                                                      Real max

                                                                                                                                      NCC x y =Correlation

                                                                                                                                      Length of image patch sdot Length of template

                                                                                                                                      DTU Compute

                                                                                                                                      2122018Introduction to Medical Image Analysis64 DTU Compute Technical University of Denmark

                                                                                                                                      Normalised Cross Correlation

                                                                                                                                      A) 010B) 033C) 083D) 062E) 098

                                                                                                                                      Der udfoslashres template matching med og normalized crosscorrelation (NCC) beregnes Hvad bliver NNC i den markerede pixel

                                                                                                                                      1

                                                                                                                                      2 2

                                                                                                                                      3

                                                                                                                                      2

                                                                                                                                      A B C D E

                                                                                                                                      Chart1

                                                                                                                                      1
                                                                                                                                      2
                                                                                                                                      2
                                                                                                                                      3
                                                                                                                                      2

                                                                                                                                      Sheet1

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                                                                                                                                      2122018Introduction to Medical Image Analysis66 DTU Compute Technical University of Denmark

                                                                                                                                      Edges An edge is where there is a

                                                                                                                                      high change in gray level values

                                                                                                                                      Objects are often separated from the background by edgesGray level profile

                                                                                                                                      DTU Compute

                                                                                                                                      2122018Introduction to Medical Image Analysis67 DTU Compute Technical University of Denmark

                                                                                                                                      Edges The profile as a function f(d) What value is high when there

                                                                                                                                      is an edgendash The slope of fndash The slope of the tangent at d

                                                                                                                                      f(d)

                                                                                                                                      119891119891prime(119889119889)

                                                                                                                                      DTU Compute

                                                                                                                                      2122018Introduction to Medical Image Analysis68 DTU Compute Technical University of Denmark

                                                                                                                                      Finite Difference Definition of slope

                                                                                                                                      Approximation

                                                                                                                                      Simpler approximationh = 1

                                                                                                                                      119891119891prime 119889119889 = limℎrarr0

                                                                                                                                      119891119891 119889119889 + ℎ minus 119891119891(119889119889)ℎ

                                                                                                                                      119891119891prime 119889119889 asymp119891119891 119889119889 + ℎ minus 119891119891(119889119889)

                                                                                                                                      ℎ

                                                                                                                                      119891119891prime 119889119889 asymp 119891119891 119889119889 + 1 minus 119891119891(119889119889)

                                                                                                                                      DTU Compute

                                                                                                                                      2122018Introduction to Medical Image Analysis69 DTU Compute Technical University of Denmark

                                                                                                                                      Edges Discrete approximation of frsquo(d) Can be implemented as a filter

                                                                                                                                      -1 0 1

                                                                                                                                      f(d-2) f(d-1) f(d) f(d+1) f(d+2) f(d+3)

                                                                                                                                      f(d)

                                                                                                                                      119891119891prime 119889119889 asymp 119891119891 119889119889 + 1 minus 119891119891(119889119889)

                                                                                                                                      DTU Compute

                                                                                                                                      2122018Introduction to Medical Image Analysis70 DTU Compute Technical University of Denmark

                                                                                                                                      Edges in 2D Changes in gray level values

                                                                                                                                      ndash Image gradientndash Gradient is the 2D derivative of a 2D function f(xy)ndash Equal to the slope of the imagendash A steep slope is equal to an edge

                                                                                                                                      120571120571119891119891 119909119909119910119910 = 119866(119892119892119909119909119892119892119910119910)

                                                                                                                                      DTU Compute

                                                                                                                                      2122018Introduction to Medical Image Analysis71 DTU Compute Technical University of Denmark

                                                                                                                                      Edge filter kernel The Prewitt filter is a typical

                                                                                                                                      edge filter Output image has high

                                                                                                                                      values where there are edges

                                                                                                                                      -1 0 1

                                                                                                                                      -1 0 1

                                                                                                                                      -1 0 1Vertical Prewitt filter

                                                                                                                                      DTU Compute

                                                                                                                                      2122018Introduction to Medical Image Analysis72 DTU Compute Technical University of Denmark

                                                                                                                                      Prewitt filter

                                                                                                                                      Original Prewitt Prewitt

                                                                                                                                      Hot colormapSmooth 15x15

                                                                                                                                      Smooth 15x15

                                                                                                                                      Prewitt

                                                                                                                                      DTU Compute

                                                                                                                                      2122018Introduction to Medical Image Analysis73 DTU Compute Technical University of Denmark

                                                                                                                                      Edge detection Edge filter

                                                                                                                                      ndash Prewitt for example Thresholding

                                                                                                                                      ndash Separate edges from non-edges

                                                                                                                                      Output is binary imagendash Edges are white

                                                                                                                                      DTU Compute

                                                                                                                                      2122018Introduction to Medical Image Analysis74 DTU Compute Technical University of Denmark

                                                                                                                                      Edge filtering

                                                                                                                                      A) MeanB) Horizontal SobelC) Vertical PrewittD) Horisontal PrewittE) Median

                                                                                                                                      Der udfoslashres en filtrering (correlation) med et filter paring billedet Der bruges ikke coefficient normalization Den filtrerede vaeligrdi i den markerede pixel bliver -119 Hvilket et 3x3 filter blev benyttet

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                                                                                                                                      02511 - Niveau af dagens emne forelaeligsingA) Meget letB) LetC) PassendeD) SvaeligrtE) Meget svaeligrt

                                                                                                                                      23

                                                                                                                                      6

                                                                                                                                      10

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                                                                                                                                      2122018Introduction to Medical Image Analysis77 DTU Compute Technical University of Denmark

                                                                                                                                      02512 - Niveau af dagens emne forelaeligsingA) Meget letB) LetC) PassendeD) SvaeligrtE) Meget svaeligrt

                                                                                                                                      0 0

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                                                                                                                                      02511 - Mit eget udbytte af dagenA) Jeg har laeligrt meget lidtB) Lidt laeligringC) PassendeD) God laeligringE) Jeg har laeligrt meget

                                                                                                                                      0 0

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                                                                                                                                      02512 - Mit eget udbytte af dagenA) Jeg har laeligrt meget lidtB) Lidt laeligringC) PassendeD) God laeligringE) Jeg har laeligrt meget

                                                                                                                                      2

                                                                                                                                      1

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                                                                                                                                      DTU Compute

                                                                                                                                      2122018Introduction to Medical Image Analysis80 DTU Compute Technical University of Denmark

                                                                                                                                      02511 - Sidste uges oslashvelser (pixelwiseoperations)A) Meget letteB) LetteC) PassendeD) SvaeligreE) Meget svaeligre

                                                                                                                                      0 0

                                                                                                                                      1

                                                                                                                                      4

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                                                                                                                                      2122018Introduction to Medical Image Analysis81 DTU Compute Technical University of Denmark

                                                                                                                                      02512 - Sidste uges oslashvelser (pixelwiseoperations)A) Meget letteB) LetteC) PassendeD) SvaeligreE) Meget svaeligre

                                                                                                                                      3

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                                                                                                                                      2122018Introduction to Medical Image Analysis82 DTU Compute Technical University of Denmark

                                                                                                                                      Denne uges brug af clickersA) click click click ndash jeg bliver

                                                                                                                                      sindssygB) For meget clickC) PassendeD) Jeg vil gerne have lidt mereE) Jeg kan ikrsquo faring nok

                                                                                                                                      0 0

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                                                                                                                                      2122018Introduction to Medical Image Analysis83 DTU Compute Technical University of Denmark

                                                                                                                                      What can you do after today Describe the difference between point processing and neighbourhood

                                                                                                                                      processing Compute a rank filtered image using the min max median and

                                                                                                                                      difference rank filters Compute a mean filtered image Decide if median or average filtering should be used for noise removal Choose the appropriate image border handling based on a given input

                                                                                                                                      image Implement and apply template matching Compute the normalised cross correlation and explain why it should be

                                                                                                                                      used Apply given image filter kernels to images Use edge filters on images Describe finite difference approximation of image gradients Describe the concept of edge detection

                                                                                                                                      DTU Compute

                                                                                                                                      2122018Introduction to Medical Image Analysis84 DTU Compute Technical University of Denmark

                                                                                                                                      Oslashvelsesrapport over oslashvelse 4 - 02511 Oslashvelser taeligller cirka 30 af karakteren Skal afleveres senest den 7 marts kl 2359 Kan afleveres af 1 eller 2 personer

                                                                                                                                      ndash I skal skrive jeres egen oslashvelsesrapportndash Brug mindst et af jeres egne billeder

                                                                                                                                      Afleveres som PDF Lad vaeligre med at kopiere opgaveteksten ind i jeres

                                                                                                                                      opgave Put Matlab kode i et Appendix og henvis fra teksten Eksempel rapport over oslashvelse findes paring

                                                                                                                                      hjemmesiden under eksamen

                                                                                                                                      DTU Compute

                                                                                                                                      2122018Introduction to Medical Image Analysis85 DTU Compute Technical University of Denmark

                                                                                                                                      Exercises

                                                                                                                                      • Introduction to Medical Image Analysis
                                                                                                                                      • Lecture 4 ndash Neighbourhood Processing
                                                                                                                                      • What can you do after today
                                                                                                                                      • Point processing
                                                                                                                                      • Point processing
                                                                                                                                      • Neighbourhood processing
                                                                                                                                      • Use of filtering
                                                                                                                                      • Salt and pepper noise
                                                                                                                                      • Salt and pepper noise
                                                                                                                                      • What is so special about noise
                                                                                                                                      • Noise ndash go away
                                                                                                                                      • What is the median Value
                                                                                                                                      • The median value
                                                                                                                                      • Noise away ndash the median filter
                                                                                                                                      • Noise removal ndash average filter
                                                                                                                                      • Noise removal ndash median filter
                                                                                                                                      • Image Filtering
                                                                                                                                      • Median filter
                                                                                                                                      • Rank filters
                                                                                                                                      • Median filter
                                                                                                                                      • Correlation
                                                                                                                                      • Why do we need similarity
                                                                                                                                      • Correlation (1D)
                                                                                                                                      • Correlation (1D)
                                                                                                                                      • Normalisation
                                                                                                                                      • Normalisation
                                                                                                                                      • Correlation on images
                                                                                                                                      • Correlation on images
                                                                                                                                      • Correlation on images
                                                                                                                                      • Draw your filter
                                                                                                                                      • Correlation on images ndash no normalisation
                                                                                                                                      • Correlation on images ndash no normalisation 2
                                                                                                                                      • Mathematics of 2D Correlation
                                                                                                                                      • Mathematics of 2D Correlation
                                                                                                                                      • Mathematics of 2D Correlation
                                                                                                                                      • Slide Number 40
                                                                                                                                      • 2D Kernel Normalisation
                                                                                                                                      • Correlation
                                                                                                                                      • Smoothing filters
                                                                                                                                      • Use of smoothing
                                                                                                                                      • Use of smoothing
                                                                                                                                      • Mean filter
                                                                                                                                      • Border handling
                                                                                                                                      • Border handling ndash extend the input
                                                                                                                                      • Correlation with zero padding
                                                                                                                                      • Border handling ndash extend the input
                                                                                                                                      • Template Matching
                                                                                                                                      • Template Matching
                                                                                                                                      • Template Matching
                                                                                                                                      • Template Matching
                                                                                                                                      • Problematic Correlation
                                                                                                                                      • Normalised Cross Correlation
                                                                                                                                      • Length of template
                                                                                                                                      • Length of image patch
                                                                                                                                      • Normalised Cross Correlation
                                                                                                                                      • Normalised Cross Correlation
                                                                                                                                      • Normalised Cross Correlation
                                                                                                                                      • Edges
                                                                                                                                      • Edges
                                                                                                                                      • Finite Difference
                                                                                                                                      • Edges
                                                                                                                                      • Edges in 2D
                                                                                                                                      • Edge filter kernel
                                                                                                                                      • Prewitt filter
                                                                                                                                      • Edge detection
                                                                                                                                      • Edge filtering
                                                                                                                                      • 02511 - Niveau af dagens emne forelaeligsing
                                                                                                                                      • 02512 - Niveau af dagens emne forelaeligsing
                                                                                                                                      • 02511 - Mit eget udbytte af dagen
                                                                                                                                      • 02512 - Mit eget udbytte af dagen
                                                                                                                                      • 02511 - Sidste uges oslashvelser (pixelwise operations)
                                                                                                                                      • 02512 - Sidste uges oslashvelser (pixelwise operations)
                                                                                                                                      • Denne uges brug af clickers
                                                                                                                                      • What can you do after today
                                                                                                                                      • Oslashvelsesrapport over oslashvelse 4 - 02511
                                                                                                                                      • Exercises
                                                                                                                                        A0
                                                                                                                                        B0
                                                                                                                                        C5
                                                                                                                                        D0
                                                                                                                                        E6
                                                                                                                                        A
                                                                                                                                        B
                                                                                                                                        C
                                                                                                                                        D
                                                                                                                                        E
                                                                                                                                        A3
                                                                                                                                        B0
                                                                                                                                        C3
                                                                                                                                        D0
                                                                                                                                        E0
                                                                                                                                        A
                                                                                                                                        B
                                                                                                                                        C
                                                                                                                                        D
                                                                                                                                        E
                                                                                                                                        A0
                                                                                                                                        B0
                                                                                                                                        C1
                                                                                                                                        D4
                                                                                                                                        E1
                                                                                                                                        A
                                                                                                                                        B
                                                                                                                                        C
                                                                                                                                        D
                                                                                                                                        E
                                                                                                                                        A2
                                                                                                                                        B1
                                                                                                                                        C3
                                                                                                                                        D2
                                                                                                                                        E0
                                                                                                                                        A
                                                                                                                                        B
                                                                                                                                        C
                                                                                                                                        D
                                                                                                                                        E
                                                                                                                                        A0
                                                                                                                                        B0
                                                                                                                                        C2
                                                                                                                                        D6
                                                                                                                                        E0
                                                                                                                                        A
                                                                                                                                        B
                                                                                                                                        C
                                                                                                                                        D
                                                                                                                                        E
                                                                                                                                        A0
                                                                                                                                        B0
                                                                                                                                        C1
                                                                                                                                        D0
                                                                                                                                        E0
                                                                                                                                        A
                                                                                                                                        B
                                                                                                                                        C
                                                                                                                                        D
                                                                                                                                        E
                                                                                                                                        A2
                                                                                                                                        B3
                                                                                                                                        C6
                                                                                                                                        D1
                                                                                                                                        E0
                                                                                                                                        A
                                                                                                                                        B
                                                                                                                                        C
                                                                                                                                        D
                                                                                                                                        E
                                                                                                                                        A0
                                                                                                                                        B8
                                                                                                                                        C1
                                                                                                                                        D1
                                                                                                                                        E0
                                                                                                                                        A
                                                                                                                                        B
                                                                                                                                        C
                                                                                                                                        D
                                                                                                                                        E
                                                                                                                                        A1
                                                                                                                                        B2
                                                                                                                                        C2
                                                                                                                                        D3
                                                                                                                                        E2
                                                                                                                                        A
                                                                                                                                        B
                                                                                                                                        C
                                                                                                                                        D
                                                                                                                                        E

                                                                                                                                        DTU Compute

                                                                                                                                        2122018Introduction to Medical Image Analysis59 DTU Compute Technical University of Denmark

                                                                                                                                        Normalised Cross Correlation

                                                                                                                                        Input (f)

                                                                                                                                        Template (h)

                                                                                                                                        Output Correlation image

                                                                                                                                        Real max

                                                                                                                                        NCC x y =Correlation

                                                                                                                                        Length of image patch sdot Length of template

                                                                                                                                        DTU Compute

                                                                                                                                        2122018Introduction to Medical Image Analysis60 DTU Compute Technical University of Denmark

                                                                                                                                        Length of template Vector length

                                                                                                                                        ndash Put all pixel values into a vectorndash Compute the length of this vector

                                                                                                                                        Describes the intensity of the templatendash Bright template has a large lengthndash Dark template has a small length

                                                                                                                                        Template (h)

                                                                                                                                        Length of template = 119895119895=minus119877119877

                                                                                                                                        119877119877

                                                                                                                                        119894119894=minus119877119877

                                                                                                                                        119877119877

                                                                                                                                        ℎ(119894119894 119895119895) ℎ(119894119894 119895119895)

                                                                                                                                        DTU Compute

                                                                                                                                        2122018Introduction to Medical Image Analysis61 DTU Compute Technical University of Denmark

                                                                                                                                        Length of image patch Vector length based on pixel values in image patch Describes the intensity of the image patch

                                                                                                                                        Template (h)

                                                                                                                                        Input (f) with patch

                                                                                                                                        DTU Compute

                                                                                                                                        2122018Introduction to Medical Image Analysis62 DTU Compute Technical University of Denmark

                                                                                                                                        Normalised Cross Correlation The length of the image patch and the length of

                                                                                                                                        template normalise the NCC If the image is very bright the NCC will be ldquopulled

                                                                                                                                        downrdquo

                                                                                                                                        NCC x y =Correlation

                                                                                                                                        Length of image patch sdot Length of template

                                                                                                                                        DTU Compute

                                                                                                                                        2122018Introduction to Medical Image Analysis63 DTU Compute Technical University of Denmark

                                                                                                                                        Normalised Cross Correlation NCC will be between

                                                                                                                                        ndash 0 No similarity between template and image patchndash 1 Template and image patch are identical

                                                                                                                                        Input (f)

                                                                                                                                        Template (h)

                                                                                                                                        Output Correlation image

                                                                                                                                        Real max

                                                                                                                                        NCC x y =Correlation

                                                                                                                                        Length of image patch sdot Length of template

                                                                                                                                        DTU Compute

                                                                                                                                        2122018Introduction to Medical Image Analysis64 DTU Compute Technical University of Denmark

                                                                                                                                        Normalised Cross Correlation

                                                                                                                                        A) 010B) 033C) 083D) 062E) 098

                                                                                                                                        Der udfoslashres template matching med og normalized crosscorrelation (NCC) beregnes Hvad bliver NNC i den markerede pixel

                                                                                                                                        1

                                                                                                                                        2 2

                                                                                                                                        3

                                                                                                                                        2

                                                                                                                                        A B C D E

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                                                                                                                                        DTU Compute

                                                                                                                                        2122018Introduction to Medical Image Analysis66 DTU Compute Technical University of Denmark

                                                                                                                                        Edges An edge is where there is a

                                                                                                                                        high change in gray level values

                                                                                                                                        Objects are often separated from the background by edgesGray level profile

                                                                                                                                        DTU Compute

                                                                                                                                        2122018Introduction to Medical Image Analysis67 DTU Compute Technical University of Denmark

                                                                                                                                        Edges The profile as a function f(d) What value is high when there

                                                                                                                                        is an edgendash The slope of fndash The slope of the tangent at d

                                                                                                                                        f(d)

                                                                                                                                        119891119891prime(119889119889)

                                                                                                                                        DTU Compute

                                                                                                                                        2122018Introduction to Medical Image Analysis68 DTU Compute Technical University of Denmark

                                                                                                                                        Finite Difference Definition of slope

                                                                                                                                        Approximation

                                                                                                                                        Simpler approximationh = 1

                                                                                                                                        119891119891prime 119889119889 = limℎrarr0

                                                                                                                                        119891119891 119889119889 + ℎ minus 119891119891(119889119889)ℎ

                                                                                                                                        119891119891prime 119889119889 asymp119891119891 119889119889 + ℎ minus 119891119891(119889119889)

                                                                                                                                        ℎ

                                                                                                                                        119891119891prime 119889119889 asymp 119891119891 119889119889 + 1 minus 119891119891(119889119889)

                                                                                                                                        DTU Compute

                                                                                                                                        2122018Introduction to Medical Image Analysis69 DTU Compute Technical University of Denmark

                                                                                                                                        Edges Discrete approximation of frsquo(d) Can be implemented as a filter

                                                                                                                                        -1 0 1

                                                                                                                                        f(d-2) f(d-1) f(d) f(d+1) f(d+2) f(d+3)

                                                                                                                                        f(d)

                                                                                                                                        119891119891prime 119889119889 asymp 119891119891 119889119889 + 1 minus 119891119891(119889119889)

                                                                                                                                        DTU Compute

                                                                                                                                        2122018Introduction to Medical Image Analysis70 DTU Compute Technical University of Denmark

                                                                                                                                        Edges in 2D Changes in gray level values

                                                                                                                                        ndash Image gradientndash Gradient is the 2D derivative of a 2D function f(xy)ndash Equal to the slope of the imagendash A steep slope is equal to an edge

                                                                                                                                        120571120571119891119891 119909119909119910119910 = 119866(119892119892119909119909119892119892119910119910)

                                                                                                                                        DTU Compute

                                                                                                                                        2122018Introduction to Medical Image Analysis71 DTU Compute Technical University of Denmark

                                                                                                                                        Edge filter kernel The Prewitt filter is a typical

                                                                                                                                        edge filter Output image has high

                                                                                                                                        values where there are edges

                                                                                                                                        -1 0 1

                                                                                                                                        -1 0 1

                                                                                                                                        -1 0 1Vertical Prewitt filter

                                                                                                                                        DTU Compute

                                                                                                                                        2122018Introduction to Medical Image Analysis72 DTU Compute Technical University of Denmark

                                                                                                                                        Prewitt filter

                                                                                                                                        Original Prewitt Prewitt

                                                                                                                                        Hot colormapSmooth 15x15

                                                                                                                                        Smooth 15x15

                                                                                                                                        Prewitt

                                                                                                                                        DTU Compute

                                                                                                                                        2122018Introduction to Medical Image Analysis73 DTU Compute Technical University of Denmark

                                                                                                                                        Edge detection Edge filter

                                                                                                                                        ndash Prewitt for example Thresholding

                                                                                                                                        ndash Separate edges from non-edges

                                                                                                                                        Output is binary imagendash Edges are white

                                                                                                                                        DTU Compute

                                                                                                                                        2122018Introduction to Medical Image Analysis74 DTU Compute Technical University of Denmark

                                                                                                                                        Edge filtering

                                                                                                                                        A) MeanB) Horizontal SobelC) Vertical PrewittD) Horisontal PrewittE) Median

                                                                                                                                        Der udfoslashres en filtrering (correlation) med et filter paring billedet Der bruges ikke coefficient normalization Den filtrerede vaeligrdi i den markerede pixel bliver -119 Hvilket et 3x3 filter blev benyttet

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                                                                                                                                        2122018Introduction to Medical Image Analysis76 DTU Compute Technical University of Denmark

                                                                                                                                        02511 - Niveau af dagens emne forelaeligsingA) Meget letB) LetC) PassendeD) SvaeligrtE) Meget svaeligrt

                                                                                                                                        23

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                                                                                                                                        2122018Introduction to Medical Image Analysis77 DTU Compute Technical University of Denmark

                                                                                                                                        02512 - Niveau af dagens emne forelaeligsingA) Meget letB) LetC) PassendeD) SvaeligrtE) Meget svaeligrt

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                                                                                                                                        2122018Introduction to Medical Image Analysis78 DTU Compute Technical University of Denmark

                                                                                                                                        02511 - Mit eget udbytte af dagenA) Jeg har laeligrt meget lidtB) Lidt laeligringC) PassendeD) God laeligringE) Jeg har laeligrt meget

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                                                                                                                                        2122018Introduction to Medical Image Analysis79 DTU Compute Technical University of Denmark

                                                                                                                                        02512 - Mit eget udbytte af dagenA) Jeg har laeligrt meget lidtB) Lidt laeligringC) PassendeD) God laeligringE) Jeg har laeligrt meget

                                                                                                                                        2

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                                                                                                                                        2122018Introduction to Medical Image Analysis80 DTU Compute Technical University of Denmark

                                                                                                                                        02511 - Sidste uges oslashvelser (pixelwiseoperations)A) Meget letteB) LetteC) PassendeD) SvaeligreE) Meget svaeligre

                                                                                                                                        0 0

                                                                                                                                        1

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                                                                                                                                        2122018Introduction to Medical Image Analysis81 DTU Compute Technical University of Denmark

                                                                                                                                        02512 - Sidste uges oslashvelser (pixelwiseoperations)A) Meget letteB) LetteC) PassendeD) SvaeligreE) Meget svaeligre

                                                                                                                                        3

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                                                                                                                                        2122018Introduction to Medical Image Analysis82 DTU Compute Technical University of Denmark

                                                                                                                                        Denne uges brug af clickersA) click click click ndash jeg bliver

                                                                                                                                        sindssygB) For meget clickC) PassendeD) Jeg vil gerne have lidt mereE) Jeg kan ikrsquo faring nok

                                                                                                                                        0 0

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                                                                                                                                        2122018Introduction to Medical Image Analysis83 DTU Compute Technical University of Denmark

                                                                                                                                        What can you do after today Describe the difference between point processing and neighbourhood

                                                                                                                                        processing Compute a rank filtered image using the min max median and

                                                                                                                                        difference rank filters Compute a mean filtered image Decide if median or average filtering should be used for noise removal Choose the appropriate image border handling based on a given input

                                                                                                                                        image Implement and apply template matching Compute the normalised cross correlation and explain why it should be

                                                                                                                                        used Apply given image filter kernels to images Use edge filters on images Describe finite difference approximation of image gradients Describe the concept of edge detection

                                                                                                                                        DTU Compute

                                                                                                                                        2122018Introduction to Medical Image Analysis84 DTU Compute Technical University of Denmark

                                                                                                                                        Oslashvelsesrapport over oslashvelse 4 - 02511 Oslashvelser taeligller cirka 30 af karakteren Skal afleveres senest den 7 marts kl 2359 Kan afleveres af 1 eller 2 personer

                                                                                                                                        ndash I skal skrive jeres egen oslashvelsesrapportndash Brug mindst et af jeres egne billeder

                                                                                                                                        Afleveres som PDF Lad vaeligre med at kopiere opgaveteksten ind i jeres

                                                                                                                                        opgave Put Matlab kode i et Appendix og henvis fra teksten Eksempel rapport over oslashvelse findes paring

                                                                                                                                        hjemmesiden under eksamen

                                                                                                                                        DTU Compute

                                                                                                                                        2122018Introduction to Medical Image Analysis85 DTU Compute Technical University of Denmark

                                                                                                                                        Exercises

                                                                                                                                        • Introduction to Medical Image Analysis
                                                                                                                                        • Lecture 4 ndash Neighbourhood Processing
                                                                                                                                        • What can you do after today
                                                                                                                                        • Point processing
                                                                                                                                        • Point processing
                                                                                                                                        • Neighbourhood processing
                                                                                                                                        • Use of filtering
                                                                                                                                        • Salt and pepper noise
                                                                                                                                        • Salt and pepper noise
                                                                                                                                        • What is so special about noise
                                                                                                                                        • Noise ndash go away
                                                                                                                                        • What is the median Value
                                                                                                                                        • The median value
                                                                                                                                        • Noise away ndash the median filter
                                                                                                                                        • Noise removal ndash average filter
                                                                                                                                        • Noise removal ndash median filter
                                                                                                                                        • Image Filtering
                                                                                                                                        • Median filter
                                                                                                                                        • Rank filters
                                                                                                                                        • Median filter
                                                                                                                                        • Correlation
                                                                                                                                        • Why do we need similarity
                                                                                                                                        • Correlation (1D)
                                                                                                                                        • Correlation (1D)
                                                                                                                                        • Normalisation
                                                                                                                                        • Normalisation
                                                                                                                                        • Correlation on images
                                                                                                                                        • Correlation on images
                                                                                                                                        • Correlation on images
                                                                                                                                        • Draw your filter
                                                                                                                                        • Correlation on images ndash no normalisation
                                                                                                                                        • Correlation on images ndash no normalisation 2
                                                                                                                                        • Mathematics of 2D Correlation
                                                                                                                                        • Mathematics of 2D Correlation
                                                                                                                                        • Mathematics of 2D Correlation
                                                                                                                                        • Slide Number 40
                                                                                                                                        • 2D Kernel Normalisation
                                                                                                                                        • Correlation
                                                                                                                                        • Smoothing filters
                                                                                                                                        • Use of smoothing
                                                                                                                                        • Use of smoothing
                                                                                                                                        • Mean filter
                                                                                                                                        • Border handling
                                                                                                                                        • Border handling ndash extend the input
                                                                                                                                        • Correlation with zero padding
                                                                                                                                        • Border handling ndash extend the input
                                                                                                                                        • Template Matching
                                                                                                                                        • Template Matching
                                                                                                                                        • Template Matching
                                                                                                                                        • Template Matching
                                                                                                                                        • Problematic Correlation
                                                                                                                                        • Normalised Cross Correlation
                                                                                                                                        • Length of template
                                                                                                                                        • Length of image patch
                                                                                                                                        • Normalised Cross Correlation
                                                                                                                                        • Normalised Cross Correlation
                                                                                                                                        • Normalised Cross Correlation
                                                                                                                                        • Edges
                                                                                                                                        • Edges
                                                                                                                                        • Finite Difference
                                                                                                                                        • Edges
                                                                                                                                        • Edges in 2D
                                                                                                                                        • Edge filter kernel
                                                                                                                                        • Prewitt filter
                                                                                                                                        • Edge detection
                                                                                                                                        • Edge filtering
                                                                                                                                        • 02511 - Niveau af dagens emne forelaeligsing
                                                                                                                                        • 02512 - Niveau af dagens emne forelaeligsing
                                                                                                                                        • 02511 - Mit eget udbytte af dagen
                                                                                                                                        • 02512 - Mit eget udbytte af dagen
                                                                                                                                        • 02511 - Sidste uges oslashvelser (pixelwise operations)
                                                                                                                                        • 02512 - Sidste uges oslashvelser (pixelwise operations)
                                                                                                                                        • Denne uges brug af clickers
                                                                                                                                        • What can you do after today
                                                                                                                                        • Oslashvelsesrapport over oslashvelse 4 - 02511
                                                                                                                                        • Exercises
                                                                                                                                          A0
                                                                                                                                          B0
                                                                                                                                          C5
                                                                                                                                          D0
                                                                                                                                          E6
                                                                                                                                          A
                                                                                                                                          B
                                                                                                                                          C
                                                                                                                                          D
                                                                                                                                          E
                                                                                                                                          A3
                                                                                                                                          B0
                                                                                                                                          C3
                                                                                                                                          D0
                                                                                                                                          E0
                                                                                                                                          A
                                                                                                                                          B
                                                                                                                                          C
                                                                                                                                          D
                                                                                                                                          E
                                                                                                                                          A0
                                                                                                                                          B0
                                                                                                                                          C1
                                                                                                                                          D4
                                                                                                                                          E1
                                                                                                                                          A
                                                                                                                                          B
                                                                                                                                          C
                                                                                                                                          D
                                                                                                                                          E
                                                                                                                                          A2
                                                                                                                                          B1
                                                                                                                                          C3
                                                                                                                                          D2
                                                                                                                                          E0
                                                                                                                                          A
                                                                                                                                          B
                                                                                                                                          C
                                                                                                                                          D
                                                                                                                                          E
                                                                                                                                          A0
                                                                                                                                          B0
                                                                                                                                          C2
                                                                                                                                          D6
                                                                                                                                          E0
                                                                                                                                          A
                                                                                                                                          B
                                                                                                                                          C
                                                                                                                                          D
                                                                                                                                          E
                                                                                                                                          A0
                                                                                                                                          B0
                                                                                                                                          C1
                                                                                                                                          D0
                                                                                                                                          E0
                                                                                                                                          A
                                                                                                                                          B
                                                                                                                                          C
                                                                                                                                          D
                                                                                                                                          E
                                                                                                                                          A2
                                                                                                                                          B3
                                                                                                                                          C6
                                                                                                                                          D1
                                                                                                                                          E0
                                                                                                                                          A
                                                                                                                                          B
                                                                                                                                          C
                                                                                                                                          D
                                                                                                                                          E
                                                                                                                                          A0
                                                                                                                                          B8
                                                                                                                                          C1
                                                                                                                                          D1
                                                                                                                                          E0
                                                                                                                                          A
                                                                                                                                          B
                                                                                                                                          C
                                                                                                                                          D
                                                                                                                                          E
                                                                                                                                          A1
                                                                                                                                          B2
                                                                                                                                          C2
                                                                                                                                          D3
                                                                                                                                          E2
                                                                                                                                          A
                                                                                                                                          B
                                                                                                                                          C
                                                                                                                                          D
                                                                                                                                          E

                                                                                                                                          DTU Compute

                                                                                                                                          2122018Introduction to Medical Image Analysis60 DTU Compute Technical University of Denmark

                                                                                                                                          Length of template Vector length

                                                                                                                                          ndash Put all pixel values into a vectorndash Compute the length of this vector

                                                                                                                                          Describes the intensity of the templatendash Bright template has a large lengthndash Dark template has a small length

                                                                                                                                          Template (h)

                                                                                                                                          Length of template = 119895119895=minus119877119877

                                                                                                                                          119877119877

                                                                                                                                          119894119894=minus119877119877

                                                                                                                                          119877119877

                                                                                                                                          ℎ(119894119894 119895119895) ℎ(119894119894 119895119895)

                                                                                                                                          DTU Compute

                                                                                                                                          2122018Introduction to Medical Image Analysis61 DTU Compute Technical University of Denmark

                                                                                                                                          Length of image patch Vector length based on pixel values in image patch Describes the intensity of the image patch

                                                                                                                                          Template (h)

                                                                                                                                          Input (f) with patch

                                                                                                                                          DTU Compute

                                                                                                                                          2122018Introduction to Medical Image Analysis62 DTU Compute Technical University of Denmark

                                                                                                                                          Normalised Cross Correlation The length of the image patch and the length of

                                                                                                                                          template normalise the NCC If the image is very bright the NCC will be ldquopulled

                                                                                                                                          downrdquo

                                                                                                                                          NCC x y =Correlation

                                                                                                                                          Length of image patch sdot Length of template

                                                                                                                                          DTU Compute

                                                                                                                                          2122018Introduction to Medical Image Analysis63 DTU Compute Technical University of Denmark

                                                                                                                                          Normalised Cross Correlation NCC will be between

                                                                                                                                          ndash 0 No similarity between template and image patchndash 1 Template and image patch are identical

                                                                                                                                          Input (f)

                                                                                                                                          Template (h)

                                                                                                                                          Output Correlation image

                                                                                                                                          Real max

                                                                                                                                          NCC x y =Correlation

                                                                                                                                          Length of image patch sdot Length of template

                                                                                                                                          DTU Compute

                                                                                                                                          2122018Introduction to Medical Image Analysis64 DTU Compute Technical University of Denmark

                                                                                                                                          Normalised Cross Correlation

                                                                                                                                          A) 010B) 033C) 083D) 062E) 098

                                                                                                                                          Der udfoslashres template matching med og normalized crosscorrelation (NCC) beregnes Hvad bliver NNC i den markerede pixel

                                                                                                                                          1

                                                                                                                                          2 2

                                                                                                                                          3

                                                                                                                                          2

                                                                                                                                          A B C D E

                                                                                                                                          Chart1

                                                                                                                                          1
                                                                                                                                          2
                                                                                                                                          2
                                                                                                                                          3
                                                                                                                                          2

                                                                                                                                          Sheet1

                                                                                                                                          DTU Compute

                                                                                                                                          2122018Introduction to Medical Image Analysis66 DTU Compute Technical University of Denmark

                                                                                                                                          Edges An edge is where there is a

                                                                                                                                          high change in gray level values

                                                                                                                                          Objects are often separated from the background by edgesGray level profile

                                                                                                                                          DTU Compute

                                                                                                                                          2122018Introduction to Medical Image Analysis67 DTU Compute Technical University of Denmark

                                                                                                                                          Edges The profile as a function f(d) What value is high when there

                                                                                                                                          is an edgendash The slope of fndash The slope of the tangent at d

                                                                                                                                          f(d)

                                                                                                                                          119891119891prime(119889119889)

                                                                                                                                          DTU Compute

                                                                                                                                          2122018Introduction to Medical Image Analysis68 DTU Compute Technical University of Denmark

                                                                                                                                          Finite Difference Definition of slope

                                                                                                                                          Approximation

                                                                                                                                          Simpler approximationh = 1

                                                                                                                                          119891119891prime 119889119889 = limℎrarr0

                                                                                                                                          119891119891 119889119889 + ℎ minus 119891119891(119889119889)ℎ

                                                                                                                                          119891119891prime 119889119889 asymp119891119891 119889119889 + ℎ minus 119891119891(119889119889)

                                                                                                                                          ℎ

                                                                                                                                          119891119891prime 119889119889 asymp 119891119891 119889119889 + 1 minus 119891119891(119889119889)

                                                                                                                                          DTU Compute

                                                                                                                                          2122018Introduction to Medical Image Analysis69 DTU Compute Technical University of Denmark

                                                                                                                                          Edges Discrete approximation of frsquo(d) Can be implemented as a filter

                                                                                                                                          -1 0 1

                                                                                                                                          f(d-2) f(d-1) f(d) f(d+1) f(d+2) f(d+3)

                                                                                                                                          f(d)

                                                                                                                                          119891119891prime 119889119889 asymp 119891119891 119889119889 + 1 minus 119891119891(119889119889)

                                                                                                                                          DTU Compute

                                                                                                                                          2122018Introduction to Medical Image Analysis70 DTU Compute Technical University of Denmark

                                                                                                                                          Edges in 2D Changes in gray level values

                                                                                                                                          ndash Image gradientndash Gradient is the 2D derivative of a 2D function f(xy)ndash Equal to the slope of the imagendash A steep slope is equal to an edge

                                                                                                                                          120571120571119891119891 119909119909119910119910 = 119866(119892119892119909119909119892119892119910119910)

                                                                                                                                          DTU Compute

                                                                                                                                          2122018Introduction to Medical Image Analysis71 DTU Compute Technical University of Denmark

                                                                                                                                          Edge filter kernel The Prewitt filter is a typical

                                                                                                                                          edge filter Output image has high

                                                                                                                                          values where there are edges

                                                                                                                                          -1 0 1

                                                                                                                                          -1 0 1

                                                                                                                                          -1 0 1Vertical Prewitt filter

                                                                                                                                          DTU Compute

                                                                                                                                          2122018Introduction to Medical Image Analysis72 DTU Compute Technical University of Denmark

                                                                                                                                          Prewitt filter

                                                                                                                                          Original Prewitt Prewitt

                                                                                                                                          Hot colormapSmooth 15x15

                                                                                                                                          Smooth 15x15

                                                                                                                                          Prewitt

                                                                                                                                          DTU Compute

                                                                                                                                          2122018Introduction to Medical Image Analysis73 DTU Compute Technical University of Denmark

                                                                                                                                          Edge detection Edge filter

                                                                                                                                          ndash Prewitt for example Thresholding

                                                                                                                                          ndash Separate edges from non-edges

                                                                                                                                          Output is binary imagendash Edges are white

                                                                                                                                          DTU Compute

                                                                                                                                          2122018Introduction to Medical Image Analysis74 DTU Compute Technical University of Denmark

                                                                                                                                          Edge filtering

                                                                                                                                          A) MeanB) Horizontal SobelC) Vertical PrewittD) Horisontal PrewittE) Median

                                                                                                                                          Der udfoslashres en filtrering (correlation) med et filter paring billedet Der bruges ikke coefficient normalization Den filtrerede vaeligrdi i den markerede pixel bliver -119 Hvilket et 3x3 filter blev benyttet

                                                                                                                                          0

                                                                                                                                          8

                                                                                                                                          1 10

                                                                                                                                          A B C D E

                                                                                                                                          Chart1

                                                                                                                                          0
                                                                                                                                          8
                                                                                                                                          1
                                                                                                                                          1
                                                                                                                                          0

                                                                                                                                          Sheet1

                                                                                                                                          DTU Compute

                                                                                                                                          2122018Introduction to Medical Image Analysis76 DTU Compute Technical University of Denmark

                                                                                                                                          02511 - Niveau af dagens emne forelaeligsingA) Meget letB) LetC) PassendeD) SvaeligrtE) Meget svaeligrt

                                                                                                                                          23

                                                                                                                                          6

                                                                                                                                          10

                                                                                                                                          A B C D E

                                                                                                                                          Chart1

                                                                                                                                          2
                                                                                                                                          3
                                                                                                                                          6
                                                                                                                                          1
                                                                                                                                          0

                                                                                                                                          Sheet1

                                                                                                                                          DTU Compute

                                                                                                                                          2122018Introduction to Medical Image Analysis77 DTU Compute Technical University of Denmark

                                                                                                                                          02512 - Niveau af dagens emne forelaeligsingA) Meget letB) LetC) PassendeD) SvaeligrtE) Meget svaeligrt

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                                                                                                                                          2122018Introduction to Medical Image Analysis78 DTU Compute Technical University of Denmark

                                                                                                                                          02511 - Mit eget udbytte af dagenA) Jeg har laeligrt meget lidtB) Lidt laeligringC) PassendeD) God laeligringE) Jeg har laeligrt meget

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                                                                                                                                          2122018Introduction to Medical Image Analysis79 DTU Compute Technical University of Denmark

                                                                                                                                          02512 - Mit eget udbytte af dagenA) Jeg har laeligrt meget lidtB) Lidt laeligringC) PassendeD) God laeligringE) Jeg har laeligrt meget

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                                                                                                                                          2122018Introduction to Medical Image Analysis80 DTU Compute Technical University of Denmark

                                                                                                                                          02511 - Sidste uges oslashvelser (pixelwiseoperations)A) Meget letteB) LetteC) PassendeD) SvaeligreE) Meget svaeligre

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                                                                                                                                          2122018Introduction to Medical Image Analysis81 DTU Compute Technical University of Denmark

                                                                                                                                          02512 - Sidste uges oslashvelser (pixelwiseoperations)A) Meget letteB) LetteC) PassendeD) SvaeligreE) Meget svaeligre

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                                                                                                                                          2122018Introduction to Medical Image Analysis82 DTU Compute Technical University of Denmark

                                                                                                                                          Denne uges brug af clickersA) click click click ndash jeg bliver

                                                                                                                                          sindssygB) For meget clickC) PassendeD) Jeg vil gerne have lidt mereE) Jeg kan ikrsquo faring nok

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                                                                                                                                          2122018Introduction to Medical Image Analysis83 DTU Compute Technical University of Denmark

                                                                                                                                          What can you do after today Describe the difference between point processing and neighbourhood

                                                                                                                                          processing Compute a rank filtered image using the min max median and

                                                                                                                                          difference rank filters Compute a mean filtered image Decide if median or average filtering should be used for noise removal Choose the appropriate image border handling based on a given input

                                                                                                                                          image Implement and apply template matching Compute the normalised cross correlation and explain why it should be

                                                                                                                                          used Apply given image filter kernels to images Use edge filters on images Describe finite difference approximation of image gradients Describe the concept of edge detection

                                                                                                                                          DTU Compute

                                                                                                                                          2122018Introduction to Medical Image Analysis84 DTU Compute Technical University of Denmark

                                                                                                                                          Oslashvelsesrapport over oslashvelse 4 - 02511 Oslashvelser taeligller cirka 30 af karakteren Skal afleveres senest den 7 marts kl 2359 Kan afleveres af 1 eller 2 personer

                                                                                                                                          ndash I skal skrive jeres egen oslashvelsesrapportndash Brug mindst et af jeres egne billeder

                                                                                                                                          Afleveres som PDF Lad vaeligre med at kopiere opgaveteksten ind i jeres

                                                                                                                                          opgave Put Matlab kode i et Appendix og henvis fra teksten Eksempel rapport over oslashvelse findes paring

                                                                                                                                          hjemmesiden under eksamen

                                                                                                                                          DTU Compute

                                                                                                                                          2122018Introduction to Medical Image Analysis85 DTU Compute Technical University of Denmark

                                                                                                                                          Exercises

                                                                                                                                          • Introduction to Medical Image Analysis
                                                                                                                                          • Lecture 4 ndash Neighbourhood Processing
                                                                                                                                          • What can you do after today
                                                                                                                                          • Point processing
                                                                                                                                          • Point processing
                                                                                                                                          • Neighbourhood processing
                                                                                                                                          • Use of filtering
                                                                                                                                          • Salt and pepper noise
                                                                                                                                          • Salt and pepper noise
                                                                                                                                          • What is so special about noise
                                                                                                                                          • Noise ndash go away
                                                                                                                                          • What is the median Value
                                                                                                                                          • The median value
                                                                                                                                          • Noise away ndash the median filter
                                                                                                                                          • Noise removal ndash average filter
                                                                                                                                          • Noise removal ndash median filter
                                                                                                                                          • Image Filtering
                                                                                                                                          • Median filter
                                                                                                                                          • Rank filters
                                                                                                                                          • Median filter
                                                                                                                                          • Correlation
                                                                                                                                          • Why do we need similarity
                                                                                                                                          • Correlation (1D)
                                                                                                                                          • Correlation (1D)
                                                                                                                                          • Normalisation
                                                                                                                                          • Normalisation
                                                                                                                                          • Correlation on images
                                                                                                                                          • Correlation on images
                                                                                                                                          • Correlation on images
                                                                                                                                          • Draw your filter
                                                                                                                                          • Correlation on images ndash no normalisation
                                                                                                                                          • Correlation on images ndash no normalisation 2
                                                                                                                                          • Mathematics of 2D Correlation
                                                                                                                                          • Mathematics of 2D Correlation
                                                                                                                                          • Mathematics of 2D Correlation
                                                                                                                                          • Slide Number 40
                                                                                                                                          • 2D Kernel Normalisation
                                                                                                                                          • Correlation
                                                                                                                                          • Smoothing filters
                                                                                                                                          • Use of smoothing
                                                                                                                                          • Use of smoothing
                                                                                                                                          • Mean filter
                                                                                                                                          • Border handling
                                                                                                                                          • Border handling ndash extend the input
                                                                                                                                          • Correlation with zero padding
                                                                                                                                          • Border handling ndash extend the input
                                                                                                                                          • Template Matching
                                                                                                                                          • Template Matching
                                                                                                                                          • Template Matching
                                                                                                                                          • Template Matching
                                                                                                                                          • Problematic Correlation
                                                                                                                                          • Normalised Cross Correlation
                                                                                                                                          • Length of template
                                                                                                                                          • Length of image patch
                                                                                                                                          • Normalised Cross Correlation
                                                                                                                                          • Normalised Cross Correlation
                                                                                                                                          • Normalised Cross Correlation
                                                                                                                                          • Edges
                                                                                                                                          • Edges
                                                                                                                                          • Finite Difference
                                                                                                                                          • Edges
                                                                                                                                          • Edges in 2D
                                                                                                                                          • Edge filter kernel
                                                                                                                                          • Prewitt filter
                                                                                                                                          • Edge detection
                                                                                                                                          • Edge filtering
                                                                                                                                          • 02511 - Niveau af dagens emne forelaeligsing
                                                                                                                                          • 02512 - Niveau af dagens emne forelaeligsing
                                                                                                                                          • 02511 - Mit eget udbytte af dagen
                                                                                                                                          • 02512 - Mit eget udbytte af dagen
                                                                                                                                          • 02511 - Sidste uges oslashvelser (pixelwise operations)
                                                                                                                                          • 02512 - Sidste uges oslashvelser (pixelwise operations)
                                                                                                                                          • Denne uges brug af clickers
                                                                                                                                          • What can you do after today
                                                                                                                                          • Oslashvelsesrapport over oslashvelse 4 - 02511
                                                                                                                                          • Exercises
                                                                                                                                            A0
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                                                                                                                                            C5
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                                                                                                                                            B1
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                                                                                                                                            E0
                                                                                                                                            A
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                                                                                                                                            B0
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                                                                                                                                            D6
                                                                                                                                            E0
                                                                                                                                            A
                                                                                                                                            B
                                                                                                                                            C
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                                                                                                                                            E
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                                                                                                                                            D0
                                                                                                                                            E0
                                                                                                                                            A
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                                                                                                                                            E
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                                                                                                                                            C6
                                                                                                                                            D1
                                                                                                                                            E0
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                                                                                                                                            D3
                                                                                                                                            E2
                                                                                                                                            A
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                                                                                                                                            C
                                                                                                                                            D
                                                                                                                                            E

                                                                                                                                            DTU Compute

                                                                                                                                            2122018Introduction to Medical Image Analysis61 DTU Compute Technical University of Denmark

                                                                                                                                            Length of image patch Vector length based on pixel values in image patch Describes the intensity of the image patch

                                                                                                                                            Template (h)

                                                                                                                                            Input (f) with patch

                                                                                                                                            DTU Compute

                                                                                                                                            2122018Introduction to Medical Image Analysis62 DTU Compute Technical University of Denmark

                                                                                                                                            Normalised Cross Correlation The length of the image patch and the length of

                                                                                                                                            template normalise the NCC If the image is very bright the NCC will be ldquopulled

                                                                                                                                            downrdquo

                                                                                                                                            NCC x y =Correlation

                                                                                                                                            Length of image patch sdot Length of template

                                                                                                                                            DTU Compute

                                                                                                                                            2122018Introduction to Medical Image Analysis63 DTU Compute Technical University of Denmark

                                                                                                                                            Normalised Cross Correlation NCC will be between

                                                                                                                                            ndash 0 No similarity between template and image patchndash 1 Template and image patch are identical

                                                                                                                                            Input (f)

                                                                                                                                            Template (h)

                                                                                                                                            Output Correlation image

                                                                                                                                            Real max

                                                                                                                                            NCC x y =Correlation

                                                                                                                                            Length of image patch sdot Length of template

                                                                                                                                            DTU Compute

                                                                                                                                            2122018Introduction to Medical Image Analysis64 DTU Compute Technical University of Denmark

                                                                                                                                            Normalised Cross Correlation

                                                                                                                                            A) 010B) 033C) 083D) 062E) 098

                                                                                                                                            Der udfoslashres template matching med og normalized crosscorrelation (NCC) beregnes Hvad bliver NNC i den markerede pixel

                                                                                                                                            1

                                                                                                                                            2 2

                                                                                                                                            3

                                                                                                                                            2

                                                                                                                                            A B C D E

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                                                                                                                                            2122018Introduction to Medical Image Analysis66 DTU Compute Technical University of Denmark

                                                                                                                                            Edges An edge is where there is a

                                                                                                                                            high change in gray level values

                                                                                                                                            Objects are often separated from the background by edgesGray level profile

                                                                                                                                            DTU Compute

                                                                                                                                            2122018Introduction to Medical Image Analysis67 DTU Compute Technical University of Denmark

                                                                                                                                            Edges The profile as a function f(d) What value is high when there

                                                                                                                                            is an edgendash The slope of fndash The slope of the tangent at d

                                                                                                                                            f(d)

                                                                                                                                            119891119891prime(119889119889)

                                                                                                                                            DTU Compute

                                                                                                                                            2122018Introduction to Medical Image Analysis68 DTU Compute Technical University of Denmark

                                                                                                                                            Finite Difference Definition of slope

                                                                                                                                            Approximation

                                                                                                                                            Simpler approximationh = 1

                                                                                                                                            119891119891prime 119889119889 = limℎrarr0

                                                                                                                                            119891119891 119889119889 + ℎ minus 119891119891(119889119889)ℎ

                                                                                                                                            119891119891prime 119889119889 asymp119891119891 119889119889 + ℎ minus 119891119891(119889119889)

                                                                                                                                            ℎ

                                                                                                                                            119891119891prime 119889119889 asymp 119891119891 119889119889 + 1 minus 119891119891(119889119889)

                                                                                                                                            DTU Compute

                                                                                                                                            2122018Introduction to Medical Image Analysis69 DTU Compute Technical University of Denmark

                                                                                                                                            Edges Discrete approximation of frsquo(d) Can be implemented as a filter

                                                                                                                                            -1 0 1

                                                                                                                                            f(d-2) f(d-1) f(d) f(d+1) f(d+2) f(d+3)

                                                                                                                                            f(d)

                                                                                                                                            119891119891prime 119889119889 asymp 119891119891 119889119889 + 1 minus 119891119891(119889119889)

                                                                                                                                            DTU Compute

                                                                                                                                            2122018Introduction to Medical Image Analysis70 DTU Compute Technical University of Denmark

                                                                                                                                            Edges in 2D Changes in gray level values

                                                                                                                                            ndash Image gradientndash Gradient is the 2D derivative of a 2D function f(xy)ndash Equal to the slope of the imagendash A steep slope is equal to an edge

                                                                                                                                            120571120571119891119891 119909119909119910119910 = 119866(119892119892119909119909119892119892119910119910)

                                                                                                                                            DTU Compute

                                                                                                                                            2122018Introduction to Medical Image Analysis71 DTU Compute Technical University of Denmark

                                                                                                                                            Edge filter kernel The Prewitt filter is a typical

                                                                                                                                            edge filter Output image has high

                                                                                                                                            values where there are edges

                                                                                                                                            -1 0 1

                                                                                                                                            -1 0 1

                                                                                                                                            -1 0 1Vertical Prewitt filter

                                                                                                                                            DTU Compute

                                                                                                                                            2122018Introduction to Medical Image Analysis72 DTU Compute Technical University of Denmark

                                                                                                                                            Prewitt filter

                                                                                                                                            Original Prewitt Prewitt

                                                                                                                                            Hot colormapSmooth 15x15

                                                                                                                                            Smooth 15x15

                                                                                                                                            Prewitt

                                                                                                                                            DTU Compute

                                                                                                                                            2122018Introduction to Medical Image Analysis73 DTU Compute Technical University of Denmark

                                                                                                                                            Edge detection Edge filter

                                                                                                                                            ndash Prewitt for example Thresholding

                                                                                                                                            ndash Separate edges from non-edges

                                                                                                                                            Output is binary imagendash Edges are white

                                                                                                                                            DTU Compute

                                                                                                                                            2122018Introduction to Medical Image Analysis74 DTU Compute Technical University of Denmark

                                                                                                                                            Edge filtering

                                                                                                                                            A) MeanB) Horizontal SobelC) Vertical PrewittD) Horisontal PrewittE) Median

                                                                                                                                            Der udfoslashres en filtrering (correlation) med et filter paring billedet Der bruges ikke coefficient normalization Den filtrerede vaeligrdi i den markerede pixel bliver -119 Hvilket et 3x3 filter blev benyttet

                                                                                                                                            0

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                                                                                                                                            2122018Introduction to Medical Image Analysis76 DTU Compute Technical University of Denmark

                                                                                                                                            02511 - Niveau af dagens emne forelaeligsingA) Meget letB) LetC) PassendeD) SvaeligrtE) Meget svaeligrt

                                                                                                                                            23

                                                                                                                                            6

                                                                                                                                            10

                                                                                                                                            A B C D E

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                                                                                                                                            DTU Compute

                                                                                                                                            2122018Introduction to Medical Image Analysis77 DTU Compute Technical University of Denmark

                                                                                                                                            02512 - Niveau af dagens emne forelaeligsingA) Meget letB) LetC) PassendeD) SvaeligrtE) Meget svaeligrt

                                                                                                                                            0 0

                                                                                                                                            1

                                                                                                                                            0 0

                                                                                                                                            A B C D E

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                                                                                                                                            0
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                                                                                                                                            DTU Compute

                                                                                                                                            2122018Introduction to Medical Image Analysis78 DTU Compute Technical University of Denmark

                                                                                                                                            02511 - Mit eget udbytte af dagenA) Jeg har laeligrt meget lidtB) Lidt laeligringC) PassendeD) God laeligringE) Jeg har laeligrt meget

                                                                                                                                            0 0

                                                                                                                                            2

                                                                                                                                            6

                                                                                                                                            0

                                                                                                                                            A B C D E

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                                                                                                                                            Sheet1

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                                                                                                                                            2122018Introduction to Medical Image Analysis79 DTU Compute Technical University of Denmark

                                                                                                                                            02512 - Mit eget udbytte af dagenA) Jeg har laeligrt meget lidtB) Lidt laeligringC) PassendeD) God laeligringE) Jeg har laeligrt meget

                                                                                                                                            2

                                                                                                                                            1

                                                                                                                                            3

                                                                                                                                            2

                                                                                                                                            0

                                                                                                                                            A B C D E

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                                                                                                                                            2
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                                                                                                                                            0

                                                                                                                                            Sheet1

                                                                                                                                            DTU Compute

                                                                                                                                            2122018Introduction to Medical Image Analysis80 DTU Compute Technical University of Denmark

                                                                                                                                            02511 - Sidste uges oslashvelser (pixelwiseoperations)A) Meget letteB) LetteC) PassendeD) SvaeligreE) Meget svaeligre

                                                                                                                                            0 0

                                                                                                                                            1

                                                                                                                                            4

                                                                                                                                            1

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                                                                                                                                            1
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                                                                                                                                            Sheet1

                                                                                                                                            DTU Compute

                                                                                                                                            2122018Introduction to Medical Image Analysis81 DTU Compute Technical University of Denmark

                                                                                                                                            02512 - Sidste uges oslashvelser (pixelwiseoperations)A) Meget letteB) LetteC) PassendeD) SvaeligreE) Meget svaeligre

                                                                                                                                            3

                                                                                                                                            0

                                                                                                                                            3

                                                                                                                                            0 0

                                                                                                                                            A B C D E

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                                                                                                                                            Sheet1

                                                                                                                                            DTU Compute

                                                                                                                                            2122018Introduction to Medical Image Analysis82 DTU Compute Technical University of Denmark

                                                                                                                                            Denne uges brug af clickersA) click click click ndash jeg bliver

                                                                                                                                            sindssygB) For meget clickC) PassendeD) Jeg vil gerne have lidt mereE) Jeg kan ikrsquo faring nok

                                                                                                                                            0 0

                                                                                                                                            5

                                                                                                                                            0

                                                                                                                                            6

                                                                                                                                            A B C D E

                                                                                                                                            Chart1

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                                                                                                                                            Sheet1

                                                                                                                                            DTU Compute

                                                                                                                                            2122018Introduction to Medical Image Analysis83 DTU Compute Technical University of Denmark

                                                                                                                                            What can you do after today Describe the difference between point processing and neighbourhood

                                                                                                                                            processing Compute a rank filtered image using the min max median and

                                                                                                                                            difference rank filters Compute a mean filtered image Decide if median or average filtering should be used for noise removal Choose the appropriate image border handling based on a given input

                                                                                                                                            image Implement and apply template matching Compute the normalised cross correlation and explain why it should be

                                                                                                                                            used Apply given image filter kernels to images Use edge filters on images Describe finite difference approximation of image gradients Describe the concept of edge detection

                                                                                                                                            DTU Compute

                                                                                                                                            2122018Introduction to Medical Image Analysis84 DTU Compute Technical University of Denmark

                                                                                                                                            Oslashvelsesrapport over oslashvelse 4 - 02511 Oslashvelser taeligller cirka 30 af karakteren Skal afleveres senest den 7 marts kl 2359 Kan afleveres af 1 eller 2 personer

                                                                                                                                            ndash I skal skrive jeres egen oslashvelsesrapportndash Brug mindst et af jeres egne billeder

                                                                                                                                            Afleveres som PDF Lad vaeligre med at kopiere opgaveteksten ind i jeres

                                                                                                                                            opgave Put Matlab kode i et Appendix og henvis fra teksten Eksempel rapport over oslashvelse findes paring

                                                                                                                                            hjemmesiden under eksamen

                                                                                                                                            DTU Compute

                                                                                                                                            2122018Introduction to Medical Image Analysis85 DTU Compute Technical University of Denmark

                                                                                                                                            Exercises

                                                                                                                                            • Introduction to Medical Image Analysis
                                                                                                                                            • Lecture 4 ndash Neighbourhood Processing
                                                                                                                                            • What can you do after today
                                                                                                                                            • Point processing
                                                                                                                                            • Point processing
                                                                                                                                            • Neighbourhood processing
                                                                                                                                            • Use of filtering
                                                                                                                                            • Salt and pepper noise
                                                                                                                                            • Salt and pepper noise
                                                                                                                                            • What is so special about noise
                                                                                                                                            • Noise ndash go away
                                                                                                                                            • What is the median Value
                                                                                                                                            • The median value
                                                                                                                                            • Noise away ndash the median filter
                                                                                                                                            • Noise removal ndash average filter
                                                                                                                                            • Noise removal ndash median filter
                                                                                                                                            • Image Filtering
                                                                                                                                            • Median filter
                                                                                                                                            • Rank filters
                                                                                                                                            • Median filter
                                                                                                                                            • Correlation
                                                                                                                                            • Why do we need similarity
                                                                                                                                            • Correlation (1D)
                                                                                                                                            • Correlation (1D)
                                                                                                                                            • Normalisation
                                                                                                                                            • Normalisation
                                                                                                                                            • Correlation on images
                                                                                                                                            • Correlation on images
                                                                                                                                            • Correlation on images
                                                                                                                                            • Draw your filter
                                                                                                                                            • Correlation on images ndash no normalisation
                                                                                                                                            • Correlation on images ndash no normalisation 2
                                                                                                                                            • Mathematics of 2D Correlation
                                                                                                                                            • Mathematics of 2D Correlation
                                                                                                                                            • Mathematics of 2D Correlation
                                                                                                                                            • Slide Number 40
                                                                                                                                            • 2D Kernel Normalisation
                                                                                                                                            • Correlation
                                                                                                                                            • Smoothing filters
                                                                                                                                            • Use of smoothing
                                                                                                                                            • Use of smoothing
                                                                                                                                            • Mean filter
                                                                                                                                            • Border handling
                                                                                                                                            • Border handling ndash extend the input
                                                                                                                                            • Correlation with zero padding
                                                                                                                                            • Border handling ndash extend the input
                                                                                                                                            • Template Matching
                                                                                                                                            • Template Matching
                                                                                                                                            • Template Matching
                                                                                                                                            • Template Matching
                                                                                                                                            • Problematic Correlation
                                                                                                                                            • Normalised Cross Correlation
                                                                                                                                            • Length of template
                                                                                                                                            • Length of image patch
                                                                                                                                            • Normalised Cross Correlation
                                                                                                                                            • Normalised Cross Correlation
                                                                                                                                            • Normalised Cross Correlation
                                                                                                                                            • Edges
                                                                                                                                            • Edges
                                                                                                                                            • Finite Difference
                                                                                                                                            • Edges
                                                                                                                                            • Edges in 2D
                                                                                                                                            • Edge filter kernel
                                                                                                                                            • Prewitt filter
                                                                                                                                            • Edge detection
                                                                                                                                            • Edge filtering
                                                                                                                                            • 02511 - Niveau af dagens emne forelaeligsing
                                                                                                                                            • 02512 - Niveau af dagens emne forelaeligsing
                                                                                                                                            • 02511 - Mit eget udbytte af dagen
                                                                                                                                            • 02512 - Mit eget udbytte af dagen
                                                                                                                                            • 02511 - Sidste uges oslashvelser (pixelwise operations)
                                                                                                                                            • 02512 - Sidste uges oslashvelser (pixelwise operations)
                                                                                                                                            • Denne uges brug af clickers
                                                                                                                                            • What can you do after today
                                                                                                                                            • Oslashvelsesrapport over oslashvelse 4 - 02511
                                                                                                                                            • Exercises
                                                                                                                                              A0
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                                                                                                                                              D
                                                                                                                                              E

                                                                                                                                              DTU Compute

                                                                                                                                              2122018Introduction to Medical Image Analysis62 DTU Compute Technical University of Denmark

                                                                                                                                              Normalised Cross Correlation The length of the image patch and the length of

                                                                                                                                              template normalise the NCC If the image is very bright the NCC will be ldquopulled

                                                                                                                                              downrdquo

                                                                                                                                              NCC x y =Correlation

                                                                                                                                              Length of image patch sdot Length of template

                                                                                                                                              DTU Compute

                                                                                                                                              2122018Introduction to Medical Image Analysis63 DTU Compute Technical University of Denmark

                                                                                                                                              Normalised Cross Correlation NCC will be between

                                                                                                                                              ndash 0 No similarity between template and image patchndash 1 Template and image patch are identical

                                                                                                                                              Input (f)

                                                                                                                                              Template (h)

                                                                                                                                              Output Correlation image

                                                                                                                                              Real max

                                                                                                                                              NCC x y =Correlation

                                                                                                                                              Length of image patch sdot Length of template

                                                                                                                                              DTU Compute

                                                                                                                                              2122018Introduction to Medical Image Analysis64 DTU Compute Technical University of Denmark

                                                                                                                                              Normalised Cross Correlation

                                                                                                                                              A) 010B) 033C) 083D) 062E) 098

                                                                                                                                              Der udfoslashres template matching med og normalized crosscorrelation (NCC) beregnes Hvad bliver NNC i den markerede pixel

                                                                                                                                              1

                                                                                                                                              2 2

                                                                                                                                              3

                                                                                                                                              2

                                                                                                                                              A B C D E

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                                                                                                                                              DTU Compute

                                                                                                                                              2122018Introduction to Medical Image Analysis66 DTU Compute Technical University of Denmark

                                                                                                                                              Edges An edge is where there is a

                                                                                                                                              high change in gray level values

                                                                                                                                              Objects are often separated from the background by edgesGray level profile

                                                                                                                                              DTU Compute

                                                                                                                                              2122018Introduction to Medical Image Analysis67 DTU Compute Technical University of Denmark

                                                                                                                                              Edges The profile as a function f(d) What value is high when there

                                                                                                                                              is an edgendash The slope of fndash The slope of the tangent at d

                                                                                                                                              f(d)

                                                                                                                                              119891119891prime(119889119889)

                                                                                                                                              DTU Compute

                                                                                                                                              2122018Introduction to Medical Image Analysis68 DTU Compute Technical University of Denmark

                                                                                                                                              Finite Difference Definition of slope

                                                                                                                                              Approximation

                                                                                                                                              Simpler approximationh = 1

                                                                                                                                              119891119891prime 119889119889 = limℎrarr0

                                                                                                                                              119891119891 119889119889 + ℎ minus 119891119891(119889119889)ℎ

                                                                                                                                              119891119891prime 119889119889 asymp119891119891 119889119889 + ℎ minus 119891119891(119889119889)

                                                                                                                                              ℎ

                                                                                                                                              119891119891prime 119889119889 asymp 119891119891 119889119889 + 1 minus 119891119891(119889119889)

                                                                                                                                              DTU Compute

                                                                                                                                              2122018Introduction to Medical Image Analysis69 DTU Compute Technical University of Denmark

                                                                                                                                              Edges Discrete approximation of frsquo(d) Can be implemented as a filter

                                                                                                                                              -1 0 1

                                                                                                                                              f(d-2) f(d-1) f(d) f(d+1) f(d+2) f(d+3)

                                                                                                                                              f(d)

                                                                                                                                              119891119891prime 119889119889 asymp 119891119891 119889119889 + 1 minus 119891119891(119889119889)

                                                                                                                                              DTU Compute

                                                                                                                                              2122018Introduction to Medical Image Analysis70 DTU Compute Technical University of Denmark

                                                                                                                                              Edges in 2D Changes in gray level values

                                                                                                                                              ndash Image gradientndash Gradient is the 2D derivative of a 2D function f(xy)ndash Equal to the slope of the imagendash A steep slope is equal to an edge

                                                                                                                                              120571120571119891119891 119909119909119910119910 = 119866(119892119892119909119909119892119892119910119910)

                                                                                                                                              DTU Compute

                                                                                                                                              2122018Introduction to Medical Image Analysis71 DTU Compute Technical University of Denmark

                                                                                                                                              Edge filter kernel The Prewitt filter is a typical

                                                                                                                                              edge filter Output image has high

                                                                                                                                              values where there are edges

                                                                                                                                              -1 0 1

                                                                                                                                              -1 0 1

                                                                                                                                              -1 0 1Vertical Prewitt filter

                                                                                                                                              DTU Compute

                                                                                                                                              2122018Introduction to Medical Image Analysis72 DTU Compute Technical University of Denmark

                                                                                                                                              Prewitt filter

                                                                                                                                              Original Prewitt Prewitt

                                                                                                                                              Hot colormapSmooth 15x15

                                                                                                                                              Smooth 15x15

                                                                                                                                              Prewitt

                                                                                                                                              DTU Compute

                                                                                                                                              2122018Introduction to Medical Image Analysis73 DTU Compute Technical University of Denmark

                                                                                                                                              Edge detection Edge filter

                                                                                                                                              ndash Prewitt for example Thresholding

                                                                                                                                              ndash Separate edges from non-edges

                                                                                                                                              Output is binary imagendash Edges are white

                                                                                                                                              DTU Compute

                                                                                                                                              2122018Introduction to Medical Image Analysis74 DTU Compute Technical University of Denmark

                                                                                                                                              Edge filtering

                                                                                                                                              A) MeanB) Horizontal SobelC) Vertical PrewittD) Horisontal PrewittE) Median

                                                                                                                                              Der udfoslashres en filtrering (correlation) med et filter paring billedet Der bruges ikke coefficient normalization Den filtrerede vaeligrdi i den markerede pixel bliver -119 Hvilket et 3x3 filter blev benyttet

                                                                                                                                              0

                                                                                                                                              8

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                                                                                                                                              2122018Introduction to Medical Image Analysis76 DTU Compute Technical University of Denmark

                                                                                                                                              02511 - Niveau af dagens emne forelaeligsingA) Meget letB) LetC) PassendeD) SvaeligrtE) Meget svaeligrt

                                                                                                                                              23

                                                                                                                                              6

                                                                                                                                              10

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                                                                                                                                              2122018Introduction to Medical Image Analysis77 DTU Compute Technical University of Denmark

                                                                                                                                              02512 - Niveau af dagens emne forelaeligsingA) Meget letB) LetC) PassendeD) SvaeligrtE) Meget svaeligrt

                                                                                                                                              0 0

                                                                                                                                              1

                                                                                                                                              0 0

                                                                                                                                              A B C D E

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                                                                                                                                              2122018Introduction to Medical Image Analysis78 DTU Compute Technical University of Denmark

                                                                                                                                              02511 - Mit eget udbytte af dagenA) Jeg har laeligrt meget lidtB) Lidt laeligringC) PassendeD) God laeligringE) Jeg har laeligrt meget

                                                                                                                                              0 0

                                                                                                                                              2

                                                                                                                                              6

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                                                                                                                                              A B C D E

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                                                                                                                                              0

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                                                                                                                                              2122018Introduction to Medical Image Analysis79 DTU Compute Technical University of Denmark

                                                                                                                                              02512 - Mit eget udbytte af dagenA) Jeg har laeligrt meget lidtB) Lidt laeligringC) PassendeD) God laeligringE) Jeg har laeligrt meget

                                                                                                                                              2

                                                                                                                                              1

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                                                                                                                                              0

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                                                                                                                                              0

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                                                                                                                                              DTU Compute

                                                                                                                                              2122018Introduction to Medical Image Analysis80 DTU Compute Technical University of Denmark

                                                                                                                                              02511 - Sidste uges oslashvelser (pixelwiseoperations)A) Meget letteB) LetteC) PassendeD) SvaeligreE) Meget svaeligre

                                                                                                                                              0 0

                                                                                                                                              1

                                                                                                                                              4

                                                                                                                                              1

                                                                                                                                              A B C D E

                                                                                                                                              Chart1

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                                                                                                                                              2122018Introduction to Medical Image Analysis81 DTU Compute Technical University of Denmark

                                                                                                                                              02512 - Sidste uges oslashvelser (pixelwiseoperations)A) Meget letteB) LetteC) PassendeD) SvaeligreE) Meget svaeligre

                                                                                                                                              3

                                                                                                                                              0

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                                                                                                                                              A B C D E

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                                                                                                                                              2122018Introduction to Medical Image Analysis82 DTU Compute Technical University of Denmark

                                                                                                                                              Denne uges brug af clickersA) click click click ndash jeg bliver

                                                                                                                                              sindssygB) For meget clickC) PassendeD) Jeg vil gerne have lidt mereE) Jeg kan ikrsquo faring nok

                                                                                                                                              0 0

                                                                                                                                              5

                                                                                                                                              0

                                                                                                                                              6

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                                                                                                                                              DTU Compute

                                                                                                                                              2122018Introduction to Medical Image Analysis83 DTU Compute Technical University of Denmark

                                                                                                                                              What can you do after today Describe the difference between point processing and neighbourhood

                                                                                                                                              processing Compute a rank filtered image using the min max median and

                                                                                                                                              difference rank filters Compute a mean filtered image Decide if median or average filtering should be used for noise removal Choose the appropriate image border handling based on a given input

                                                                                                                                              image Implement and apply template matching Compute the normalised cross correlation and explain why it should be

                                                                                                                                              used Apply given image filter kernels to images Use edge filters on images Describe finite difference approximation of image gradients Describe the concept of edge detection

                                                                                                                                              DTU Compute

                                                                                                                                              2122018Introduction to Medical Image Analysis84 DTU Compute Technical University of Denmark

                                                                                                                                              Oslashvelsesrapport over oslashvelse 4 - 02511 Oslashvelser taeligller cirka 30 af karakteren Skal afleveres senest den 7 marts kl 2359 Kan afleveres af 1 eller 2 personer

                                                                                                                                              ndash I skal skrive jeres egen oslashvelsesrapportndash Brug mindst et af jeres egne billeder

                                                                                                                                              Afleveres som PDF Lad vaeligre med at kopiere opgaveteksten ind i jeres

                                                                                                                                              opgave Put Matlab kode i et Appendix og henvis fra teksten Eksempel rapport over oslashvelse findes paring

                                                                                                                                              hjemmesiden under eksamen

                                                                                                                                              DTU Compute

                                                                                                                                              2122018Introduction to Medical Image Analysis85 DTU Compute Technical University of Denmark

                                                                                                                                              Exercises

                                                                                                                                              • Introduction to Medical Image Analysis
                                                                                                                                              • Lecture 4 ndash Neighbourhood Processing
                                                                                                                                              • What can you do after today
                                                                                                                                              • Point processing
                                                                                                                                              • Point processing
                                                                                                                                              • Neighbourhood processing
                                                                                                                                              • Use of filtering
                                                                                                                                              • Salt and pepper noise
                                                                                                                                              • Salt and pepper noise
                                                                                                                                              • What is so special about noise
                                                                                                                                              • Noise ndash go away
                                                                                                                                              • What is the median Value
                                                                                                                                              • The median value
                                                                                                                                              • Noise away ndash the median filter
                                                                                                                                              • Noise removal ndash average filter
                                                                                                                                              • Noise removal ndash median filter
                                                                                                                                              • Image Filtering
                                                                                                                                              • Median filter
                                                                                                                                              • Rank filters
                                                                                                                                              • Median filter
                                                                                                                                              • Correlation
                                                                                                                                              • Why do we need similarity
                                                                                                                                              • Correlation (1D)
                                                                                                                                              • Correlation (1D)
                                                                                                                                              • Normalisation
                                                                                                                                              • Normalisation
                                                                                                                                              • Correlation on images
                                                                                                                                              • Correlation on images
                                                                                                                                              • Correlation on images
                                                                                                                                              • Draw your filter
                                                                                                                                              • Correlation on images ndash no normalisation
                                                                                                                                              • Correlation on images ndash no normalisation 2
                                                                                                                                              • Mathematics of 2D Correlation
                                                                                                                                              • Mathematics of 2D Correlation
                                                                                                                                              • Mathematics of 2D Correlation
                                                                                                                                              • Slide Number 40
                                                                                                                                              • 2D Kernel Normalisation
                                                                                                                                              • Correlation
                                                                                                                                              • Smoothing filters
                                                                                                                                              • Use of smoothing
                                                                                                                                              • Use of smoothing
                                                                                                                                              • Mean filter
                                                                                                                                              • Border handling
                                                                                                                                              • Border handling ndash extend the input
                                                                                                                                              • Correlation with zero padding
                                                                                                                                              • Border handling ndash extend the input
                                                                                                                                              • Template Matching
                                                                                                                                              • Template Matching
                                                                                                                                              • Template Matching
                                                                                                                                              • Template Matching
                                                                                                                                              • Problematic Correlation
                                                                                                                                              • Normalised Cross Correlation
                                                                                                                                              • Length of template
                                                                                                                                              • Length of image patch
                                                                                                                                              • Normalised Cross Correlation
                                                                                                                                              • Normalised Cross Correlation
                                                                                                                                              • Normalised Cross Correlation
                                                                                                                                              • Edges
                                                                                                                                              • Edges
                                                                                                                                              • Finite Difference
                                                                                                                                              • Edges
                                                                                                                                              • Edges in 2D
                                                                                                                                              • Edge filter kernel
                                                                                                                                              • Prewitt filter
                                                                                                                                              • Edge detection
                                                                                                                                              • Edge filtering
                                                                                                                                              • 02511 - Niveau af dagens emne forelaeligsing
                                                                                                                                              • 02512 - Niveau af dagens emne forelaeligsing
                                                                                                                                              • 02511 - Mit eget udbytte af dagen
                                                                                                                                              • 02512 - Mit eget udbytte af dagen
                                                                                                                                              • 02511 - Sidste uges oslashvelser (pixelwise operations)
                                                                                                                                              • 02512 - Sidste uges oslashvelser (pixelwise operations)
                                                                                                                                              • Denne uges brug af clickers
                                                                                                                                              • What can you do after today
                                                                                                                                              • Oslashvelsesrapport over oslashvelse 4 - 02511
                                                                                                                                              • Exercises
                                                                                                                                                A0
                                                                                                                                                B0
                                                                                                                                                C5
                                                                                                                                                D0
                                                                                                                                                E6
                                                                                                                                                A
                                                                                                                                                B
                                                                                                                                                C
                                                                                                                                                D
                                                                                                                                                E
                                                                                                                                                A3
                                                                                                                                                B0
                                                                                                                                                C3
                                                                                                                                                D0
                                                                                                                                                E0
                                                                                                                                                A
                                                                                                                                                B
                                                                                                                                                C
                                                                                                                                                D
                                                                                                                                                E
                                                                                                                                                A0
                                                                                                                                                B0
                                                                                                                                                C1
                                                                                                                                                D4
                                                                                                                                                E1
                                                                                                                                                A
                                                                                                                                                B
                                                                                                                                                C
                                                                                                                                                D
                                                                                                                                                E
                                                                                                                                                A2
                                                                                                                                                B1
                                                                                                                                                C3
                                                                                                                                                D2
                                                                                                                                                E0
                                                                                                                                                A
                                                                                                                                                B
                                                                                                                                                C
                                                                                                                                                D
                                                                                                                                                E
                                                                                                                                                A0
                                                                                                                                                B0
                                                                                                                                                C2
                                                                                                                                                D6
                                                                                                                                                E0
                                                                                                                                                A
                                                                                                                                                B
                                                                                                                                                C
                                                                                                                                                D
                                                                                                                                                E
                                                                                                                                                A0
                                                                                                                                                B0
                                                                                                                                                C1
                                                                                                                                                D0
                                                                                                                                                E0
                                                                                                                                                A
                                                                                                                                                B
                                                                                                                                                C
                                                                                                                                                D
                                                                                                                                                E
                                                                                                                                                A2
                                                                                                                                                B3
                                                                                                                                                C6
                                                                                                                                                D1
                                                                                                                                                E0
                                                                                                                                                A
                                                                                                                                                B
                                                                                                                                                C
                                                                                                                                                D
                                                                                                                                                E
                                                                                                                                                A0
                                                                                                                                                B8
                                                                                                                                                C1
                                                                                                                                                D1
                                                                                                                                                E0
                                                                                                                                                A
                                                                                                                                                B
                                                                                                                                                C
                                                                                                                                                D
                                                                                                                                                E
                                                                                                                                                A1
                                                                                                                                                B2
                                                                                                                                                C2
                                                                                                                                                D3
                                                                                                                                                E2
                                                                                                                                                A
                                                                                                                                                B
                                                                                                                                                C
                                                                                                                                                D
                                                                                                                                                E

                                                                                                                                                DTU Compute

                                                                                                                                                2122018Introduction to Medical Image Analysis63 DTU Compute Technical University of Denmark

                                                                                                                                                Normalised Cross Correlation NCC will be between

                                                                                                                                                ndash 0 No similarity between template and image patchndash 1 Template and image patch are identical

                                                                                                                                                Input (f)

                                                                                                                                                Template (h)

                                                                                                                                                Output Correlation image

                                                                                                                                                Real max

                                                                                                                                                NCC x y =Correlation

                                                                                                                                                Length of image patch sdot Length of template

                                                                                                                                                DTU Compute

                                                                                                                                                2122018Introduction to Medical Image Analysis64 DTU Compute Technical University of Denmark

                                                                                                                                                Normalised Cross Correlation

                                                                                                                                                A) 010B) 033C) 083D) 062E) 098

                                                                                                                                                Der udfoslashres template matching med og normalized crosscorrelation (NCC) beregnes Hvad bliver NNC i den markerede pixel

                                                                                                                                                1

                                                                                                                                                2 2

                                                                                                                                                3

                                                                                                                                                2

                                                                                                                                                A B C D E

                                                                                                                                                Chart1

                                                                                                                                                1
                                                                                                                                                2
                                                                                                                                                2
                                                                                                                                                3
                                                                                                                                                2

                                                                                                                                                Sheet1

                                                                                                                                                DTU Compute

                                                                                                                                                2122018Introduction to Medical Image Analysis66 DTU Compute Technical University of Denmark

                                                                                                                                                Edges An edge is where there is a

                                                                                                                                                high change in gray level values

                                                                                                                                                Objects are often separated from the background by edgesGray level profile

                                                                                                                                                DTU Compute

                                                                                                                                                2122018Introduction to Medical Image Analysis67 DTU Compute Technical University of Denmark

                                                                                                                                                Edges The profile as a function f(d) What value is high when there

                                                                                                                                                is an edgendash The slope of fndash The slope of the tangent at d

                                                                                                                                                f(d)

                                                                                                                                                119891119891prime(119889119889)

                                                                                                                                                DTU Compute

                                                                                                                                                2122018Introduction to Medical Image Analysis68 DTU Compute Technical University of Denmark

                                                                                                                                                Finite Difference Definition of slope

                                                                                                                                                Approximation

                                                                                                                                                Simpler approximationh = 1

                                                                                                                                                119891119891prime 119889119889 = limℎrarr0

                                                                                                                                                119891119891 119889119889 + ℎ minus 119891119891(119889119889)ℎ

                                                                                                                                                119891119891prime 119889119889 asymp119891119891 119889119889 + ℎ minus 119891119891(119889119889)

                                                                                                                                                ℎ

                                                                                                                                                119891119891prime 119889119889 asymp 119891119891 119889119889 + 1 minus 119891119891(119889119889)

                                                                                                                                                DTU Compute

                                                                                                                                                2122018Introduction to Medical Image Analysis69 DTU Compute Technical University of Denmark

                                                                                                                                                Edges Discrete approximation of frsquo(d) Can be implemented as a filter

                                                                                                                                                -1 0 1

                                                                                                                                                f(d-2) f(d-1) f(d) f(d+1) f(d+2) f(d+3)

                                                                                                                                                f(d)

                                                                                                                                                119891119891prime 119889119889 asymp 119891119891 119889119889 + 1 minus 119891119891(119889119889)

                                                                                                                                                DTU Compute

                                                                                                                                                2122018Introduction to Medical Image Analysis70 DTU Compute Technical University of Denmark

                                                                                                                                                Edges in 2D Changes in gray level values

                                                                                                                                                ndash Image gradientndash Gradient is the 2D derivative of a 2D function f(xy)ndash Equal to the slope of the imagendash A steep slope is equal to an edge

                                                                                                                                                120571120571119891119891 119909119909119910119910 = 119866(119892119892119909119909119892119892119910119910)

                                                                                                                                                DTU Compute

                                                                                                                                                2122018Introduction to Medical Image Analysis71 DTU Compute Technical University of Denmark

                                                                                                                                                Edge filter kernel The Prewitt filter is a typical

                                                                                                                                                edge filter Output image has high

                                                                                                                                                values where there are edges

                                                                                                                                                -1 0 1

                                                                                                                                                -1 0 1

                                                                                                                                                -1 0 1Vertical Prewitt filter

                                                                                                                                                DTU Compute

                                                                                                                                                2122018Introduction to Medical Image Analysis72 DTU Compute Technical University of Denmark

                                                                                                                                                Prewitt filter

                                                                                                                                                Original Prewitt Prewitt

                                                                                                                                                Hot colormapSmooth 15x15

                                                                                                                                                Smooth 15x15

                                                                                                                                                Prewitt

                                                                                                                                                DTU Compute

                                                                                                                                                2122018Introduction to Medical Image Analysis73 DTU Compute Technical University of Denmark

                                                                                                                                                Edge detection Edge filter

                                                                                                                                                ndash Prewitt for example Thresholding

                                                                                                                                                ndash Separate edges from non-edges

                                                                                                                                                Output is binary imagendash Edges are white

                                                                                                                                                DTU Compute

                                                                                                                                                2122018Introduction to Medical Image Analysis74 DTU Compute Technical University of Denmark

                                                                                                                                                Edge filtering

                                                                                                                                                A) MeanB) Horizontal SobelC) Vertical PrewittD) Horisontal PrewittE) Median

                                                                                                                                                Der udfoslashres en filtrering (correlation) med et filter paring billedet Der bruges ikke coefficient normalization Den filtrerede vaeligrdi i den markerede pixel bliver -119 Hvilket et 3x3 filter blev benyttet

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                                                                                                                                                2122018Introduction to Medical Image Analysis76 DTU Compute Technical University of Denmark

                                                                                                                                                02511 - Niveau af dagens emne forelaeligsingA) Meget letB) LetC) PassendeD) SvaeligrtE) Meget svaeligrt

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                                                                                                                                                2122018Introduction to Medical Image Analysis77 DTU Compute Technical University of Denmark

                                                                                                                                                02512 - Niveau af dagens emne forelaeligsingA) Meget letB) LetC) PassendeD) SvaeligrtE) Meget svaeligrt

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                                                                                                                                                2122018Introduction to Medical Image Analysis78 DTU Compute Technical University of Denmark

                                                                                                                                                02511 - Mit eget udbytte af dagenA) Jeg har laeligrt meget lidtB) Lidt laeligringC) PassendeD) God laeligringE) Jeg har laeligrt meget

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                                                                                                                                                2122018Introduction to Medical Image Analysis79 DTU Compute Technical University of Denmark

                                                                                                                                                02512 - Mit eget udbytte af dagenA) Jeg har laeligrt meget lidtB) Lidt laeligringC) PassendeD) God laeligringE) Jeg har laeligrt meget

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                                                                                                                                                2122018Introduction to Medical Image Analysis80 DTU Compute Technical University of Denmark

                                                                                                                                                02511 - Sidste uges oslashvelser (pixelwiseoperations)A) Meget letteB) LetteC) PassendeD) SvaeligreE) Meget svaeligre

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                                                                                                                                                2122018Introduction to Medical Image Analysis81 DTU Compute Technical University of Denmark

                                                                                                                                                02512 - Sidste uges oslashvelser (pixelwiseoperations)A) Meget letteB) LetteC) PassendeD) SvaeligreE) Meget svaeligre

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                                                                                                                                                2122018Introduction to Medical Image Analysis82 DTU Compute Technical University of Denmark

                                                                                                                                                Denne uges brug af clickersA) click click click ndash jeg bliver

                                                                                                                                                sindssygB) For meget clickC) PassendeD) Jeg vil gerne have lidt mereE) Jeg kan ikrsquo faring nok

                                                                                                                                                0 0

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                                                                                                                                                DTU Compute

                                                                                                                                                2122018Introduction to Medical Image Analysis83 DTU Compute Technical University of Denmark

                                                                                                                                                What can you do after today Describe the difference between point processing and neighbourhood

                                                                                                                                                processing Compute a rank filtered image using the min max median and

                                                                                                                                                difference rank filters Compute a mean filtered image Decide if median or average filtering should be used for noise removal Choose the appropriate image border handling based on a given input

                                                                                                                                                image Implement and apply template matching Compute the normalised cross correlation and explain why it should be

                                                                                                                                                used Apply given image filter kernels to images Use edge filters on images Describe finite difference approximation of image gradients Describe the concept of edge detection

                                                                                                                                                DTU Compute

                                                                                                                                                2122018Introduction to Medical Image Analysis84 DTU Compute Technical University of Denmark

                                                                                                                                                Oslashvelsesrapport over oslashvelse 4 - 02511 Oslashvelser taeligller cirka 30 af karakteren Skal afleveres senest den 7 marts kl 2359 Kan afleveres af 1 eller 2 personer

                                                                                                                                                ndash I skal skrive jeres egen oslashvelsesrapportndash Brug mindst et af jeres egne billeder

                                                                                                                                                Afleveres som PDF Lad vaeligre med at kopiere opgaveteksten ind i jeres

                                                                                                                                                opgave Put Matlab kode i et Appendix og henvis fra teksten Eksempel rapport over oslashvelse findes paring

                                                                                                                                                hjemmesiden under eksamen

                                                                                                                                                DTU Compute

                                                                                                                                                2122018Introduction to Medical Image Analysis85 DTU Compute Technical University of Denmark

                                                                                                                                                Exercises

                                                                                                                                                • Introduction to Medical Image Analysis
                                                                                                                                                • Lecture 4 ndash Neighbourhood Processing
                                                                                                                                                • What can you do after today
                                                                                                                                                • Point processing
                                                                                                                                                • Point processing
                                                                                                                                                • Neighbourhood processing
                                                                                                                                                • Use of filtering
                                                                                                                                                • Salt and pepper noise
                                                                                                                                                • Salt and pepper noise
                                                                                                                                                • What is so special about noise
                                                                                                                                                • Noise ndash go away
                                                                                                                                                • What is the median Value
                                                                                                                                                • The median value
                                                                                                                                                • Noise away ndash the median filter
                                                                                                                                                • Noise removal ndash average filter
                                                                                                                                                • Noise removal ndash median filter
                                                                                                                                                • Image Filtering
                                                                                                                                                • Median filter
                                                                                                                                                • Rank filters
                                                                                                                                                • Median filter
                                                                                                                                                • Correlation
                                                                                                                                                • Why do we need similarity
                                                                                                                                                • Correlation (1D)
                                                                                                                                                • Correlation (1D)
                                                                                                                                                • Normalisation
                                                                                                                                                • Normalisation
                                                                                                                                                • Correlation on images
                                                                                                                                                • Correlation on images
                                                                                                                                                • Correlation on images
                                                                                                                                                • Draw your filter
                                                                                                                                                • Correlation on images ndash no normalisation
                                                                                                                                                • Correlation on images ndash no normalisation 2
                                                                                                                                                • Mathematics of 2D Correlation
                                                                                                                                                • Mathematics of 2D Correlation
                                                                                                                                                • Mathematics of 2D Correlation
                                                                                                                                                • Slide Number 40
                                                                                                                                                • 2D Kernel Normalisation
                                                                                                                                                • Correlation
                                                                                                                                                • Smoothing filters
                                                                                                                                                • Use of smoothing
                                                                                                                                                • Use of smoothing
                                                                                                                                                • Mean filter
                                                                                                                                                • Border handling
                                                                                                                                                • Border handling ndash extend the input
                                                                                                                                                • Correlation with zero padding
                                                                                                                                                • Border handling ndash extend the input
                                                                                                                                                • Template Matching
                                                                                                                                                • Template Matching
                                                                                                                                                • Template Matching
                                                                                                                                                • Template Matching
                                                                                                                                                • Problematic Correlation
                                                                                                                                                • Normalised Cross Correlation
                                                                                                                                                • Length of template
                                                                                                                                                • Length of image patch
                                                                                                                                                • Normalised Cross Correlation
                                                                                                                                                • Normalised Cross Correlation
                                                                                                                                                • Normalised Cross Correlation
                                                                                                                                                • Edges
                                                                                                                                                • Edges
                                                                                                                                                • Finite Difference
                                                                                                                                                • Edges
                                                                                                                                                • Edges in 2D
                                                                                                                                                • Edge filter kernel
                                                                                                                                                • Prewitt filter
                                                                                                                                                • Edge detection
                                                                                                                                                • Edge filtering
                                                                                                                                                • 02511 - Niveau af dagens emne forelaeligsing
                                                                                                                                                • 02512 - Niveau af dagens emne forelaeligsing
                                                                                                                                                • 02511 - Mit eget udbytte af dagen
                                                                                                                                                • 02512 - Mit eget udbytte af dagen
                                                                                                                                                • 02511 - Sidste uges oslashvelser (pixelwise operations)
                                                                                                                                                • 02512 - Sidste uges oslashvelser (pixelwise operations)
                                                                                                                                                • Denne uges brug af clickers
                                                                                                                                                • What can you do after today
                                                                                                                                                • Oslashvelsesrapport over oslashvelse 4 - 02511
                                                                                                                                                • Exercises
                                                                                                                                                  A0
                                                                                                                                                  B0
                                                                                                                                                  C5
                                                                                                                                                  D0
                                                                                                                                                  E6
                                                                                                                                                  A
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                                                                                                                                                  D
                                                                                                                                                  E
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                                                                                                                                                  B0
                                                                                                                                                  C3
                                                                                                                                                  D0
                                                                                                                                                  E0
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                                                                                                                                                  D
                                                                                                                                                  E
                                                                                                                                                  A0
                                                                                                                                                  B0
                                                                                                                                                  C1
                                                                                                                                                  D4
                                                                                                                                                  E1
                                                                                                                                                  A
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                                                                                                                                                  C
                                                                                                                                                  D
                                                                                                                                                  E
                                                                                                                                                  A2
                                                                                                                                                  B1
                                                                                                                                                  C3
                                                                                                                                                  D2
                                                                                                                                                  E0
                                                                                                                                                  A
                                                                                                                                                  B
                                                                                                                                                  C
                                                                                                                                                  D
                                                                                                                                                  E
                                                                                                                                                  A0
                                                                                                                                                  B0
                                                                                                                                                  C2
                                                                                                                                                  D6
                                                                                                                                                  E0
                                                                                                                                                  A
                                                                                                                                                  B
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                                                                                                                                                  D
                                                                                                                                                  E
                                                                                                                                                  A0
                                                                                                                                                  B0
                                                                                                                                                  C1
                                                                                                                                                  D0
                                                                                                                                                  E0
                                                                                                                                                  A
                                                                                                                                                  B
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                                                                                                                                                  D
                                                                                                                                                  E
                                                                                                                                                  A2
                                                                                                                                                  B3
                                                                                                                                                  C6
                                                                                                                                                  D1
                                                                                                                                                  E0
                                                                                                                                                  A
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                                                                                                                                                  A0
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                                                                                                                                                  C1
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                                                                                                                                                  E0
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                                                                                                                                                  D
                                                                                                                                                  E
                                                                                                                                                  A1
                                                                                                                                                  B2
                                                                                                                                                  C2
                                                                                                                                                  D3
                                                                                                                                                  E2
                                                                                                                                                  A
                                                                                                                                                  B
                                                                                                                                                  C
                                                                                                                                                  D
                                                                                                                                                  E

                                                                                                                                                  DTU Compute

                                                                                                                                                  2122018Introduction to Medical Image Analysis64 DTU Compute Technical University of Denmark

                                                                                                                                                  Normalised Cross Correlation

                                                                                                                                                  A) 010B) 033C) 083D) 062E) 098

                                                                                                                                                  Der udfoslashres template matching med og normalized crosscorrelation (NCC) beregnes Hvad bliver NNC i den markerede pixel

                                                                                                                                                  1

                                                                                                                                                  2 2

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                                                                                                                                                  2122018Introduction to Medical Image Analysis66 DTU Compute Technical University of Denmark

                                                                                                                                                  Edges An edge is where there is a

                                                                                                                                                  high change in gray level values

                                                                                                                                                  Objects are often separated from the background by edgesGray level profile

                                                                                                                                                  DTU Compute

                                                                                                                                                  2122018Introduction to Medical Image Analysis67 DTU Compute Technical University of Denmark

                                                                                                                                                  Edges The profile as a function f(d) What value is high when there

                                                                                                                                                  is an edgendash The slope of fndash The slope of the tangent at d

                                                                                                                                                  f(d)

                                                                                                                                                  119891119891prime(119889119889)

                                                                                                                                                  DTU Compute

                                                                                                                                                  2122018Introduction to Medical Image Analysis68 DTU Compute Technical University of Denmark

                                                                                                                                                  Finite Difference Definition of slope

                                                                                                                                                  Approximation

                                                                                                                                                  Simpler approximationh = 1

                                                                                                                                                  119891119891prime 119889119889 = limℎrarr0

                                                                                                                                                  119891119891 119889119889 + ℎ minus 119891119891(119889119889)ℎ

                                                                                                                                                  119891119891prime 119889119889 asymp119891119891 119889119889 + ℎ minus 119891119891(119889119889)

                                                                                                                                                  ℎ

                                                                                                                                                  119891119891prime 119889119889 asymp 119891119891 119889119889 + 1 minus 119891119891(119889119889)

                                                                                                                                                  DTU Compute

                                                                                                                                                  2122018Introduction to Medical Image Analysis69 DTU Compute Technical University of Denmark

                                                                                                                                                  Edges Discrete approximation of frsquo(d) Can be implemented as a filter

                                                                                                                                                  -1 0 1

                                                                                                                                                  f(d-2) f(d-1) f(d) f(d+1) f(d+2) f(d+3)

                                                                                                                                                  f(d)

                                                                                                                                                  119891119891prime 119889119889 asymp 119891119891 119889119889 + 1 minus 119891119891(119889119889)

                                                                                                                                                  DTU Compute

                                                                                                                                                  2122018Introduction to Medical Image Analysis70 DTU Compute Technical University of Denmark

                                                                                                                                                  Edges in 2D Changes in gray level values

                                                                                                                                                  ndash Image gradientndash Gradient is the 2D derivative of a 2D function f(xy)ndash Equal to the slope of the imagendash A steep slope is equal to an edge

                                                                                                                                                  120571120571119891119891 119909119909119910119910 = 119866(119892119892119909119909119892119892119910119910)

                                                                                                                                                  DTU Compute

                                                                                                                                                  2122018Introduction to Medical Image Analysis71 DTU Compute Technical University of Denmark

                                                                                                                                                  Edge filter kernel The Prewitt filter is a typical

                                                                                                                                                  edge filter Output image has high

                                                                                                                                                  values where there are edges

                                                                                                                                                  -1 0 1

                                                                                                                                                  -1 0 1

                                                                                                                                                  -1 0 1Vertical Prewitt filter

                                                                                                                                                  DTU Compute

                                                                                                                                                  2122018Introduction to Medical Image Analysis72 DTU Compute Technical University of Denmark

                                                                                                                                                  Prewitt filter

                                                                                                                                                  Original Prewitt Prewitt

                                                                                                                                                  Hot colormapSmooth 15x15

                                                                                                                                                  Smooth 15x15

                                                                                                                                                  Prewitt

                                                                                                                                                  DTU Compute

                                                                                                                                                  2122018Introduction to Medical Image Analysis73 DTU Compute Technical University of Denmark

                                                                                                                                                  Edge detection Edge filter

                                                                                                                                                  ndash Prewitt for example Thresholding

                                                                                                                                                  ndash Separate edges from non-edges

                                                                                                                                                  Output is binary imagendash Edges are white

                                                                                                                                                  DTU Compute

                                                                                                                                                  2122018Introduction to Medical Image Analysis74 DTU Compute Technical University of Denmark

                                                                                                                                                  Edge filtering

                                                                                                                                                  A) MeanB) Horizontal SobelC) Vertical PrewittD) Horisontal PrewittE) Median

                                                                                                                                                  Der udfoslashres en filtrering (correlation) med et filter paring billedet Der bruges ikke coefficient normalization Den filtrerede vaeligrdi i den markerede pixel bliver -119 Hvilket et 3x3 filter blev benyttet

                                                                                                                                                  0

                                                                                                                                                  8

                                                                                                                                                  1 10

                                                                                                                                                  A B C D E

                                                                                                                                                  Chart1

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                                                                                                                                                  DTU Compute

                                                                                                                                                  2122018Introduction to Medical Image Analysis76 DTU Compute Technical University of Denmark

                                                                                                                                                  02511 - Niveau af dagens emne forelaeligsingA) Meget letB) LetC) PassendeD) SvaeligrtE) Meget svaeligrt

                                                                                                                                                  23

                                                                                                                                                  6

                                                                                                                                                  10

                                                                                                                                                  A B C D E

                                                                                                                                                  Chart1

                                                                                                                                                  2
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                                                                                                                                                  1
                                                                                                                                                  0

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                                                                                                                                                  DTU Compute

                                                                                                                                                  2122018Introduction to Medical Image Analysis77 DTU Compute Technical University of Denmark

                                                                                                                                                  02512 - Niveau af dagens emne forelaeligsingA) Meget letB) LetC) PassendeD) SvaeligrtE) Meget svaeligrt

                                                                                                                                                  0 0

                                                                                                                                                  1

                                                                                                                                                  0 0

                                                                                                                                                  A B C D E

                                                                                                                                                  Chart1

                                                                                                                                                  0
                                                                                                                                                  0
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                                                                                                                                                  0
                                                                                                                                                  0

                                                                                                                                                  Sheet1

                                                                                                                                                  DTU Compute

                                                                                                                                                  2122018Introduction to Medical Image Analysis78 DTU Compute Technical University of Denmark

                                                                                                                                                  02511 - Mit eget udbytte af dagenA) Jeg har laeligrt meget lidtB) Lidt laeligringC) PassendeD) God laeligringE) Jeg har laeligrt meget

                                                                                                                                                  0 0

                                                                                                                                                  2

                                                                                                                                                  6

                                                                                                                                                  0

                                                                                                                                                  A B C D E

                                                                                                                                                  Chart1

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                                                                                                                                                  0
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                                                                                                                                                  6
                                                                                                                                                  0

                                                                                                                                                  Sheet1

                                                                                                                                                  DTU Compute

                                                                                                                                                  2122018Introduction to Medical Image Analysis79 DTU Compute Technical University of Denmark

                                                                                                                                                  02512 - Mit eget udbytte af dagenA) Jeg har laeligrt meget lidtB) Lidt laeligringC) PassendeD) God laeligringE) Jeg har laeligrt meget

                                                                                                                                                  2

                                                                                                                                                  1

                                                                                                                                                  3

                                                                                                                                                  2

                                                                                                                                                  0

                                                                                                                                                  A B C D E

                                                                                                                                                  Chart1

                                                                                                                                                  2
                                                                                                                                                  1
                                                                                                                                                  3
                                                                                                                                                  2
                                                                                                                                                  0

                                                                                                                                                  Sheet1

                                                                                                                                                  DTU Compute

                                                                                                                                                  2122018Introduction to Medical Image Analysis80 DTU Compute Technical University of Denmark

                                                                                                                                                  02511 - Sidste uges oslashvelser (pixelwiseoperations)A) Meget letteB) LetteC) PassendeD) SvaeligreE) Meget svaeligre

                                                                                                                                                  0 0

                                                                                                                                                  1

                                                                                                                                                  4

                                                                                                                                                  1

                                                                                                                                                  A B C D E

                                                                                                                                                  Chart1

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                                                                                                                                                  4
                                                                                                                                                  1

                                                                                                                                                  Sheet1

                                                                                                                                                  DTU Compute

                                                                                                                                                  2122018Introduction to Medical Image Analysis81 DTU Compute Technical University of Denmark

                                                                                                                                                  02512 - Sidste uges oslashvelser (pixelwiseoperations)A) Meget letteB) LetteC) PassendeD) SvaeligreE) Meget svaeligre

                                                                                                                                                  3

                                                                                                                                                  0

                                                                                                                                                  3

                                                                                                                                                  0 0

                                                                                                                                                  A B C D E

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                                                                                                                                                  0
                                                                                                                                                  3
                                                                                                                                                  0
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                                                                                                                                                  Sheet1

                                                                                                                                                  DTU Compute

                                                                                                                                                  2122018Introduction to Medical Image Analysis82 DTU Compute Technical University of Denmark

                                                                                                                                                  Denne uges brug af clickersA) click click click ndash jeg bliver

                                                                                                                                                  sindssygB) For meget clickC) PassendeD) Jeg vil gerne have lidt mereE) Jeg kan ikrsquo faring nok

                                                                                                                                                  0 0

                                                                                                                                                  5

                                                                                                                                                  0

                                                                                                                                                  6

                                                                                                                                                  A B C D E

                                                                                                                                                  Chart1

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                                                                                                                                                  Sheet1

                                                                                                                                                  DTU Compute

                                                                                                                                                  2122018Introduction to Medical Image Analysis83 DTU Compute Technical University of Denmark

                                                                                                                                                  What can you do after today Describe the difference between point processing and neighbourhood

                                                                                                                                                  processing Compute a rank filtered image using the min max median and

                                                                                                                                                  difference rank filters Compute a mean filtered image Decide if median or average filtering should be used for noise removal Choose the appropriate image border handling based on a given input

                                                                                                                                                  image Implement and apply template matching Compute the normalised cross correlation and explain why it should be

                                                                                                                                                  used Apply given image filter kernels to images Use edge filters on images Describe finite difference approximation of image gradients Describe the concept of edge detection

                                                                                                                                                  DTU Compute

                                                                                                                                                  2122018Introduction to Medical Image Analysis84 DTU Compute Technical University of Denmark

                                                                                                                                                  Oslashvelsesrapport over oslashvelse 4 - 02511 Oslashvelser taeligller cirka 30 af karakteren Skal afleveres senest den 7 marts kl 2359 Kan afleveres af 1 eller 2 personer

                                                                                                                                                  ndash I skal skrive jeres egen oslashvelsesrapportndash Brug mindst et af jeres egne billeder

                                                                                                                                                  Afleveres som PDF Lad vaeligre med at kopiere opgaveteksten ind i jeres

                                                                                                                                                  opgave Put Matlab kode i et Appendix og henvis fra teksten Eksempel rapport over oslashvelse findes paring

                                                                                                                                                  hjemmesiden under eksamen

                                                                                                                                                  DTU Compute

                                                                                                                                                  2122018Introduction to Medical Image Analysis85 DTU Compute Technical University of Denmark

                                                                                                                                                  Exercises

                                                                                                                                                  • Introduction to Medical Image Analysis
                                                                                                                                                  • Lecture 4 ndash Neighbourhood Processing
                                                                                                                                                  • What can you do after today
                                                                                                                                                  • Point processing
                                                                                                                                                  • Point processing
                                                                                                                                                  • Neighbourhood processing
                                                                                                                                                  • Use of filtering
                                                                                                                                                  • Salt and pepper noise
                                                                                                                                                  • Salt and pepper noise
                                                                                                                                                  • What is so special about noise
                                                                                                                                                  • Noise ndash go away
                                                                                                                                                  • What is the median Value
                                                                                                                                                  • The median value
                                                                                                                                                  • Noise away ndash the median filter
                                                                                                                                                  • Noise removal ndash average filter
                                                                                                                                                  • Noise removal ndash median filter
                                                                                                                                                  • Image Filtering
                                                                                                                                                  • Median filter
                                                                                                                                                  • Rank filters
                                                                                                                                                  • Median filter
                                                                                                                                                  • Correlation
                                                                                                                                                  • Why do we need similarity
                                                                                                                                                  • Correlation (1D)
                                                                                                                                                  • Correlation (1D)
                                                                                                                                                  • Normalisation
                                                                                                                                                  • Normalisation
                                                                                                                                                  • Correlation on images
                                                                                                                                                  • Correlation on images
                                                                                                                                                  • Correlation on images
                                                                                                                                                  • Draw your filter
                                                                                                                                                  • Correlation on images ndash no normalisation
                                                                                                                                                  • Correlation on images ndash no normalisation 2
                                                                                                                                                  • Mathematics of 2D Correlation
                                                                                                                                                  • Mathematics of 2D Correlation
                                                                                                                                                  • Mathematics of 2D Correlation
                                                                                                                                                  • Slide Number 40
                                                                                                                                                  • 2D Kernel Normalisation
                                                                                                                                                  • Correlation
                                                                                                                                                  • Smoothing filters
                                                                                                                                                  • Use of smoothing
                                                                                                                                                  • Use of smoothing
                                                                                                                                                  • Mean filter
                                                                                                                                                  • Border handling
                                                                                                                                                  • Border handling ndash extend the input
                                                                                                                                                  • Correlation with zero padding
                                                                                                                                                  • Border handling ndash extend the input
                                                                                                                                                  • Template Matching
                                                                                                                                                  • Template Matching
                                                                                                                                                  • Template Matching
                                                                                                                                                  • Template Matching
                                                                                                                                                  • Problematic Correlation
                                                                                                                                                  • Normalised Cross Correlation
                                                                                                                                                  • Length of template
                                                                                                                                                  • Length of image patch
                                                                                                                                                  • Normalised Cross Correlation
                                                                                                                                                  • Normalised Cross Correlation
                                                                                                                                                  • Normalised Cross Correlation
                                                                                                                                                  • Edges
                                                                                                                                                  • Edges
                                                                                                                                                  • Finite Difference
                                                                                                                                                  • Edges
                                                                                                                                                  • Edges in 2D
                                                                                                                                                  • Edge filter kernel
                                                                                                                                                  • Prewitt filter
                                                                                                                                                  • Edge detection
                                                                                                                                                  • Edge filtering
                                                                                                                                                  • 02511 - Niveau af dagens emne forelaeligsing
                                                                                                                                                  • 02512 - Niveau af dagens emne forelaeligsing
                                                                                                                                                  • 02511 - Mit eget udbytte af dagen
                                                                                                                                                  • 02512 - Mit eget udbytte af dagen
                                                                                                                                                  • 02511 - Sidste uges oslashvelser (pixelwise operations)
                                                                                                                                                  • 02512 - Sidste uges oslashvelser (pixelwise operations)
                                                                                                                                                  • Denne uges brug af clickers
                                                                                                                                                  • What can you do after today
                                                                                                                                                  • Oslashvelsesrapport over oslashvelse 4 - 02511
                                                                                                                                                  • Exercises
                                                                                                                                                    A0
                                                                                                                                                    B0
                                                                                                                                                    C5
                                                                                                                                                    D0
                                                                                                                                                    E6
                                                                                                                                                    A
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                                                                                                                                                    D4
                                                                                                                                                    E1
                                                                                                                                                    A
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                                                                                                                                                    E
                                                                                                                                                    A2
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                                                                                                                                                    D2
                                                                                                                                                    E0
                                                                                                                                                    A
                                                                                                                                                    B
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                                                                                                                                                    D
                                                                                                                                                    E
                                                                                                                                                    A0
                                                                                                                                                    B0
                                                                                                                                                    C2
                                                                                                                                                    D6
                                                                                                                                                    E0
                                                                                                                                                    A
                                                                                                                                                    B
                                                                                                                                                    C
                                                                                                                                                    D
                                                                                                                                                    E
                                                                                                                                                    A0
                                                                                                                                                    B0
                                                                                                                                                    C1
                                                                                                                                                    D0
                                                                                                                                                    E0
                                                                                                                                                    A
                                                                                                                                                    B
                                                                                                                                                    C
                                                                                                                                                    D
                                                                                                                                                    E
                                                                                                                                                    A2
                                                                                                                                                    B3
                                                                                                                                                    C6
                                                                                                                                                    D1
                                                                                                                                                    E0
                                                                                                                                                    A
                                                                                                                                                    B
                                                                                                                                                    C
                                                                                                                                                    D
                                                                                                                                                    E
                                                                                                                                                    A0
                                                                                                                                                    B8
                                                                                                                                                    C1
                                                                                                                                                    D1
                                                                                                                                                    E0
                                                                                                                                                    A
                                                                                                                                                    B
                                                                                                                                                    C
                                                                                                                                                    D
                                                                                                                                                    E
                                                                                                                                                    A1
                                                                                                                                                    B2
                                                                                                                                                    C2
                                                                                                                                                    D3
                                                                                                                                                    E2
                                                                                                                                                    A
                                                                                                                                                    B
                                                                                                                                                    C
                                                                                                                                                    D
                                                                                                                                                    E

                                                                                                                                                    Chart1

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                                                                                                                                                    2122018Introduction to Medical Image Analysis66 DTU Compute Technical University of Denmark

                                                                                                                                                    Edges An edge is where there is a

                                                                                                                                                    high change in gray level values

                                                                                                                                                    Objects are often separated from the background by edgesGray level profile

                                                                                                                                                    DTU Compute

                                                                                                                                                    2122018Introduction to Medical Image Analysis67 DTU Compute Technical University of Denmark

                                                                                                                                                    Edges The profile as a function f(d) What value is high when there

                                                                                                                                                    is an edgendash The slope of fndash The slope of the tangent at d

                                                                                                                                                    f(d)

                                                                                                                                                    119891119891prime(119889119889)

                                                                                                                                                    DTU Compute

                                                                                                                                                    2122018Introduction to Medical Image Analysis68 DTU Compute Technical University of Denmark

                                                                                                                                                    Finite Difference Definition of slope

                                                                                                                                                    Approximation

                                                                                                                                                    Simpler approximationh = 1

                                                                                                                                                    119891119891prime 119889119889 = limℎrarr0

                                                                                                                                                    119891119891 119889119889 + ℎ minus 119891119891(119889119889)ℎ

                                                                                                                                                    119891119891prime 119889119889 asymp119891119891 119889119889 + ℎ minus 119891119891(119889119889)

                                                                                                                                                    ℎ

                                                                                                                                                    119891119891prime 119889119889 asymp 119891119891 119889119889 + 1 minus 119891119891(119889119889)

                                                                                                                                                    DTU Compute

                                                                                                                                                    2122018Introduction to Medical Image Analysis69 DTU Compute Technical University of Denmark

                                                                                                                                                    Edges Discrete approximation of frsquo(d) Can be implemented as a filter

                                                                                                                                                    -1 0 1

                                                                                                                                                    f(d-2) f(d-1) f(d) f(d+1) f(d+2) f(d+3)

                                                                                                                                                    f(d)

                                                                                                                                                    119891119891prime 119889119889 asymp 119891119891 119889119889 + 1 minus 119891119891(119889119889)

                                                                                                                                                    DTU Compute

                                                                                                                                                    2122018Introduction to Medical Image Analysis70 DTU Compute Technical University of Denmark

                                                                                                                                                    Edges in 2D Changes in gray level values

                                                                                                                                                    ndash Image gradientndash Gradient is the 2D derivative of a 2D function f(xy)ndash Equal to the slope of the imagendash A steep slope is equal to an edge

                                                                                                                                                    120571120571119891119891 119909119909119910119910 = 119866(119892119892119909119909119892119892119910119910)

                                                                                                                                                    DTU Compute

                                                                                                                                                    2122018Introduction to Medical Image Analysis71 DTU Compute Technical University of Denmark

                                                                                                                                                    Edge filter kernel The Prewitt filter is a typical

                                                                                                                                                    edge filter Output image has high

                                                                                                                                                    values where there are edges

                                                                                                                                                    -1 0 1

                                                                                                                                                    -1 0 1

                                                                                                                                                    -1 0 1Vertical Prewitt filter

                                                                                                                                                    DTU Compute

                                                                                                                                                    2122018Introduction to Medical Image Analysis72 DTU Compute Technical University of Denmark

                                                                                                                                                    Prewitt filter

                                                                                                                                                    Original Prewitt Prewitt

                                                                                                                                                    Hot colormapSmooth 15x15

                                                                                                                                                    Smooth 15x15

                                                                                                                                                    Prewitt

                                                                                                                                                    DTU Compute

                                                                                                                                                    2122018Introduction to Medical Image Analysis73 DTU Compute Technical University of Denmark

                                                                                                                                                    Edge detection Edge filter

                                                                                                                                                    ndash Prewitt for example Thresholding

                                                                                                                                                    ndash Separate edges from non-edges

                                                                                                                                                    Output is binary imagendash Edges are white

                                                                                                                                                    DTU Compute

                                                                                                                                                    2122018Introduction to Medical Image Analysis74 DTU Compute Technical University of Denmark

                                                                                                                                                    Edge filtering

                                                                                                                                                    A) MeanB) Horizontal SobelC) Vertical PrewittD) Horisontal PrewittE) Median

                                                                                                                                                    Der udfoslashres en filtrering (correlation) med et filter paring billedet Der bruges ikke coefficient normalization Den filtrerede vaeligrdi i den markerede pixel bliver -119 Hvilket et 3x3 filter blev benyttet

                                                                                                                                                    0

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                                                                                                                                                    A B C D E

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                                                                                                                                                    2122018Introduction to Medical Image Analysis76 DTU Compute Technical University of Denmark

                                                                                                                                                    02511 - Niveau af dagens emne forelaeligsingA) Meget letB) LetC) PassendeD) SvaeligrtE) Meget svaeligrt

                                                                                                                                                    23

                                                                                                                                                    6

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                                                                                                                                                    A B C D E

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                                                                                                                                                    2122018Introduction to Medical Image Analysis77 DTU Compute Technical University of Denmark

                                                                                                                                                    02512 - Niveau af dagens emne forelaeligsingA) Meget letB) LetC) PassendeD) SvaeligrtE) Meget svaeligrt

                                                                                                                                                    0 0

                                                                                                                                                    1

                                                                                                                                                    0 0

                                                                                                                                                    A B C D E

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                                                                                                                                                    2122018Introduction to Medical Image Analysis78 DTU Compute Technical University of Denmark

                                                                                                                                                    02511 - Mit eget udbytte af dagenA) Jeg har laeligrt meget lidtB) Lidt laeligringC) PassendeD) God laeligringE) Jeg har laeligrt meget

                                                                                                                                                    0 0

                                                                                                                                                    2

                                                                                                                                                    6

                                                                                                                                                    0

                                                                                                                                                    A B C D E

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                                                                                                                                                    2122018Introduction to Medical Image Analysis79 DTU Compute Technical University of Denmark

                                                                                                                                                    02512 - Mit eget udbytte af dagenA) Jeg har laeligrt meget lidtB) Lidt laeligringC) PassendeD) God laeligringE) Jeg har laeligrt meget

                                                                                                                                                    2

                                                                                                                                                    1

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                                                                                                                                                    2122018Introduction to Medical Image Analysis80 DTU Compute Technical University of Denmark

                                                                                                                                                    02511 - Sidste uges oslashvelser (pixelwiseoperations)A) Meget letteB) LetteC) PassendeD) SvaeligreE) Meget svaeligre

                                                                                                                                                    0 0

                                                                                                                                                    1

                                                                                                                                                    4

                                                                                                                                                    1

                                                                                                                                                    A B C D E

                                                                                                                                                    Chart1

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                                                                                                                                                    2122018Introduction to Medical Image Analysis81 DTU Compute Technical University of Denmark

                                                                                                                                                    02512 - Sidste uges oslashvelser (pixelwiseoperations)A) Meget letteB) LetteC) PassendeD) SvaeligreE) Meget svaeligre

                                                                                                                                                    3

                                                                                                                                                    0

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                                                                                                                                                    2122018Introduction to Medical Image Analysis82 DTU Compute Technical University of Denmark

                                                                                                                                                    Denne uges brug af clickersA) click click click ndash jeg bliver

                                                                                                                                                    sindssygB) For meget clickC) PassendeD) Jeg vil gerne have lidt mereE) Jeg kan ikrsquo faring nok

                                                                                                                                                    0 0

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                                                                                                                                                    2122018Introduction to Medical Image Analysis83 DTU Compute Technical University of Denmark

                                                                                                                                                    What can you do after today Describe the difference between point processing and neighbourhood

                                                                                                                                                    processing Compute a rank filtered image using the min max median and

                                                                                                                                                    difference rank filters Compute a mean filtered image Decide if median or average filtering should be used for noise removal Choose the appropriate image border handling based on a given input

                                                                                                                                                    image Implement and apply template matching Compute the normalised cross correlation and explain why it should be

                                                                                                                                                    used Apply given image filter kernels to images Use edge filters on images Describe finite difference approximation of image gradients Describe the concept of edge detection

                                                                                                                                                    DTU Compute

                                                                                                                                                    2122018Introduction to Medical Image Analysis84 DTU Compute Technical University of Denmark

                                                                                                                                                    Oslashvelsesrapport over oslashvelse 4 - 02511 Oslashvelser taeligller cirka 30 af karakteren Skal afleveres senest den 7 marts kl 2359 Kan afleveres af 1 eller 2 personer

                                                                                                                                                    ndash I skal skrive jeres egen oslashvelsesrapportndash Brug mindst et af jeres egne billeder

                                                                                                                                                    Afleveres som PDF Lad vaeligre med at kopiere opgaveteksten ind i jeres

                                                                                                                                                    opgave Put Matlab kode i et Appendix og henvis fra teksten Eksempel rapport over oslashvelse findes paring

                                                                                                                                                    hjemmesiden under eksamen

                                                                                                                                                    DTU Compute

                                                                                                                                                    2122018Introduction to Medical Image Analysis85 DTU Compute Technical University of Denmark

                                                                                                                                                    Exercises

                                                                                                                                                    • Introduction to Medical Image Analysis
                                                                                                                                                    • Lecture 4 ndash Neighbourhood Processing
                                                                                                                                                    • What can you do after today
                                                                                                                                                    • Point processing
                                                                                                                                                    • Point processing
                                                                                                                                                    • Neighbourhood processing
                                                                                                                                                    • Use of filtering
                                                                                                                                                    • Salt and pepper noise
                                                                                                                                                    • Salt and pepper noise
                                                                                                                                                    • What is so special about noise
                                                                                                                                                    • Noise ndash go away
                                                                                                                                                    • What is the median Value
                                                                                                                                                    • The median value
                                                                                                                                                    • Noise away ndash the median filter
                                                                                                                                                    • Noise removal ndash average filter
                                                                                                                                                    • Noise removal ndash median filter
                                                                                                                                                    • Image Filtering
                                                                                                                                                    • Median filter
                                                                                                                                                    • Rank filters
                                                                                                                                                    • Median filter
                                                                                                                                                    • Correlation
                                                                                                                                                    • Why do we need similarity
                                                                                                                                                    • Correlation (1D)
                                                                                                                                                    • Correlation (1D)
                                                                                                                                                    • Normalisation
                                                                                                                                                    • Normalisation
                                                                                                                                                    • Correlation on images
                                                                                                                                                    • Correlation on images
                                                                                                                                                    • Correlation on images
                                                                                                                                                    • Draw your filter
                                                                                                                                                    • Correlation on images ndash no normalisation
                                                                                                                                                    • Correlation on images ndash no normalisation 2
                                                                                                                                                    • Mathematics of 2D Correlation
                                                                                                                                                    • Mathematics of 2D Correlation
                                                                                                                                                    • Mathematics of 2D Correlation
                                                                                                                                                    • Slide Number 40
                                                                                                                                                    • 2D Kernel Normalisation
                                                                                                                                                    • Correlation
                                                                                                                                                    • Smoothing filters
                                                                                                                                                    • Use of smoothing
                                                                                                                                                    • Use of smoothing
                                                                                                                                                    • Mean filter
                                                                                                                                                    • Border handling
                                                                                                                                                    • Border handling ndash extend the input
                                                                                                                                                    • Correlation with zero padding
                                                                                                                                                    • Border handling ndash extend the input
                                                                                                                                                    • Template Matching
                                                                                                                                                    • Template Matching
                                                                                                                                                    • Template Matching
                                                                                                                                                    • Template Matching
                                                                                                                                                    • Problematic Correlation
                                                                                                                                                    • Normalised Cross Correlation
                                                                                                                                                    • Length of template
                                                                                                                                                    • Length of image patch
                                                                                                                                                    • Normalised Cross Correlation
                                                                                                                                                    • Normalised Cross Correlation
                                                                                                                                                    • Normalised Cross Correlation
                                                                                                                                                    • Edges
                                                                                                                                                    • Edges
                                                                                                                                                    • Finite Difference
                                                                                                                                                    • Edges
                                                                                                                                                    • Edges in 2D
                                                                                                                                                    • Edge filter kernel
                                                                                                                                                    • Prewitt filter
                                                                                                                                                    • Edge detection
                                                                                                                                                    • Edge filtering
                                                                                                                                                    • 02511 - Niveau af dagens emne forelaeligsing
                                                                                                                                                    • 02512 - Niveau af dagens emne forelaeligsing
                                                                                                                                                    • 02511 - Mit eget udbytte af dagen
                                                                                                                                                    • 02512 - Mit eget udbytte af dagen
                                                                                                                                                    • 02511 - Sidste uges oslashvelser (pixelwise operations)
                                                                                                                                                    • 02512 - Sidste uges oslashvelser (pixelwise operations)
                                                                                                                                                    • Denne uges brug af clickers
                                                                                                                                                    • What can you do after today
                                                                                                                                                    • Oslashvelsesrapport over oslashvelse 4 - 02511
                                                                                                                                                    • Exercises
                                                                                                                                                      A0
                                                                                                                                                      B0
                                                                                                                                                      C5
                                                                                                                                                      D0
                                                                                                                                                      E6
                                                                                                                                                      A
                                                                                                                                                      B
                                                                                                                                                      C
                                                                                                                                                      D
                                                                                                                                                      E
                                                                                                                                                      A3
                                                                                                                                                      B0
                                                                                                                                                      C3
                                                                                                                                                      D0
                                                                                                                                                      E0
                                                                                                                                                      A
                                                                                                                                                      B
                                                                                                                                                      C
                                                                                                                                                      D
                                                                                                                                                      E
                                                                                                                                                      A0
                                                                                                                                                      B0
                                                                                                                                                      C1
                                                                                                                                                      D4
                                                                                                                                                      E1
                                                                                                                                                      A
                                                                                                                                                      B
                                                                                                                                                      C
                                                                                                                                                      D
                                                                                                                                                      E
                                                                                                                                                      A2
                                                                                                                                                      B1
                                                                                                                                                      C3
                                                                                                                                                      D2
                                                                                                                                                      E0
                                                                                                                                                      A
                                                                                                                                                      B
                                                                                                                                                      C
                                                                                                                                                      D
                                                                                                                                                      E
                                                                                                                                                      A0
                                                                                                                                                      B0
                                                                                                                                                      C2
                                                                                                                                                      D6
                                                                                                                                                      E0
                                                                                                                                                      A
                                                                                                                                                      B
                                                                                                                                                      C
                                                                                                                                                      D
                                                                                                                                                      E
                                                                                                                                                      A0
                                                                                                                                                      B0
                                                                                                                                                      C1
                                                                                                                                                      D0
                                                                                                                                                      E0
                                                                                                                                                      A
                                                                                                                                                      B
                                                                                                                                                      C
                                                                                                                                                      D
                                                                                                                                                      E
                                                                                                                                                      A2
                                                                                                                                                      B3
                                                                                                                                                      C6
                                                                                                                                                      D1
                                                                                                                                                      E0
                                                                                                                                                      A
                                                                                                                                                      B
                                                                                                                                                      C
                                                                                                                                                      D
                                                                                                                                                      E
                                                                                                                                                      A0
                                                                                                                                                      B8
                                                                                                                                                      C1
                                                                                                                                                      D1
                                                                                                                                                      E0
                                                                                                                                                      A
                                                                                                                                                      B
                                                                                                                                                      C
                                                                                                                                                      D
                                                                                                                                                      E
                                                                                                                                                      A1
                                                                                                                                                      B2
                                                                                                                                                      C2
                                                                                                                                                      D3
                                                                                                                                                      E2
                                                                                                                                                      A
                                                                                                                                                      B
                                                                                                                                                      C
                                                                                                                                                      D
                                                                                                                                                      E

                                                                                                                                                      Sheet1

                                                                                                                                                      DTU Compute

                                                                                                                                                      2122018Introduction to Medical Image Analysis66 DTU Compute Technical University of Denmark

                                                                                                                                                      Edges An edge is where there is a

                                                                                                                                                      high change in gray level values

                                                                                                                                                      Objects are often separated from the background by edgesGray level profile

                                                                                                                                                      DTU Compute

                                                                                                                                                      2122018Introduction to Medical Image Analysis67 DTU Compute Technical University of Denmark

                                                                                                                                                      Edges The profile as a function f(d) What value is high when there

                                                                                                                                                      is an edgendash The slope of fndash The slope of the tangent at d

                                                                                                                                                      f(d)

                                                                                                                                                      119891119891prime(119889119889)

                                                                                                                                                      DTU Compute

                                                                                                                                                      2122018Introduction to Medical Image Analysis68 DTU Compute Technical University of Denmark

                                                                                                                                                      Finite Difference Definition of slope

                                                                                                                                                      Approximation

                                                                                                                                                      Simpler approximationh = 1

                                                                                                                                                      119891119891prime 119889119889 = limℎrarr0

                                                                                                                                                      119891119891 119889119889 + ℎ minus 119891119891(119889119889)ℎ

                                                                                                                                                      119891119891prime 119889119889 asymp119891119891 119889119889 + ℎ minus 119891119891(119889119889)

                                                                                                                                                      ℎ

                                                                                                                                                      119891119891prime 119889119889 asymp 119891119891 119889119889 + 1 minus 119891119891(119889119889)

                                                                                                                                                      DTU Compute

                                                                                                                                                      2122018Introduction to Medical Image Analysis69 DTU Compute Technical University of Denmark

                                                                                                                                                      Edges Discrete approximation of frsquo(d) Can be implemented as a filter

                                                                                                                                                      -1 0 1

                                                                                                                                                      f(d-2) f(d-1) f(d) f(d+1) f(d+2) f(d+3)

                                                                                                                                                      f(d)

                                                                                                                                                      119891119891prime 119889119889 asymp 119891119891 119889119889 + 1 minus 119891119891(119889119889)

                                                                                                                                                      DTU Compute

                                                                                                                                                      2122018Introduction to Medical Image Analysis70 DTU Compute Technical University of Denmark

                                                                                                                                                      Edges in 2D Changes in gray level values

                                                                                                                                                      ndash Image gradientndash Gradient is the 2D derivative of a 2D function f(xy)ndash Equal to the slope of the imagendash A steep slope is equal to an edge

                                                                                                                                                      120571120571119891119891 119909119909119910119910 = 119866(119892119892119909119909119892119892119910119910)

                                                                                                                                                      DTU Compute

                                                                                                                                                      2122018Introduction to Medical Image Analysis71 DTU Compute Technical University of Denmark

                                                                                                                                                      Edge filter kernel The Prewitt filter is a typical

                                                                                                                                                      edge filter Output image has high

                                                                                                                                                      values where there are edges

                                                                                                                                                      -1 0 1

                                                                                                                                                      -1 0 1

                                                                                                                                                      -1 0 1Vertical Prewitt filter

                                                                                                                                                      DTU Compute

                                                                                                                                                      2122018Introduction to Medical Image Analysis72 DTU Compute Technical University of Denmark

                                                                                                                                                      Prewitt filter

                                                                                                                                                      Original Prewitt Prewitt

                                                                                                                                                      Hot colormapSmooth 15x15

                                                                                                                                                      Smooth 15x15

                                                                                                                                                      Prewitt

                                                                                                                                                      DTU Compute

                                                                                                                                                      2122018Introduction to Medical Image Analysis73 DTU Compute Technical University of Denmark

                                                                                                                                                      Edge detection Edge filter

                                                                                                                                                      ndash Prewitt for example Thresholding

                                                                                                                                                      ndash Separate edges from non-edges

                                                                                                                                                      Output is binary imagendash Edges are white

                                                                                                                                                      DTU Compute

                                                                                                                                                      2122018Introduction to Medical Image Analysis74 DTU Compute Technical University of Denmark

                                                                                                                                                      Edge filtering

                                                                                                                                                      A) MeanB) Horizontal SobelC) Vertical PrewittD) Horisontal PrewittE) Median

                                                                                                                                                      Der udfoslashres en filtrering (correlation) med et filter paring billedet Der bruges ikke coefficient normalization Den filtrerede vaeligrdi i den markerede pixel bliver -119 Hvilket et 3x3 filter blev benyttet

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                                                                                                                                                      02511 - Niveau af dagens emne forelaeligsingA) Meget letB) LetC) PassendeD) SvaeligrtE) Meget svaeligrt

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                                                                                                                                                      02512 - Niveau af dagens emne forelaeligsingA) Meget letB) LetC) PassendeD) SvaeligrtE) Meget svaeligrt

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                                                                                                                                                      02511 - Mit eget udbytte af dagenA) Jeg har laeligrt meget lidtB) Lidt laeligringC) PassendeD) God laeligringE) Jeg har laeligrt meget

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                                                                                                                                                      2122018Introduction to Medical Image Analysis79 DTU Compute Technical University of Denmark

                                                                                                                                                      02512 - Mit eget udbytte af dagenA) Jeg har laeligrt meget lidtB) Lidt laeligringC) PassendeD) God laeligringE) Jeg har laeligrt meget

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                                                                                                                                                      02511 - Sidste uges oslashvelser (pixelwiseoperations)A) Meget letteB) LetteC) PassendeD) SvaeligreE) Meget svaeligre

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                                                                                                                                                      2122018Introduction to Medical Image Analysis81 DTU Compute Technical University of Denmark

                                                                                                                                                      02512 - Sidste uges oslashvelser (pixelwiseoperations)A) Meget letteB) LetteC) PassendeD) SvaeligreE) Meget svaeligre

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                                                                                                                                                      2122018Introduction to Medical Image Analysis82 DTU Compute Technical University of Denmark

                                                                                                                                                      Denne uges brug af clickersA) click click click ndash jeg bliver

                                                                                                                                                      sindssygB) For meget clickC) PassendeD) Jeg vil gerne have lidt mereE) Jeg kan ikrsquo faring nok

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                                                                                                                                                      2122018Introduction to Medical Image Analysis83 DTU Compute Technical University of Denmark

                                                                                                                                                      What can you do after today Describe the difference between point processing and neighbourhood

                                                                                                                                                      processing Compute a rank filtered image using the min max median and

                                                                                                                                                      difference rank filters Compute a mean filtered image Decide if median or average filtering should be used for noise removal Choose the appropriate image border handling based on a given input

                                                                                                                                                      image Implement and apply template matching Compute the normalised cross correlation and explain why it should be

                                                                                                                                                      used Apply given image filter kernels to images Use edge filters on images Describe finite difference approximation of image gradients Describe the concept of edge detection

                                                                                                                                                      DTU Compute

                                                                                                                                                      2122018Introduction to Medical Image Analysis84 DTU Compute Technical University of Denmark

                                                                                                                                                      Oslashvelsesrapport over oslashvelse 4 - 02511 Oslashvelser taeligller cirka 30 af karakteren Skal afleveres senest den 7 marts kl 2359 Kan afleveres af 1 eller 2 personer

                                                                                                                                                      ndash I skal skrive jeres egen oslashvelsesrapportndash Brug mindst et af jeres egne billeder

                                                                                                                                                      Afleveres som PDF Lad vaeligre med at kopiere opgaveteksten ind i jeres

                                                                                                                                                      opgave Put Matlab kode i et Appendix og henvis fra teksten Eksempel rapport over oslashvelse findes paring

                                                                                                                                                      hjemmesiden under eksamen

                                                                                                                                                      DTU Compute

                                                                                                                                                      2122018Introduction to Medical Image Analysis85 DTU Compute Technical University of Denmark

                                                                                                                                                      Exercises

                                                                                                                                                      • Introduction to Medical Image Analysis
                                                                                                                                                      • Lecture 4 ndash Neighbourhood Processing
                                                                                                                                                      • What can you do after today
                                                                                                                                                      • Point processing
                                                                                                                                                      • Point processing
                                                                                                                                                      • Neighbourhood processing
                                                                                                                                                      • Use of filtering
                                                                                                                                                      • Salt and pepper noise
                                                                                                                                                      • Salt and pepper noise
                                                                                                                                                      • What is so special about noise
                                                                                                                                                      • Noise ndash go away
                                                                                                                                                      • What is the median Value
                                                                                                                                                      • The median value
                                                                                                                                                      • Noise away ndash the median filter
                                                                                                                                                      • Noise removal ndash average filter
                                                                                                                                                      • Noise removal ndash median filter
                                                                                                                                                      • Image Filtering
                                                                                                                                                      • Median filter
                                                                                                                                                      • Rank filters
                                                                                                                                                      • Median filter
                                                                                                                                                      • Correlation
                                                                                                                                                      • Why do we need similarity
                                                                                                                                                      • Correlation (1D)
                                                                                                                                                      • Correlation (1D)
                                                                                                                                                      • Normalisation
                                                                                                                                                      • Normalisation
                                                                                                                                                      • Correlation on images
                                                                                                                                                      • Correlation on images
                                                                                                                                                      • Correlation on images
                                                                                                                                                      • Draw your filter
                                                                                                                                                      • Correlation on images ndash no normalisation
                                                                                                                                                      • Correlation on images ndash no normalisation 2
                                                                                                                                                      • Mathematics of 2D Correlation
                                                                                                                                                      • Mathematics of 2D Correlation
                                                                                                                                                      • Mathematics of 2D Correlation
                                                                                                                                                      • Slide Number 40
                                                                                                                                                      • 2D Kernel Normalisation
                                                                                                                                                      • Correlation
                                                                                                                                                      • Smoothing filters
                                                                                                                                                      • Use of smoothing
                                                                                                                                                      • Use of smoothing
                                                                                                                                                      • Mean filter
                                                                                                                                                      • Border handling
                                                                                                                                                      • Border handling ndash extend the input
                                                                                                                                                      • Correlation with zero padding
                                                                                                                                                      • Border handling ndash extend the input
                                                                                                                                                      • Template Matching
                                                                                                                                                      • Template Matching
                                                                                                                                                      • Template Matching
                                                                                                                                                      • Template Matching
                                                                                                                                                      • Problematic Correlation
                                                                                                                                                      • Normalised Cross Correlation
                                                                                                                                                      • Length of template
                                                                                                                                                      • Length of image patch
                                                                                                                                                      • Normalised Cross Correlation
                                                                                                                                                      • Normalised Cross Correlation
                                                                                                                                                      • Normalised Cross Correlation
                                                                                                                                                      • Edges
                                                                                                                                                      • Edges
                                                                                                                                                      • Finite Difference
                                                                                                                                                      • Edges
                                                                                                                                                      • Edges in 2D
                                                                                                                                                      • Edge filter kernel
                                                                                                                                                      • Prewitt filter
                                                                                                                                                      • Edge detection
                                                                                                                                                      • Edge filtering
                                                                                                                                                      • 02511 - Niveau af dagens emne forelaeligsing
                                                                                                                                                      • 02512 - Niveau af dagens emne forelaeligsing
                                                                                                                                                      • 02511 - Mit eget udbytte af dagen
                                                                                                                                                      • 02512 - Mit eget udbytte af dagen
                                                                                                                                                      • 02511 - Sidste uges oslashvelser (pixelwise operations)
                                                                                                                                                      • 02512 - Sidste uges oslashvelser (pixelwise operations)
                                                                                                                                                      • Denne uges brug af clickers
                                                                                                                                                      • What can you do after today
                                                                                                                                                      • Oslashvelsesrapport over oslashvelse 4 - 02511
                                                                                                                                                      • Exercises
                                                                                                                                                        A0
                                                                                                                                                        B0
                                                                                                                                                        C5
                                                                                                                                                        D0
                                                                                                                                                        E6
                                                                                                                                                        A
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                                                                                                                                                        E1
                                                                                                                                                        A
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                                                                                                                                                        C
                                                                                                                                                        D
                                                                                                                                                        E
                                                                                                                                                        A2
                                                                                                                                                        B1
                                                                                                                                                        C3
                                                                                                                                                        D2
                                                                                                                                                        E0
                                                                                                                                                        A
                                                                                                                                                        B
                                                                                                                                                        C
                                                                                                                                                        D
                                                                                                                                                        E
                                                                                                                                                        A0
                                                                                                                                                        B0
                                                                                                                                                        C2
                                                                                                                                                        D6
                                                                                                                                                        E0
                                                                                                                                                        A
                                                                                                                                                        B
                                                                                                                                                        C
                                                                                                                                                        D
                                                                                                                                                        E
                                                                                                                                                        A0
                                                                                                                                                        B0
                                                                                                                                                        C1
                                                                                                                                                        D0
                                                                                                                                                        E0
                                                                                                                                                        A
                                                                                                                                                        B
                                                                                                                                                        C
                                                                                                                                                        D
                                                                                                                                                        E
                                                                                                                                                        A2
                                                                                                                                                        B3
                                                                                                                                                        C6
                                                                                                                                                        D1
                                                                                                                                                        E0
                                                                                                                                                        A
                                                                                                                                                        B
                                                                                                                                                        C
                                                                                                                                                        D
                                                                                                                                                        E
                                                                                                                                                        A0
                                                                                                                                                        B8
                                                                                                                                                        C1
                                                                                                                                                        D1
                                                                                                                                                        E0
                                                                                                                                                        A
                                                                                                                                                        B
                                                                                                                                                        C
                                                                                                                                                        D
                                                                                                                                                        E
                                                                                                                                                        A1
                                                                                                                                                        B2
                                                                                                                                                        C2
                                                                                                                                                        D3
                                                                                                                                                        E2

                                                                                                                                                        DTU Compute

                                                                                                                                                        2122018Introduction to Medical Image Analysis66 DTU Compute Technical University of Denmark

                                                                                                                                                        Edges An edge is where there is a

                                                                                                                                                        high change in gray level values

                                                                                                                                                        Objects are often separated from the background by edgesGray level profile

                                                                                                                                                        DTU Compute

                                                                                                                                                        2122018Introduction to Medical Image Analysis67 DTU Compute Technical University of Denmark

                                                                                                                                                        Edges The profile as a function f(d) What value is high when there

                                                                                                                                                        is an edgendash The slope of fndash The slope of the tangent at d

                                                                                                                                                        f(d)

                                                                                                                                                        119891119891prime(119889119889)

                                                                                                                                                        DTU Compute

                                                                                                                                                        2122018Introduction to Medical Image Analysis68 DTU Compute Technical University of Denmark

                                                                                                                                                        Finite Difference Definition of slope

                                                                                                                                                        Approximation

                                                                                                                                                        Simpler approximationh = 1

                                                                                                                                                        119891119891prime 119889119889 = limℎrarr0

                                                                                                                                                        119891119891 119889119889 + ℎ minus 119891119891(119889119889)ℎ

                                                                                                                                                        119891119891prime 119889119889 asymp119891119891 119889119889 + ℎ minus 119891119891(119889119889)

                                                                                                                                                        ℎ

                                                                                                                                                        119891119891prime 119889119889 asymp 119891119891 119889119889 + 1 minus 119891119891(119889119889)

                                                                                                                                                        DTU Compute

                                                                                                                                                        2122018Introduction to Medical Image Analysis69 DTU Compute Technical University of Denmark

                                                                                                                                                        Edges Discrete approximation of frsquo(d) Can be implemented as a filter

                                                                                                                                                        -1 0 1

                                                                                                                                                        f(d-2) f(d-1) f(d) f(d+1) f(d+2) f(d+3)

                                                                                                                                                        f(d)

                                                                                                                                                        119891119891prime 119889119889 asymp 119891119891 119889119889 + 1 minus 119891119891(119889119889)

                                                                                                                                                        DTU Compute

                                                                                                                                                        2122018Introduction to Medical Image Analysis70 DTU Compute Technical University of Denmark

                                                                                                                                                        Edges in 2D Changes in gray level values

                                                                                                                                                        ndash Image gradientndash Gradient is the 2D derivative of a 2D function f(xy)ndash Equal to the slope of the imagendash A steep slope is equal to an edge

                                                                                                                                                        120571120571119891119891 119909119909119910119910 = 119866(119892119892119909119909119892119892119910119910)

                                                                                                                                                        DTU Compute

                                                                                                                                                        2122018Introduction to Medical Image Analysis71 DTU Compute Technical University of Denmark

                                                                                                                                                        Edge filter kernel The Prewitt filter is a typical

                                                                                                                                                        edge filter Output image has high

                                                                                                                                                        values where there are edges

                                                                                                                                                        -1 0 1

                                                                                                                                                        -1 0 1

                                                                                                                                                        -1 0 1Vertical Prewitt filter

                                                                                                                                                        DTU Compute

                                                                                                                                                        2122018Introduction to Medical Image Analysis72 DTU Compute Technical University of Denmark

                                                                                                                                                        Prewitt filter

                                                                                                                                                        Original Prewitt Prewitt

                                                                                                                                                        Hot colormapSmooth 15x15

                                                                                                                                                        Smooth 15x15

                                                                                                                                                        Prewitt

                                                                                                                                                        DTU Compute

                                                                                                                                                        2122018Introduction to Medical Image Analysis73 DTU Compute Technical University of Denmark

                                                                                                                                                        Edge detection Edge filter

                                                                                                                                                        ndash Prewitt for example Thresholding

                                                                                                                                                        ndash Separate edges from non-edges

                                                                                                                                                        Output is binary imagendash Edges are white

                                                                                                                                                        DTU Compute

                                                                                                                                                        2122018Introduction to Medical Image Analysis74 DTU Compute Technical University of Denmark

                                                                                                                                                        Edge filtering

                                                                                                                                                        A) MeanB) Horizontal SobelC) Vertical PrewittD) Horisontal PrewittE) Median

                                                                                                                                                        Der udfoslashres en filtrering (correlation) med et filter paring billedet Der bruges ikke coefficient normalization Den filtrerede vaeligrdi i den markerede pixel bliver -119 Hvilket et 3x3 filter blev benyttet

                                                                                                                                                        0

                                                                                                                                                        8

                                                                                                                                                        1 10

                                                                                                                                                        A B C D E

                                                                                                                                                        Chart1

                                                                                                                                                        0
                                                                                                                                                        8
                                                                                                                                                        1
                                                                                                                                                        1
                                                                                                                                                        0

                                                                                                                                                        Sheet1

                                                                                                                                                        DTU Compute

                                                                                                                                                        2122018Introduction to Medical Image Analysis76 DTU Compute Technical University of Denmark

                                                                                                                                                        02511 - Niveau af dagens emne forelaeligsingA) Meget letB) LetC) PassendeD) SvaeligrtE) Meget svaeligrt

                                                                                                                                                        23

                                                                                                                                                        6

                                                                                                                                                        10

                                                                                                                                                        A B C D E

                                                                                                                                                        Chart1

                                                                                                                                                        2
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                                                                                                                                                        6
                                                                                                                                                        1
                                                                                                                                                        0

                                                                                                                                                        Sheet1

                                                                                                                                                        DTU Compute

                                                                                                                                                        2122018Introduction to Medical Image Analysis77 DTU Compute Technical University of Denmark

                                                                                                                                                        02512 - Niveau af dagens emne forelaeligsingA) Meget letB) LetC) PassendeD) SvaeligrtE) Meget svaeligrt

                                                                                                                                                        0 0

                                                                                                                                                        1

                                                                                                                                                        0 0

                                                                                                                                                        A B C D E

                                                                                                                                                        Chart1

                                                                                                                                                        0
                                                                                                                                                        0
                                                                                                                                                        1
                                                                                                                                                        0
                                                                                                                                                        0

                                                                                                                                                        Sheet1

                                                                                                                                                        DTU Compute

                                                                                                                                                        2122018Introduction to Medical Image Analysis78 DTU Compute Technical University of Denmark

                                                                                                                                                        02511 - Mit eget udbytte af dagenA) Jeg har laeligrt meget lidtB) Lidt laeligringC) PassendeD) God laeligringE) Jeg har laeligrt meget

                                                                                                                                                        0 0

                                                                                                                                                        2

                                                                                                                                                        6

                                                                                                                                                        0

                                                                                                                                                        A B C D E

                                                                                                                                                        Chart1

                                                                                                                                                        0
                                                                                                                                                        0
                                                                                                                                                        2
                                                                                                                                                        6
                                                                                                                                                        0

                                                                                                                                                        Sheet1

                                                                                                                                                        DTU Compute

                                                                                                                                                        2122018Introduction to Medical Image Analysis79 DTU Compute Technical University of Denmark

                                                                                                                                                        02512 - Mit eget udbytte af dagenA) Jeg har laeligrt meget lidtB) Lidt laeligringC) PassendeD) God laeligringE) Jeg har laeligrt meget

                                                                                                                                                        2

                                                                                                                                                        1

                                                                                                                                                        3

                                                                                                                                                        2

                                                                                                                                                        0

                                                                                                                                                        A B C D E

                                                                                                                                                        Chart1

                                                                                                                                                        2
                                                                                                                                                        1
                                                                                                                                                        3
                                                                                                                                                        2
                                                                                                                                                        0

                                                                                                                                                        Sheet1

                                                                                                                                                        DTU Compute

                                                                                                                                                        2122018Introduction to Medical Image Analysis80 DTU Compute Technical University of Denmark

                                                                                                                                                        02511 - Sidste uges oslashvelser (pixelwiseoperations)A) Meget letteB) LetteC) PassendeD) SvaeligreE) Meget svaeligre

                                                                                                                                                        0 0

                                                                                                                                                        1

                                                                                                                                                        4

                                                                                                                                                        1

                                                                                                                                                        A B C D E

                                                                                                                                                        Chart1

                                                                                                                                                        0
                                                                                                                                                        0
                                                                                                                                                        1
                                                                                                                                                        4
                                                                                                                                                        1

                                                                                                                                                        Sheet1

                                                                                                                                                        DTU Compute

                                                                                                                                                        2122018Introduction to Medical Image Analysis81 DTU Compute Technical University of Denmark

                                                                                                                                                        02512 - Sidste uges oslashvelser (pixelwiseoperations)A) Meget letteB) LetteC) PassendeD) SvaeligreE) Meget svaeligre

                                                                                                                                                        3

                                                                                                                                                        0

                                                                                                                                                        3

                                                                                                                                                        0 0

                                                                                                                                                        A B C D E

                                                                                                                                                        Chart1

                                                                                                                                                        3
                                                                                                                                                        0
                                                                                                                                                        3
                                                                                                                                                        0
                                                                                                                                                        0

                                                                                                                                                        Sheet1

                                                                                                                                                        DTU Compute

                                                                                                                                                        2122018Introduction to Medical Image Analysis82 DTU Compute Technical University of Denmark

                                                                                                                                                        Denne uges brug af clickersA) click click click ndash jeg bliver

                                                                                                                                                        sindssygB) For meget clickC) PassendeD) Jeg vil gerne have lidt mereE) Jeg kan ikrsquo faring nok

                                                                                                                                                        0 0

                                                                                                                                                        5

                                                                                                                                                        0

                                                                                                                                                        6

                                                                                                                                                        A B C D E

                                                                                                                                                        Chart1

                                                                                                                                                        0
                                                                                                                                                        0
                                                                                                                                                        5
                                                                                                                                                        0
                                                                                                                                                        6

                                                                                                                                                        Sheet1

                                                                                                                                                        DTU Compute

                                                                                                                                                        2122018Introduction to Medical Image Analysis83 DTU Compute Technical University of Denmark

                                                                                                                                                        What can you do after today Describe the difference between point processing and neighbourhood

                                                                                                                                                        processing Compute a rank filtered image using the min max median and

                                                                                                                                                        difference rank filters Compute a mean filtered image Decide if median or average filtering should be used for noise removal Choose the appropriate image border handling based on a given input

                                                                                                                                                        image Implement and apply template matching Compute the normalised cross correlation and explain why it should be

                                                                                                                                                        used Apply given image filter kernels to images Use edge filters on images Describe finite difference approximation of image gradients Describe the concept of edge detection

                                                                                                                                                        DTU Compute

                                                                                                                                                        2122018Introduction to Medical Image Analysis84 DTU Compute Technical University of Denmark

                                                                                                                                                        Oslashvelsesrapport over oslashvelse 4 - 02511 Oslashvelser taeligller cirka 30 af karakteren Skal afleveres senest den 7 marts kl 2359 Kan afleveres af 1 eller 2 personer

                                                                                                                                                        ndash I skal skrive jeres egen oslashvelsesrapportndash Brug mindst et af jeres egne billeder

                                                                                                                                                        Afleveres som PDF Lad vaeligre med at kopiere opgaveteksten ind i jeres

                                                                                                                                                        opgave Put Matlab kode i et Appendix og henvis fra teksten Eksempel rapport over oslashvelse findes paring

                                                                                                                                                        hjemmesiden under eksamen

                                                                                                                                                        DTU Compute

                                                                                                                                                        2122018Introduction to Medical Image Analysis85 DTU Compute Technical University of Denmark

                                                                                                                                                        Exercises

                                                                                                                                                        • Introduction to Medical Image Analysis
                                                                                                                                                        • Lecture 4 ndash Neighbourhood Processing
                                                                                                                                                        • What can you do after today
                                                                                                                                                        • Point processing
                                                                                                                                                        • Point processing
                                                                                                                                                        • Neighbourhood processing
                                                                                                                                                        • Use of filtering
                                                                                                                                                        • Salt and pepper noise
                                                                                                                                                        • Salt and pepper noise
                                                                                                                                                        • What is so special about noise
                                                                                                                                                        • Noise ndash go away
                                                                                                                                                        • What is the median Value
                                                                                                                                                        • The median value
                                                                                                                                                        • Noise away ndash the median filter
                                                                                                                                                        • Noise removal ndash average filter
                                                                                                                                                        • Noise removal ndash median filter
                                                                                                                                                        • Image Filtering
                                                                                                                                                        • Median filter
                                                                                                                                                        • Rank filters
                                                                                                                                                        • Median filter
                                                                                                                                                        • Correlation
                                                                                                                                                        • Why do we need similarity
                                                                                                                                                        • Correlation (1D)
                                                                                                                                                        • Correlation (1D)
                                                                                                                                                        • Normalisation
                                                                                                                                                        • Normalisation
                                                                                                                                                        • Correlation on images
                                                                                                                                                        • Correlation on images
                                                                                                                                                        • Correlation on images
                                                                                                                                                        • Draw your filter
                                                                                                                                                        • Correlation on images ndash no normalisation
                                                                                                                                                        • Correlation on images ndash no normalisation 2
                                                                                                                                                        • Mathematics of 2D Correlation
                                                                                                                                                        • Mathematics of 2D Correlation
                                                                                                                                                        • Mathematics of 2D Correlation
                                                                                                                                                        • Slide Number 40
                                                                                                                                                        • 2D Kernel Normalisation
                                                                                                                                                        • Correlation
                                                                                                                                                        • Smoothing filters
                                                                                                                                                        • Use of smoothing
                                                                                                                                                        • Use of smoothing
                                                                                                                                                        • Mean filter
                                                                                                                                                        • Border handling
                                                                                                                                                        • Border handling ndash extend the input
                                                                                                                                                        • Correlation with zero padding
                                                                                                                                                        • Border handling ndash extend the input
                                                                                                                                                        • Template Matching
                                                                                                                                                        • Template Matching
                                                                                                                                                        • Template Matching
                                                                                                                                                        • Template Matching
                                                                                                                                                        • Problematic Correlation
                                                                                                                                                        • Normalised Cross Correlation
                                                                                                                                                        • Length of template
                                                                                                                                                        • Length of image patch
                                                                                                                                                        • Normalised Cross Correlation
                                                                                                                                                        • Normalised Cross Correlation
                                                                                                                                                        • Normalised Cross Correlation
                                                                                                                                                        • Edges
                                                                                                                                                        • Edges
                                                                                                                                                        • Finite Difference
                                                                                                                                                        • Edges
                                                                                                                                                        • Edges in 2D
                                                                                                                                                        • Edge filter kernel
                                                                                                                                                        • Prewitt filter
                                                                                                                                                        • Edge detection
                                                                                                                                                        • Edge filtering
                                                                                                                                                        • 02511 - Niveau af dagens emne forelaeligsing
                                                                                                                                                        • 02512 - Niveau af dagens emne forelaeligsing
                                                                                                                                                        • 02511 - Mit eget udbytte af dagen
                                                                                                                                                        • 02512 - Mit eget udbytte af dagen
                                                                                                                                                        • 02511 - Sidste uges oslashvelser (pixelwise operations)
                                                                                                                                                        • 02512 - Sidste uges oslashvelser (pixelwise operations)
                                                                                                                                                        • Denne uges brug af clickers
                                                                                                                                                        • What can you do after today
                                                                                                                                                        • Oslashvelsesrapport over oslashvelse 4 - 02511
                                                                                                                                                        • Exercises
                                                                                                                                                          A0
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                                                                                                                                                          E0
                                                                                                                                                          A
                                                                                                                                                          B
                                                                                                                                                          C
                                                                                                                                                          D
                                                                                                                                                          E

                                                                                                                                                          DTU Compute

                                                                                                                                                          2122018Introduction to Medical Image Analysis67 DTU Compute Technical University of Denmark

                                                                                                                                                          Edges The profile as a function f(d) What value is high when there

                                                                                                                                                          is an edgendash The slope of fndash The slope of the tangent at d

                                                                                                                                                          f(d)

                                                                                                                                                          119891119891prime(119889119889)

                                                                                                                                                          DTU Compute

                                                                                                                                                          2122018Introduction to Medical Image Analysis68 DTU Compute Technical University of Denmark

                                                                                                                                                          Finite Difference Definition of slope

                                                                                                                                                          Approximation

                                                                                                                                                          Simpler approximationh = 1

                                                                                                                                                          119891119891prime 119889119889 = limℎrarr0

                                                                                                                                                          119891119891 119889119889 + ℎ minus 119891119891(119889119889)ℎ

                                                                                                                                                          119891119891prime 119889119889 asymp119891119891 119889119889 + ℎ minus 119891119891(119889119889)

                                                                                                                                                          ℎ

                                                                                                                                                          119891119891prime 119889119889 asymp 119891119891 119889119889 + 1 minus 119891119891(119889119889)

                                                                                                                                                          DTU Compute

                                                                                                                                                          2122018Introduction to Medical Image Analysis69 DTU Compute Technical University of Denmark

                                                                                                                                                          Edges Discrete approximation of frsquo(d) Can be implemented as a filter

                                                                                                                                                          -1 0 1

                                                                                                                                                          f(d-2) f(d-1) f(d) f(d+1) f(d+2) f(d+3)

                                                                                                                                                          f(d)

                                                                                                                                                          119891119891prime 119889119889 asymp 119891119891 119889119889 + 1 minus 119891119891(119889119889)

                                                                                                                                                          DTU Compute

                                                                                                                                                          2122018Introduction to Medical Image Analysis70 DTU Compute Technical University of Denmark

                                                                                                                                                          Edges in 2D Changes in gray level values

                                                                                                                                                          ndash Image gradientndash Gradient is the 2D derivative of a 2D function f(xy)ndash Equal to the slope of the imagendash A steep slope is equal to an edge

                                                                                                                                                          120571120571119891119891 119909119909119910119910 = 119866(119892119892119909119909119892119892119910119910)

                                                                                                                                                          DTU Compute

                                                                                                                                                          2122018Introduction to Medical Image Analysis71 DTU Compute Technical University of Denmark

                                                                                                                                                          Edge filter kernel The Prewitt filter is a typical

                                                                                                                                                          edge filter Output image has high

                                                                                                                                                          values where there are edges

                                                                                                                                                          -1 0 1

                                                                                                                                                          -1 0 1

                                                                                                                                                          -1 0 1Vertical Prewitt filter

                                                                                                                                                          DTU Compute

                                                                                                                                                          2122018Introduction to Medical Image Analysis72 DTU Compute Technical University of Denmark

                                                                                                                                                          Prewitt filter

                                                                                                                                                          Original Prewitt Prewitt

                                                                                                                                                          Hot colormapSmooth 15x15

                                                                                                                                                          Smooth 15x15

                                                                                                                                                          Prewitt

                                                                                                                                                          DTU Compute

                                                                                                                                                          2122018Introduction to Medical Image Analysis73 DTU Compute Technical University of Denmark

                                                                                                                                                          Edge detection Edge filter

                                                                                                                                                          ndash Prewitt for example Thresholding

                                                                                                                                                          ndash Separate edges from non-edges

                                                                                                                                                          Output is binary imagendash Edges are white

                                                                                                                                                          DTU Compute

                                                                                                                                                          2122018Introduction to Medical Image Analysis74 DTU Compute Technical University of Denmark

                                                                                                                                                          Edge filtering

                                                                                                                                                          A) MeanB) Horizontal SobelC) Vertical PrewittD) Horisontal PrewittE) Median

                                                                                                                                                          Der udfoslashres en filtrering (correlation) med et filter paring billedet Der bruges ikke coefficient normalization Den filtrerede vaeligrdi i den markerede pixel bliver -119 Hvilket et 3x3 filter blev benyttet

                                                                                                                                                          0

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                                                                                                                                                          2122018Introduction to Medical Image Analysis76 DTU Compute Technical University of Denmark

                                                                                                                                                          02511 - Niveau af dagens emne forelaeligsingA) Meget letB) LetC) PassendeD) SvaeligrtE) Meget svaeligrt

                                                                                                                                                          23

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                                                                                                                                                          2122018Introduction to Medical Image Analysis77 DTU Compute Technical University of Denmark

                                                                                                                                                          02512 - Niveau af dagens emne forelaeligsingA) Meget letB) LetC) PassendeD) SvaeligrtE) Meget svaeligrt

                                                                                                                                                          0 0

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                                                                                                                                                          2122018Introduction to Medical Image Analysis78 DTU Compute Technical University of Denmark

                                                                                                                                                          02511 - Mit eget udbytte af dagenA) Jeg har laeligrt meget lidtB) Lidt laeligringC) PassendeD) God laeligringE) Jeg har laeligrt meget

                                                                                                                                                          0 0

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                                                                                                                                                          2122018Introduction to Medical Image Analysis79 DTU Compute Technical University of Denmark

                                                                                                                                                          02512 - Mit eget udbytte af dagenA) Jeg har laeligrt meget lidtB) Lidt laeligringC) PassendeD) God laeligringE) Jeg har laeligrt meget

                                                                                                                                                          2

                                                                                                                                                          1

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                                                                                                                                                          2122018Introduction to Medical Image Analysis80 DTU Compute Technical University of Denmark

                                                                                                                                                          02511 - Sidste uges oslashvelser (pixelwiseoperations)A) Meget letteB) LetteC) PassendeD) SvaeligreE) Meget svaeligre

                                                                                                                                                          0 0

                                                                                                                                                          1

                                                                                                                                                          4

                                                                                                                                                          1

                                                                                                                                                          A B C D E

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                                                                                                                                                          2122018Introduction to Medical Image Analysis81 DTU Compute Technical University of Denmark

                                                                                                                                                          02512 - Sidste uges oslashvelser (pixelwiseoperations)A) Meget letteB) LetteC) PassendeD) SvaeligreE) Meget svaeligre

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                                                                                                                                                          2122018Introduction to Medical Image Analysis82 DTU Compute Technical University of Denmark

                                                                                                                                                          Denne uges brug af clickersA) click click click ndash jeg bliver

                                                                                                                                                          sindssygB) For meget clickC) PassendeD) Jeg vil gerne have lidt mereE) Jeg kan ikrsquo faring nok

                                                                                                                                                          0 0

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                                                                                                                                                          DTU Compute

                                                                                                                                                          2122018Introduction to Medical Image Analysis83 DTU Compute Technical University of Denmark

                                                                                                                                                          What can you do after today Describe the difference between point processing and neighbourhood

                                                                                                                                                          processing Compute a rank filtered image using the min max median and

                                                                                                                                                          difference rank filters Compute a mean filtered image Decide if median or average filtering should be used for noise removal Choose the appropriate image border handling based on a given input

                                                                                                                                                          image Implement and apply template matching Compute the normalised cross correlation and explain why it should be

                                                                                                                                                          used Apply given image filter kernels to images Use edge filters on images Describe finite difference approximation of image gradients Describe the concept of edge detection

                                                                                                                                                          DTU Compute

                                                                                                                                                          2122018Introduction to Medical Image Analysis84 DTU Compute Technical University of Denmark

                                                                                                                                                          Oslashvelsesrapport over oslashvelse 4 - 02511 Oslashvelser taeligller cirka 30 af karakteren Skal afleveres senest den 7 marts kl 2359 Kan afleveres af 1 eller 2 personer

                                                                                                                                                          ndash I skal skrive jeres egen oslashvelsesrapportndash Brug mindst et af jeres egne billeder

                                                                                                                                                          Afleveres som PDF Lad vaeligre med at kopiere opgaveteksten ind i jeres

                                                                                                                                                          opgave Put Matlab kode i et Appendix og henvis fra teksten Eksempel rapport over oslashvelse findes paring

                                                                                                                                                          hjemmesiden under eksamen

                                                                                                                                                          DTU Compute

                                                                                                                                                          2122018Introduction to Medical Image Analysis85 DTU Compute Technical University of Denmark

                                                                                                                                                          Exercises

                                                                                                                                                          • Introduction to Medical Image Analysis
                                                                                                                                                          • Lecture 4 ndash Neighbourhood Processing
                                                                                                                                                          • What can you do after today
                                                                                                                                                          • Point processing
                                                                                                                                                          • Point processing
                                                                                                                                                          • Neighbourhood processing
                                                                                                                                                          • Use of filtering
                                                                                                                                                          • Salt and pepper noise
                                                                                                                                                          • Salt and pepper noise
                                                                                                                                                          • What is so special about noise
                                                                                                                                                          • Noise ndash go away
                                                                                                                                                          • What is the median Value
                                                                                                                                                          • The median value
                                                                                                                                                          • Noise away ndash the median filter
                                                                                                                                                          • Noise removal ndash average filter
                                                                                                                                                          • Noise removal ndash median filter
                                                                                                                                                          • Image Filtering
                                                                                                                                                          • Median filter
                                                                                                                                                          • Rank filters
                                                                                                                                                          • Median filter
                                                                                                                                                          • Correlation
                                                                                                                                                          • Why do we need similarity
                                                                                                                                                          • Correlation (1D)
                                                                                                                                                          • Correlation (1D)
                                                                                                                                                          • Normalisation
                                                                                                                                                          • Normalisation
                                                                                                                                                          • Correlation on images
                                                                                                                                                          • Correlation on images
                                                                                                                                                          • Correlation on images
                                                                                                                                                          • Draw your filter
                                                                                                                                                          • Correlation on images ndash no normalisation
                                                                                                                                                          • Correlation on images ndash no normalisation 2
                                                                                                                                                          • Mathematics of 2D Correlation
                                                                                                                                                          • Mathematics of 2D Correlation
                                                                                                                                                          • Mathematics of 2D Correlation
                                                                                                                                                          • Slide Number 40
                                                                                                                                                          • 2D Kernel Normalisation
                                                                                                                                                          • Correlation
                                                                                                                                                          • Smoothing filters
                                                                                                                                                          • Use of smoothing
                                                                                                                                                          • Use of smoothing
                                                                                                                                                          • Mean filter
                                                                                                                                                          • Border handling
                                                                                                                                                          • Border handling ndash extend the input
                                                                                                                                                          • Correlation with zero padding
                                                                                                                                                          • Border handling ndash extend the input
                                                                                                                                                          • Template Matching
                                                                                                                                                          • Template Matching
                                                                                                                                                          • Template Matching
                                                                                                                                                          • Template Matching
                                                                                                                                                          • Problematic Correlation
                                                                                                                                                          • Normalised Cross Correlation
                                                                                                                                                          • Length of template
                                                                                                                                                          • Length of image patch
                                                                                                                                                          • Normalised Cross Correlation
                                                                                                                                                          • Normalised Cross Correlation
                                                                                                                                                          • Normalised Cross Correlation
                                                                                                                                                          • Edges
                                                                                                                                                          • Edges
                                                                                                                                                          • Finite Difference
                                                                                                                                                          • Edges
                                                                                                                                                          • Edges in 2D
                                                                                                                                                          • Edge filter kernel
                                                                                                                                                          • Prewitt filter
                                                                                                                                                          • Edge detection
                                                                                                                                                          • Edge filtering
                                                                                                                                                          • 02511 - Niveau af dagens emne forelaeligsing
                                                                                                                                                          • 02512 - Niveau af dagens emne forelaeligsing
                                                                                                                                                          • 02511 - Mit eget udbytte af dagen
                                                                                                                                                          • 02512 - Mit eget udbytte af dagen
                                                                                                                                                          • 02511 - Sidste uges oslashvelser (pixelwise operations)
                                                                                                                                                          • 02512 - Sidste uges oslashvelser (pixelwise operations)
                                                                                                                                                          • Denne uges brug af clickers
                                                                                                                                                          • What can you do after today
                                                                                                                                                          • Oslashvelsesrapport over oslashvelse 4 - 02511
                                                                                                                                                          • Exercises
                                                                                                                                                            A0
                                                                                                                                                            B0
                                                                                                                                                            C5
                                                                                                                                                            D0
                                                                                                                                                            E6
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                                                                                                                                                            E0
                                                                                                                                                            A
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                                                                                                                                                            D6
                                                                                                                                                            E0
                                                                                                                                                            A
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                                                                                                                                                            A0
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                                                                                                                                                            D0
                                                                                                                                                            E0
                                                                                                                                                            A
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                                                                                                                                                            E
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                                                                                                                                                            D1
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                                                                                                                                                            A
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                                                                                                                                                            B8
                                                                                                                                                            C1
                                                                                                                                                            D1
                                                                                                                                                            E0
                                                                                                                                                            A
                                                                                                                                                            B
                                                                                                                                                            C
                                                                                                                                                            D
                                                                                                                                                            E

                                                                                                                                                            DTU Compute

                                                                                                                                                            2122018Introduction to Medical Image Analysis68 DTU Compute Technical University of Denmark

                                                                                                                                                            Finite Difference Definition of slope

                                                                                                                                                            Approximation

                                                                                                                                                            Simpler approximationh = 1

                                                                                                                                                            119891119891prime 119889119889 = limℎrarr0

                                                                                                                                                            119891119891 119889119889 + ℎ minus 119891119891(119889119889)ℎ

                                                                                                                                                            119891119891prime 119889119889 asymp119891119891 119889119889 + ℎ minus 119891119891(119889119889)

                                                                                                                                                            ℎ

                                                                                                                                                            119891119891prime 119889119889 asymp 119891119891 119889119889 + 1 minus 119891119891(119889119889)

                                                                                                                                                            DTU Compute

                                                                                                                                                            2122018Introduction to Medical Image Analysis69 DTU Compute Technical University of Denmark

                                                                                                                                                            Edges Discrete approximation of frsquo(d) Can be implemented as a filter

                                                                                                                                                            -1 0 1

                                                                                                                                                            f(d-2) f(d-1) f(d) f(d+1) f(d+2) f(d+3)

                                                                                                                                                            f(d)

                                                                                                                                                            119891119891prime 119889119889 asymp 119891119891 119889119889 + 1 minus 119891119891(119889119889)

                                                                                                                                                            DTU Compute

                                                                                                                                                            2122018Introduction to Medical Image Analysis70 DTU Compute Technical University of Denmark

                                                                                                                                                            Edges in 2D Changes in gray level values

                                                                                                                                                            ndash Image gradientndash Gradient is the 2D derivative of a 2D function f(xy)ndash Equal to the slope of the imagendash A steep slope is equal to an edge

                                                                                                                                                            120571120571119891119891 119909119909119910119910 = 119866(119892119892119909119909119892119892119910119910)

                                                                                                                                                            DTU Compute

                                                                                                                                                            2122018Introduction to Medical Image Analysis71 DTU Compute Technical University of Denmark

                                                                                                                                                            Edge filter kernel The Prewitt filter is a typical

                                                                                                                                                            edge filter Output image has high

                                                                                                                                                            values where there are edges

                                                                                                                                                            -1 0 1

                                                                                                                                                            -1 0 1

                                                                                                                                                            -1 0 1Vertical Prewitt filter

                                                                                                                                                            DTU Compute

                                                                                                                                                            2122018Introduction to Medical Image Analysis72 DTU Compute Technical University of Denmark

                                                                                                                                                            Prewitt filter

                                                                                                                                                            Original Prewitt Prewitt

                                                                                                                                                            Hot colormapSmooth 15x15

                                                                                                                                                            Smooth 15x15

                                                                                                                                                            Prewitt

                                                                                                                                                            DTU Compute

                                                                                                                                                            2122018Introduction to Medical Image Analysis73 DTU Compute Technical University of Denmark

                                                                                                                                                            Edge detection Edge filter

                                                                                                                                                            ndash Prewitt for example Thresholding

                                                                                                                                                            ndash Separate edges from non-edges

                                                                                                                                                            Output is binary imagendash Edges are white

                                                                                                                                                            DTU Compute

                                                                                                                                                            2122018Introduction to Medical Image Analysis74 DTU Compute Technical University of Denmark

                                                                                                                                                            Edge filtering

                                                                                                                                                            A) MeanB) Horizontal SobelC) Vertical PrewittD) Horisontal PrewittE) Median

                                                                                                                                                            Der udfoslashres en filtrering (correlation) med et filter paring billedet Der bruges ikke coefficient normalization Den filtrerede vaeligrdi i den markerede pixel bliver -119 Hvilket et 3x3 filter blev benyttet

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                                                                                                                                                            2122018Introduction to Medical Image Analysis76 DTU Compute Technical University of Denmark

                                                                                                                                                            02511 - Niveau af dagens emne forelaeligsingA) Meget letB) LetC) PassendeD) SvaeligrtE) Meget svaeligrt

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                                                                                                                                                            2122018Introduction to Medical Image Analysis77 DTU Compute Technical University of Denmark

                                                                                                                                                            02512 - Niveau af dagens emne forelaeligsingA) Meget letB) LetC) PassendeD) SvaeligrtE) Meget svaeligrt

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                                                                                                                                                            02511 - Mit eget udbytte af dagenA) Jeg har laeligrt meget lidtB) Lidt laeligringC) PassendeD) God laeligringE) Jeg har laeligrt meget

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                                                                                                                                                            02512 - Mit eget udbytte af dagenA) Jeg har laeligrt meget lidtB) Lidt laeligringC) PassendeD) God laeligringE) Jeg har laeligrt meget

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                                                                                                                                                            02511 - Sidste uges oslashvelser (pixelwiseoperations)A) Meget letteB) LetteC) PassendeD) SvaeligreE) Meget svaeligre

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                                                                                                                                                            2122018Introduction to Medical Image Analysis82 DTU Compute Technical University of Denmark

                                                                                                                                                            Denne uges brug af clickersA) click click click ndash jeg bliver

                                                                                                                                                            sindssygB) For meget clickC) PassendeD) Jeg vil gerne have lidt mereE) Jeg kan ikrsquo faring nok

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                                                                                                                                                            2122018Introduction to Medical Image Analysis83 DTU Compute Technical University of Denmark

                                                                                                                                                            What can you do after today Describe the difference between point processing and neighbourhood

                                                                                                                                                            processing Compute a rank filtered image using the min max median and

                                                                                                                                                            difference rank filters Compute a mean filtered image Decide if median or average filtering should be used for noise removal Choose the appropriate image border handling based on a given input

                                                                                                                                                            image Implement and apply template matching Compute the normalised cross correlation and explain why it should be

                                                                                                                                                            used Apply given image filter kernels to images Use edge filters on images Describe finite difference approximation of image gradients Describe the concept of edge detection

                                                                                                                                                            DTU Compute

                                                                                                                                                            2122018Introduction to Medical Image Analysis84 DTU Compute Technical University of Denmark

                                                                                                                                                            Oslashvelsesrapport over oslashvelse 4 - 02511 Oslashvelser taeligller cirka 30 af karakteren Skal afleveres senest den 7 marts kl 2359 Kan afleveres af 1 eller 2 personer

                                                                                                                                                            ndash I skal skrive jeres egen oslashvelsesrapportndash Brug mindst et af jeres egne billeder

                                                                                                                                                            Afleveres som PDF Lad vaeligre med at kopiere opgaveteksten ind i jeres

                                                                                                                                                            opgave Put Matlab kode i et Appendix og henvis fra teksten Eksempel rapport over oslashvelse findes paring

                                                                                                                                                            hjemmesiden under eksamen

                                                                                                                                                            DTU Compute

                                                                                                                                                            2122018Introduction to Medical Image Analysis85 DTU Compute Technical University of Denmark

                                                                                                                                                            Exercises

                                                                                                                                                            • Introduction to Medical Image Analysis
                                                                                                                                                            • Lecture 4 ndash Neighbourhood Processing
                                                                                                                                                            • What can you do after today
                                                                                                                                                            • Point processing
                                                                                                                                                            • Point processing
                                                                                                                                                            • Neighbourhood processing
                                                                                                                                                            • Use of filtering
                                                                                                                                                            • Salt and pepper noise
                                                                                                                                                            • Salt and pepper noise
                                                                                                                                                            • What is so special about noise
                                                                                                                                                            • Noise ndash go away
                                                                                                                                                            • What is the median Value
                                                                                                                                                            • The median value
                                                                                                                                                            • Noise away ndash the median filter
                                                                                                                                                            • Noise removal ndash average filter
                                                                                                                                                            • Noise removal ndash median filter
                                                                                                                                                            • Image Filtering
                                                                                                                                                            • Median filter
                                                                                                                                                            • Rank filters
                                                                                                                                                            • Median filter
                                                                                                                                                            • Correlation
                                                                                                                                                            • Why do we need similarity
                                                                                                                                                            • Correlation (1D)
                                                                                                                                                            • Correlation (1D)
                                                                                                                                                            • Normalisation
                                                                                                                                                            • Normalisation
                                                                                                                                                            • Correlation on images
                                                                                                                                                            • Correlation on images
                                                                                                                                                            • Correlation on images
                                                                                                                                                            • Draw your filter
                                                                                                                                                            • Correlation on images ndash no normalisation
                                                                                                                                                            • Correlation on images ndash no normalisation 2
                                                                                                                                                            • Mathematics of 2D Correlation
                                                                                                                                                            • Mathematics of 2D Correlation
                                                                                                                                                            • Mathematics of 2D Correlation
                                                                                                                                                            • Slide Number 40
                                                                                                                                                            • 2D Kernel Normalisation
                                                                                                                                                            • Correlation
                                                                                                                                                            • Smoothing filters
                                                                                                                                                            • Use of smoothing
                                                                                                                                                            • Use of smoothing
                                                                                                                                                            • Mean filter
                                                                                                                                                            • Border handling
                                                                                                                                                            • Border handling ndash extend the input
                                                                                                                                                            • Correlation with zero padding
                                                                                                                                                            • Border handling ndash extend the input
                                                                                                                                                            • Template Matching
                                                                                                                                                            • Template Matching
                                                                                                                                                            • Template Matching
                                                                                                                                                            • Template Matching
                                                                                                                                                            • Problematic Correlation
                                                                                                                                                            • Normalised Cross Correlation
                                                                                                                                                            • Length of template
                                                                                                                                                            • Length of image patch
                                                                                                                                                            • Normalised Cross Correlation
                                                                                                                                                            • Normalised Cross Correlation
                                                                                                                                                            • Normalised Cross Correlation
                                                                                                                                                            • Edges
                                                                                                                                                            • Edges
                                                                                                                                                            • Finite Difference
                                                                                                                                                            • Edges
                                                                                                                                                            • Edges in 2D
                                                                                                                                                            • Edge filter kernel
                                                                                                                                                            • Prewitt filter
                                                                                                                                                            • Edge detection
                                                                                                                                                            • Edge filtering
                                                                                                                                                            • 02511 - Niveau af dagens emne forelaeligsing
                                                                                                                                                            • 02512 - Niveau af dagens emne forelaeligsing
                                                                                                                                                            • 02511 - Mit eget udbytte af dagen
                                                                                                                                                            • 02512 - Mit eget udbytte af dagen
                                                                                                                                                            • 02511 - Sidste uges oslashvelser (pixelwise operations)
                                                                                                                                                            • 02512 - Sidste uges oslashvelser (pixelwise operations)
                                                                                                                                                            • Denne uges brug af clickers
                                                                                                                                                            • What can you do after today
                                                                                                                                                            • Oslashvelsesrapport over oslashvelse 4 - 02511
                                                                                                                                                            • Exercises
                                                                                                                                                              A0
                                                                                                                                                              B0
                                                                                                                                                              C5
                                                                                                                                                              D0
                                                                                                                                                              E6
                                                                                                                                                              A
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                                                                                                                                                              C
                                                                                                                                                              D
                                                                                                                                                              E
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                                                                                                                                                              B0
                                                                                                                                                              C3
                                                                                                                                                              D0
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                                                                                                                                                              A
                                                                                                                                                              B
                                                                                                                                                              C
                                                                                                                                                              D
                                                                                                                                                              E
                                                                                                                                                              A0
                                                                                                                                                              B0
                                                                                                                                                              C1
                                                                                                                                                              D4
                                                                                                                                                              E1
                                                                                                                                                              A
                                                                                                                                                              B
                                                                                                                                                              C
                                                                                                                                                              D
                                                                                                                                                              E
                                                                                                                                                              A2
                                                                                                                                                              B1
                                                                                                                                                              C3
                                                                                                                                                              D2
                                                                                                                                                              E0
                                                                                                                                                              A
                                                                                                                                                              B
                                                                                                                                                              C
                                                                                                                                                              D
                                                                                                                                                              E
                                                                                                                                                              A0
                                                                                                                                                              B0
                                                                                                                                                              C2
                                                                                                                                                              D6
                                                                                                                                                              E0
                                                                                                                                                              A
                                                                                                                                                              B
                                                                                                                                                              C
                                                                                                                                                              D
                                                                                                                                                              E
                                                                                                                                                              A0
                                                                                                                                                              B0
                                                                                                                                                              C1
                                                                                                                                                              D0
                                                                                                                                                              E0
                                                                                                                                                              A
                                                                                                                                                              B
                                                                                                                                                              C
                                                                                                                                                              D
                                                                                                                                                              E
                                                                                                                                                              A2
                                                                                                                                                              B3
                                                                                                                                                              C6
                                                                                                                                                              D1
                                                                                                                                                              E0
                                                                                                                                                              A
                                                                                                                                                              B
                                                                                                                                                              C
                                                                                                                                                              D
                                                                                                                                                              E
                                                                                                                                                              A0
                                                                                                                                                              B8
                                                                                                                                                              C1
                                                                                                                                                              D1
                                                                                                                                                              E0
                                                                                                                                                              A
                                                                                                                                                              B
                                                                                                                                                              C
                                                                                                                                                              D
                                                                                                                                                              E

                                                                                                                                                              DTU Compute

                                                                                                                                                              2122018Introduction to Medical Image Analysis69 DTU Compute Technical University of Denmark

                                                                                                                                                              Edges Discrete approximation of frsquo(d) Can be implemented as a filter

                                                                                                                                                              -1 0 1

                                                                                                                                                              f(d-2) f(d-1) f(d) f(d+1) f(d+2) f(d+3)

                                                                                                                                                              f(d)

                                                                                                                                                              119891119891prime 119889119889 asymp 119891119891 119889119889 + 1 minus 119891119891(119889119889)

                                                                                                                                                              DTU Compute

                                                                                                                                                              2122018Introduction to Medical Image Analysis70 DTU Compute Technical University of Denmark

                                                                                                                                                              Edges in 2D Changes in gray level values

                                                                                                                                                              ndash Image gradientndash Gradient is the 2D derivative of a 2D function f(xy)ndash Equal to the slope of the imagendash A steep slope is equal to an edge

                                                                                                                                                              120571120571119891119891 119909119909119910119910 = 119866(119892119892119909119909119892119892119910119910)

                                                                                                                                                              DTU Compute

                                                                                                                                                              2122018Introduction to Medical Image Analysis71 DTU Compute Technical University of Denmark

                                                                                                                                                              Edge filter kernel The Prewitt filter is a typical

                                                                                                                                                              edge filter Output image has high

                                                                                                                                                              values where there are edges

                                                                                                                                                              -1 0 1

                                                                                                                                                              -1 0 1

                                                                                                                                                              -1 0 1Vertical Prewitt filter

                                                                                                                                                              DTU Compute

                                                                                                                                                              2122018Introduction to Medical Image Analysis72 DTU Compute Technical University of Denmark

                                                                                                                                                              Prewitt filter

                                                                                                                                                              Original Prewitt Prewitt

                                                                                                                                                              Hot colormapSmooth 15x15

                                                                                                                                                              Smooth 15x15

                                                                                                                                                              Prewitt

                                                                                                                                                              DTU Compute

                                                                                                                                                              2122018Introduction to Medical Image Analysis73 DTU Compute Technical University of Denmark

                                                                                                                                                              Edge detection Edge filter

                                                                                                                                                              ndash Prewitt for example Thresholding

                                                                                                                                                              ndash Separate edges from non-edges

                                                                                                                                                              Output is binary imagendash Edges are white

                                                                                                                                                              DTU Compute

                                                                                                                                                              2122018Introduction to Medical Image Analysis74 DTU Compute Technical University of Denmark

                                                                                                                                                              Edge filtering

                                                                                                                                                              A) MeanB) Horizontal SobelC) Vertical PrewittD) Horisontal PrewittE) Median

                                                                                                                                                              Der udfoslashres en filtrering (correlation) med et filter paring billedet Der bruges ikke coefficient normalization Den filtrerede vaeligrdi i den markerede pixel bliver -119 Hvilket et 3x3 filter blev benyttet

                                                                                                                                                              0

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                                                                                                                                                              1 10

                                                                                                                                                              A B C D E

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                                                                                                                                                              2122018Introduction to Medical Image Analysis76 DTU Compute Technical University of Denmark

                                                                                                                                                              02511 - Niveau af dagens emne forelaeligsingA) Meget letB) LetC) PassendeD) SvaeligrtE) Meget svaeligrt

                                                                                                                                                              23

                                                                                                                                                              6

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                                                                                                                                                              A B C D E

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                                                                                                                                                              02512 - Niveau af dagens emne forelaeligsingA) Meget letB) LetC) PassendeD) SvaeligrtE) Meget svaeligrt

                                                                                                                                                              0 0

                                                                                                                                                              1

                                                                                                                                                              0 0

                                                                                                                                                              A B C D E

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                                                                                                                                                              2122018Introduction to Medical Image Analysis78 DTU Compute Technical University of Denmark

                                                                                                                                                              02511 - Mit eget udbytte af dagenA) Jeg har laeligrt meget lidtB) Lidt laeligringC) PassendeD) God laeligringE) Jeg har laeligrt meget

                                                                                                                                                              0 0

                                                                                                                                                              2

                                                                                                                                                              6

                                                                                                                                                              0

                                                                                                                                                              A B C D E

                                                                                                                                                              Chart1

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                                                                                                                                                              6
                                                                                                                                                              0

                                                                                                                                                              Sheet1

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                                                                                                                                                              2122018Introduction to Medical Image Analysis79 DTU Compute Technical University of Denmark

                                                                                                                                                              02512 - Mit eget udbytte af dagenA) Jeg har laeligrt meget lidtB) Lidt laeligringC) PassendeD) God laeligringE) Jeg har laeligrt meget

                                                                                                                                                              2

                                                                                                                                                              1

                                                                                                                                                              3

                                                                                                                                                              2

                                                                                                                                                              0

                                                                                                                                                              A B C D E

                                                                                                                                                              Chart1

                                                                                                                                                              2
                                                                                                                                                              1
                                                                                                                                                              3
                                                                                                                                                              2
                                                                                                                                                              0

                                                                                                                                                              Sheet1

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                                                                                                                                                              2122018Introduction to Medical Image Analysis80 DTU Compute Technical University of Denmark

                                                                                                                                                              02511 - Sidste uges oslashvelser (pixelwiseoperations)A) Meget letteB) LetteC) PassendeD) SvaeligreE) Meget svaeligre

                                                                                                                                                              0 0

                                                                                                                                                              1

                                                                                                                                                              4

                                                                                                                                                              1

                                                                                                                                                              A B C D E

                                                                                                                                                              Chart1

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                                                                                                                                                              4
                                                                                                                                                              1

                                                                                                                                                              Sheet1

                                                                                                                                                              DTU Compute

                                                                                                                                                              2122018Introduction to Medical Image Analysis81 DTU Compute Technical University of Denmark

                                                                                                                                                              02512 - Sidste uges oslashvelser (pixelwiseoperations)A) Meget letteB) LetteC) PassendeD) SvaeligreE) Meget svaeligre

                                                                                                                                                              3

                                                                                                                                                              0

                                                                                                                                                              3

                                                                                                                                                              0 0

                                                                                                                                                              A B C D E

                                                                                                                                                              Chart1

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                                                                                                                                                              0
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                                                                                                                                                              DTU Compute

                                                                                                                                                              2122018Introduction to Medical Image Analysis82 DTU Compute Technical University of Denmark

                                                                                                                                                              Denne uges brug af clickersA) click click click ndash jeg bliver

                                                                                                                                                              sindssygB) For meget clickC) PassendeD) Jeg vil gerne have lidt mereE) Jeg kan ikrsquo faring nok

                                                                                                                                                              0 0

                                                                                                                                                              5

                                                                                                                                                              0

                                                                                                                                                              6

                                                                                                                                                              A B C D E

                                                                                                                                                              Chart1

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                                                                                                                                                              Sheet1

                                                                                                                                                              DTU Compute

                                                                                                                                                              2122018Introduction to Medical Image Analysis83 DTU Compute Technical University of Denmark

                                                                                                                                                              What can you do after today Describe the difference between point processing and neighbourhood

                                                                                                                                                              processing Compute a rank filtered image using the min max median and

                                                                                                                                                              difference rank filters Compute a mean filtered image Decide if median or average filtering should be used for noise removal Choose the appropriate image border handling based on a given input

                                                                                                                                                              image Implement and apply template matching Compute the normalised cross correlation and explain why it should be

                                                                                                                                                              used Apply given image filter kernels to images Use edge filters on images Describe finite difference approximation of image gradients Describe the concept of edge detection

                                                                                                                                                              DTU Compute

                                                                                                                                                              2122018Introduction to Medical Image Analysis84 DTU Compute Technical University of Denmark

                                                                                                                                                              Oslashvelsesrapport over oslashvelse 4 - 02511 Oslashvelser taeligller cirka 30 af karakteren Skal afleveres senest den 7 marts kl 2359 Kan afleveres af 1 eller 2 personer

                                                                                                                                                              ndash I skal skrive jeres egen oslashvelsesrapportndash Brug mindst et af jeres egne billeder

                                                                                                                                                              Afleveres som PDF Lad vaeligre med at kopiere opgaveteksten ind i jeres

                                                                                                                                                              opgave Put Matlab kode i et Appendix og henvis fra teksten Eksempel rapport over oslashvelse findes paring

                                                                                                                                                              hjemmesiden under eksamen

                                                                                                                                                              DTU Compute

                                                                                                                                                              2122018Introduction to Medical Image Analysis85 DTU Compute Technical University of Denmark

                                                                                                                                                              Exercises

                                                                                                                                                              • Introduction to Medical Image Analysis
                                                                                                                                                              • Lecture 4 ndash Neighbourhood Processing
                                                                                                                                                              • What can you do after today
                                                                                                                                                              • Point processing
                                                                                                                                                              • Point processing
                                                                                                                                                              • Neighbourhood processing
                                                                                                                                                              • Use of filtering
                                                                                                                                                              • Salt and pepper noise
                                                                                                                                                              • Salt and pepper noise
                                                                                                                                                              • What is so special about noise
                                                                                                                                                              • Noise ndash go away
                                                                                                                                                              • What is the median Value
                                                                                                                                                              • The median value
                                                                                                                                                              • Noise away ndash the median filter
                                                                                                                                                              • Noise removal ndash average filter
                                                                                                                                                              • Noise removal ndash median filter
                                                                                                                                                              • Image Filtering
                                                                                                                                                              • Median filter
                                                                                                                                                              • Rank filters
                                                                                                                                                              • Median filter
                                                                                                                                                              • Correlation
                                                                                                                                                              • Why do we need similarity
                                                                                                                                                              • Correlation (1D)
                                                                                                                                                              • Correlation (1D)
                                                                                                                                                              • Normalisation
                                                                                                                                                              • Normalisation
                                                                                                                                                              • Correlation on images
                                                                                                                                                              • Correlation on images
                                                                                                                                                              • Correlation on images
                                                                                                                                                              • Draw your filter
                                                                                                                                                              • Correlation on images ndash no normalisation
                                                                                                                                                              • Correlation on images ndash no normalisation 2
                                                                                                                                                              • Mathematics of 2D Correlation
                                                                                                                                                              • Mathematics of 2D Correlation
                                                                                                                                                              • Mathematics of 2D Correlation
                                                                                                                                                              • Slide Number 40
                                                                                                                                                              • 2D Kernel Normalisation
                                                                                                                                                              • Correlation
                                                                                                                                                              • Smoothing filters
                                                                                                                                                              • Use of smoothing
                                                                                                                                                              • Use of smoothing
                                                                                                                                                              • Mean filter
                                                                                                                                                              • Border handling
                                                                                                                                                              • Border handling ndash extend the input
                                                                                                                                                              • Correlation with zero padding
                                                                                                                                                              • Border handling ndash extend the input
                                                                                                                                                              • Template Matching
                                                                                                                                                              • Template Matching
                                                                                                                                                              • Template Matching
                                                                                                                                                              • Template Matching
                                                                                                                                                              • Problematic Correlation
                                                                                                                                                              • Normalised Cross Correlation
                                                                                                                                                              • Length of template
                                                                                                                                                              • Length of image patch
                                                                                                                                                              • Normalised Cross Correlation
                                                                                                                                                              • Normalised Cross Correlation
                                                                                                                                                              • Normalised Cross Correlation
                                                                                                                                                              • Edges
                                                                                                                                                              • Edges
                                                                                                                                                              • Finite Difference
                                                                                                                                                              • Edges
                                                                                                                                                              • Edges in 2D
                                                                                                                                                              • Edge filter kernel
                                                                                                                                                              • Prewitt filter
                                                                                                                                                              • Edge detection
                                                                                                                                                              • Edge filtering
                                                                                                                                                              • 02511 - Niveau af dagens emne forelaeligsing
                                                                                                                                                              • 02512 - Niveau af dagens emne forelaeligsing
                                                                                                                                                              • 02511 - Mit eget udbytte af dagen
                                                                                                                                                              • 02512 - Mit eget udbytte af dagen
                                                                                                                                                              • 02511 - Sidste uges oslashvelser (pixelwise operations)
                                                                                                                                                              • 02512 - Sidste uges oslashvelser (pixelwise operations)
                                                                                                                                                              • Denne uges brug af clickers
                                                                                                                                                              • What can you do after today
                                                                                                                                                              • Oslashvelsesrapport over oslashvelse 4 - 02511
                                                                                                                                                              • Exercises
                                                                                                                                                                A0
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                                                                                                                                                                E
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                                                                                                                                                                A0
                                                                                                                                                                B8
                                                                                                                                                                C1
                                                                                                                                                                D1
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                                                                                                                                                                A
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                                                                                                                                                                E

                                                                                                                                                                DTU Compute

                                                                                                                                                                2122018Introduction to Medical Image Analysis70 DTU Compute Technical University of Denmark

                                                                                                                                                                Edges in 2D Changes in gray level values

                                                                                                                                                                ndash Image gradientndash Gradient is the 2D derivative of a 2D function f(xy)ndash Equal to the slope of the imagendash A steep slope is equal to an edge

                                                                                                                                                                120571120571119891119891 119909119909119910119910 = 119866(119892119892119909119909119892119892119910119910)

                                                                                                                                                                DTU Compute

                                                                                                                                                                2122018Introduction to Medical Image Analysis71 DTU Compute Technical University of Denmark

                                                                                                                                                                Edge filter kernel The Prewitt filter is a typical

                                                                                                                                                                edge filter Output image has high

                                                                                                                                                                values where there are edges

                                                                                                                                                                -1 0 1

                                                                                                                                                                -1 0 1

                                                                                                                                                                -1 0 1Vertical Prewitt filter

                                                                                                                                                                DTU Compute

                                                                                                                                                                2122018Introduction to Medical Image Analysis72 DTU Compute Technical University of Denmark

                                                                                                                                                                Prewitt filter

                                                                                                                                                                Original Prewitt Prewitt

                                                                                                                                                                Hot colormapSmooth 15x15

                                                                                                                                                                Smooth 15x15

                                                                                                                                                                Prewitt

                                                                                                                                                                DTU Compute

                                                                                                                                                                2122018Introduction to Medical Image Analysis73 DTU Compute Technical University of Denmark

                                                                                                                                                                Edge detection Edge filter

                                                                                                                                                                ndash Prewitt for example Thresholding

                                                                                                                                                                ndash Separate edges from non-edges

                                                                                                                                                                Output is binary imagendash Edges are white

                                                                                                                                                                DTU Compute

                                                                                                                                                                2122018Introduction to Medical Image Analysis74 DTU Compute Technical University of Denmark

                                                                                                                                                                Edge filtering

                                                                                                                                                                A) MeanB) Horizontal SobelC) Vertical PrewittD) Horisontal PrewittE) Median

                                                                                                                                                                Der udfoslashres en filtrering (correlation) med et filter paring billedet Der bruges ikke coefficient normalization Den filtrerede vaeligrdi i den markerede pixel bliver -119 Hvilket et 3x3 filter blev benyttet

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                                                                                                                                                                2122018Introduction to Medical Image Analysis76 DTU Compute Technical University of Denmark

                                                                                                                                                                02511 - Niveau af dagens emne forelaeligsingA) Meget letB) LetC) PassendeD) SvaeligrtE) Meget svaeligrt

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                                                                                                                                                                2122018Introduction to Medical Image Analysis77 DTU Compute Technical University of Denmark

                                                                                                                                                                02512 - Niveau af dagens emne forelaeligsingA) Meget letB) LetC) PassendeD) SvaeligrtE) Meget svaeligrt

                                                                                                                                                                0 0

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                                                                                                                                                                DTU Compute

                                                                                                                                                                2122018Introduction to Medical Image Analysis78 DTU Compute Technical University of Denmark

                                                                                                                                                                02511 - Mit eget udbytte af dagenA) Jeg har laeligrt meget lidtB) Lidt laeligringC) PassendeD) God laeligringE) Jeg har laeligrt meget

                                                                                                                                                                0 0

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                                                                                                                                                                DTU Compute

                                                                                                                                                                2122018Introduction to Medical Image Analysis79 DTU Compute Technical University of Denmark

                                                                                                                                                                02512 - Mit eget udbytte af dagenA) Jeg har laeligrt meget lidtB) Lidt laeligringC) PassendeD) God laeligringE) Jeg har laeligrt meget

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                                                                                                                                                                DTU Compute

                                                                                                                                                                2122018Introduction to Medical Image Analysis80 DTU Compute Technical University of Denmark

                                                                                                                                                                02511 - Sidste uges oslashvelser (pixelwiseoperations)A) Meget letteB) LetteC) PassendeD) SvaeligreE) Meget svaeligre

                                                                                                                                                                0 0

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                                                                                                                                                                DTU Compute

                                                                                                                                                                2122018Introduction to Medical Image Analysis81 DTU Compute Technical University of Denmark

                                                                                                                                                                02512 - Sidste uges oslashvelser (pixelwiseoperations)A) Meget letteB) LetteC) PassendeD) SvaeligreE) Meget svaeligre

                                                                                                                                                                3

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                                                                                                                                                                DTU Compute

                                                                                                                                                                2122018Introduction to Medical Image Analysis82 DTU Compute Technical University of Denmark

                                                                                                                                                                Denne uges brug af clickersA) click click click ndash jeg bliver

                                                                                                                                                                sindssygB) For meget clickC) PassendeD) Jeg vil gerne have lidt mereE) Jeg kan ikrsquo faring nok

                                                                                                                                                                0 0

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                                                                                                                                                                DTU Compute

                                                                                                                                                                2122018Introduction to Medical Image Analysis83 DTU Compute Technical University of Denmark

                                                                                                                                                                What can you do after today Describe the difference between point processing and neighbourhood

                                                                                                                                                                processing Compute a rank filtered image using the min max median and

                                                                                                                                                                difference rank filters Compute a mean filtered image Decide if median or average filtering should be used for noise removal Choose the appropriate image border handling based on a given input

                                                                                                                                                                image Implement and apply template matching Compute the normalised cross correlation and explain why it should be

                                                                                                                                                                used Apply given image filter kernels to images Use edge filters on images Describe finite difference approximation of image gradients Describe the concept of edge detection

                                                                                                                                                                DTU Compute

                                                                                                                                                                2122018Introduction to Medical Image Analysis84 DTU Compute Technical University of Denmark

                                                                                                                                                                Oslashvelsesrapport over oslashvelse 4 - 02511 Oslashvelser taeligller cirka 30 af karakteren Skal afleveres senest den 7 marts kl 2359 Kan afleveres af 1 eller 2 personer

                                                                                                                                                                ndash I skal skrive jeres egen oslashvelsesrapportndash Brug mindst et af jeres egne billeder

                                                                                                                                                                Afleveres som PDF Lad vaeligre med at kopiere opgaveteksten ind i jeres

                                                                                                                                                                opgave Put Matlab kode i et Appendix og henvis fra teksten Eksempel rapport over oslashvelse findes paring

                                                                                                                                                                hjemmesiden under eksamen

                                                                                                                                                                DTU Compute

                                                                                                                                                                2122018Introduction to Medical Image Analysis85 DTU Compute Technical University of Denmark

                                                                                                                                                                Exercises

                                                                                                                                                                • Introduction to Medical Image Analysis
                                                                                                                                                                • Lecture 4 ndash Neighbourhood Processing
                                                                                                                                                                • What can you do after today
                                                                                                                                                                • Point processing
                                                                                                                                                                • Point processing
                                                                                                                                                                • Neighbourhood processing
                                                                                                                                                                • Use of filtering
                                                                                                                                                                • Salt and pepper noise
                                                                                                                                                                • Salt and pepper noise
                                                                                                                                                                • What is so special about noise
                                                                                                                                                                • Noise ndash go away
                                                                                                                                                                • What is the median Value
                                                                                                                                                                • The median value
                                                                                                                                                                • Noise away ndash the median filter
                                                                                                                                                                • Noise removal ndash average filter
                                                                                                                                                                • Noise removal ndash median filter
                                                                                                                                                                • Image Filtering
                                                                                                                                                                • Median filter
                                                                                                                                                                • Rank filters
                                                                                                                                                                • Median filter
                                                                                                                                                                • Correlation
                                                                                                                                                                • Why do we need similarity
                                                                                                                                                                • Correlation (1D)
                                                                                                                                                                • Correlation (1D)
                                                                                                                                                                • Normalisation
                                                                                                                                                                • Normalisation
                                                                                                                                                                • Correlation on images
                                                                                                                                                                • Correlation on images
                                                                                                                                                                • Correlation on images
                                                                                                                                                                • Draw your filter
                                                                                                                                                                • Correlation on images ndash no normalisation
                                                                                                                                                                • Correlation on images ndash no normalisation 2
                                                                                                                                                                • Mathematics of 2D Correlation
                                                                                                                                                                • Mathematics of 2D Correlation
                                                                                                                                                                • Mathematics of 2D Correlation
                                                                                                                                                                • Slide Number 40
                                                                                                                                                                • 2D Kernel Normalisation
                                                                                                                                                                • Correlation
                                                                                                                                                                • Smoothing filters
                                                                                                                                                                • Use of smoothing
                                                                                                                                                                • Use of smoothing
                                                                                                                                                                • Mean filter
                                                                                                                                                                • Border handling
                                                                                                                                                                • Border handling ndash extend the input
                                                                                                                                                                • Correlation with zero padding
                                                                                                                                                                • Border handling ndash extend the input
                                                                                                                                                                • Template Matching
                                                                                                                                                                • Template Matching
                                                                                                                                                                • Template Matching
                                                                                                                                                                • Template Matching
                                                                                                                                                                • Problematic Correlation
                                                                                                                                                                • Normalised Cross Correlation
                                                                                                                                                                • Length of template
                                                                                                                                                                • Length of image patch
                                                                                                                                                                • Normalised Cross Correlation
                                                                                                                                                                • Normalised Cross Correlation
                                                                                                                                                                • Normalised Cross Correlation
                                                                                                                                                                • Edges
                                                                                                                                                                • Edges
                                                                                                                                                                • Finite Difference
                                                                                                                                                                • Edges
                                                                                                                                                                • Edges in 2D
                                                                                                                                                                • Edge filter kernel
                                                                                                                                                                • Prewitt filter
                                                                                                                                                                • Edge detection
                                                                                                                                                                • Edge filtering
                                                                                                                                                                • 02511 - Niveau af dagens emne forelaeligsing
                                                                                                                                                                • 02512 - Niveau af dagens emne forelaeligsing
                                                                                                                                                                • 02511 - Mit eget udbytte af dagen
                                                                                                                                                                • 02512 - Mit eget udbytte af dagen
                                                                                                                                                                • 02511 - Sidste uges oslashvelser (pixelwise operations)
                                                                                                                                                                • 02512 - Sidste uges oslashvelser (pixelwise operations)
                                                                                                                                                                • Denne uges brug af clickers
                                                                                                                                                                • What can you do after today
                                                                                                                                                                • Oslashvelsesrapport over oslashvelse 4 - 02511
                                                                                                                                                                • Exercises
                                                                                                                                                                  A0
                                                                                                                                                                  B0
                                                                                                                                                                  C5
                                                                                                                                                                  D0
                                                                                                                                                                  E6
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                                                                                                                                                                  D4
                                                                                                                                                                  E1
                                                                                                                                                                  A
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                                                                                                                                                                  E
                                                                                                                                                                  A2
                                                                                                                                                                  B1
                                                                                                                                                                  C3
                                                                                                                                                                  D2
                                                                                                                                                                  E0
                                                                                                                                                                  A
                                                                                                                                                                  B
                                                                                                                                                                  C
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                                                                                                                                                                  E
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                                                                                                                                                                  A0
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                                                                                                                                                                  D0
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                                                                                                                                                                  A
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                                                                                                                                                                  E
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                                                                                                                                                                  D1
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                                                                                                                                                                  A
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                                                                                                                                                                  C1
                                                                                                                                                                  D1
                                                                                                                                                                  E0
                                                                                                                                                                  A
                                                                                                                                                                  B
                                                                                                                                                                  C
                                                                                                                                                                  D
                                                                                                                                                                  E

                                                                                                                                                                  DTU Compute

                                                                                                                                                                  2122018Introduction to Medical Image Analysis71 DTU Compute Technical University of Denmark

                                                                                                                                                                  Edge filter kernel The Prewitt filter is a typical

                                                                                                                                                                  edge filter Output image has high

                                                                                                                                                                  values where there are edges

                                                                                                                                                                  -1 0 1

                                                                                                                                                                  -1 0 1

                                                                                                                                                                  -1 0 1Vertical Prewitt filter

                                                                                                                                                                  DTU Compute

                                                                                                                                                                  2122018Introduction to Medical Image Analysis72 DTU Compute Technical University of Denmark

                                                                                                                                                                  Prewitt filter

                                                                                                                                                                  Original Prewitt Prewitt

                                                                                                                                                                  Hot colormapSmooth 15x15

                                                                                                                                                                  Smooth 15x15

                                                                                                                                                                  Prewitt

                                                                                                                                                                  DTU Compute

                                                                                                                                                                  2122018Introduction to Medical Image Analysis73 DTU Compute Technical University of Denmark

                                                                                                                                                                  Edge detection Edge filter

                                                                                                                                                                  ndash Prewitt for example Thresholding

                                                                                                                                                                  ndash Separate edges from non-edges

                                                                                                                                                                  Output is binary imagendash Edges are white

                                                                                                                                                                  DTU Compute

                                                                                                                                                                  2122018Introduction to Medical Image Analysis74 DTU Compute Technical University of Denmark

                                                                                                                                                                  Edge filtering

                                                                                                                                                                  A) MeanB) Horizontal SobelC) Vertical PrewittD) Horisontal PrewittE) Median

                                                                                                                                                                  Der udfoslashres en filtrering (correlation) med et filter paring billedet Der bruges ikke coefficient normalization Den filtrerede vaeligrdi i den markerede pixel bliver -119 Hvilket et 3x3 filter blev benyttet

                                                                                                                                                                  0

                                                                                                                                                                  8

                                                                                                                                                                  1 10

                                                                                                                                                                  A B C D E

                                                                                                                                                                  Chart1

                                                                                                                                                                  0
                                                                                                                                                                  8
                                                                                                                                                                  1
                                                                                                                                                                  1
                                                                                                                                                                  0

                                                                                                                                                                  Sheet1

                                                                                                                                                                  DTU Compute

                                                                                                                                                                  2122018Introduction to Medical Image Analysis76 DTU Compute Technical University of Denmark

                                                                                                                                                                  02511 - Niveau af dagens emne forelaeligsingA) Meget letB) LetC) PassendeD) SvaeligrtE) Meget svaeligrt

                                                                                                                                                                  23

                                                                                                                                                                  6

                                                                                                                                                                  10

                                                                                                                                                                  A B C D E

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                                                                                                                                                                  0

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                                                                                                                                                                  2122018Introduction to Medical Image Analysis77 DTU Compute Technical University of Denmark

                                                                                                                                                                  02512 - Niveau af dagens emne forelaeligsingA) Meget letB) LetC) PassendeD) SvaeligrtE) Meget svaeligrt

                                                                                                                                                                  0 0

                                                                                                                                                                  1

                                                                                                                                                                  0 0

                                                                                                                                                                  A B C D E

                                                                                                                                                                  Chart1

                                                                                                                                                                  0
                                                                                                                                                                  0
                                                                                                                                                                  1
                                                                                                                                                                  0
                                                                                                                                                                  0

                                                                                                                                                                  Sheet1

                                                                                                                                                                  DTU Compute

                                                                                                                                                                  2122018Introduction to Medical Image Analysis78 DTU Compute Technical University of Denmark

                                                                                                                                                                  02511 - Mit eget udbytte af dagenA) Jeg har laeligrt meget lidtB) Lidt laeligringC) PassendeD) God laeligringE) Jeg har laeligrt meget

                                                                                                                                                                  0 0

                                                                                                                                                                  2

                                                                                                                                                                  6

                                                                                                                                                                  0

                                                                                                                                                                  A B C D E

                                                                                                                                                                  Chart1

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                                                                                                                                                                  0
                                                                                                                                                                  2
                                                                                                                                                                  6
                                                                                                                                                                  0

                                                                                                                                                                  Sheet1

                                                                                                                                                                  DTU Compute

                                                                                                                                                                  2122018Introduction to Medical Image Analysis79 DTU Compute Technical University of Denmark

                                                                                                                                                                  02512 - Mit eget udbytte af dagenA) Jeg har laeligrt meget lidtB) Lidt laeligringC) PassendeD) God laeligringE) Jeg har laeligrt meget

                                                                                                                                                                  2

                                                                                                                                                                  1

                                                                                                                                                                  3

                                                                                                                                                                  2

                                                                                                                                                                  0

                                                                                                                                                                  A B C D E

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                                                                                                                                                                  2
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                                                                                                                                                                  Sheet1

                                                                                                                                                                  DTU Compute

                                                                                                                                                                  2122018Introduction to Medical Image Analysis80 DTU Compute Technical University of Denmark

                                                                                                                                                                  02511 - Sidste uges oslashvelser (pixelwiseoperations)A) Meget letteB) LetteC) PassendeD) SvaeligreE) Meget svaeligre

                                                                                                                                                                  0 0

                                                                                                                                                                  1

                                                                                                                                                                  4

                                                                                                                                                                  1

                                                                                                                                                                  A B C D E

                                                                                                                                                                  Chart1

                                                                                                                                                                  0
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                                                                                                                                                                  1
                                                                                                                                                                  4
                                                                                                                                                                  1

                                                                                                                                                                  Sheet1

                                                                                                                                                                  DTU Compute

                                                                                                                                                                  2122018Introduction to Medical Image Analysis81 DTU Compute Technical University of Denmark

                                                                                                                                                                  02512 - Sidste uges oslashvelser (pixelwiseoperations)A) Meget letteB) LetteC) PassendeD) SvaeligreE) Meget svaeligre

                                                                                                                                                                  3

                                                                                                                                                                  0

                                                                                                                                                                  3

                                                                                                                                                                  0 0

                                                                                                                                                                  A B C D E

                                                                                                                                                                  Chart1

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                                                                                                                                                                  0
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                                                                                                                                                                  0

                                                                                                                                                                  Sheet1

                                                                                                                                                                  DTU Compute

                                                                                                                                                                  2122018Introduction to Medical Image Analysis82 DTU Compute Technical University of Denmark

                                                                                                                                                                  Denne uges brug af clickersA) click click click ndash jeg bliver

                                                                                                                                                                  sindssygB) For meget clickC) PassendeD) Jeg vil gerne have lidt mereE) Jeg kan ikrsquo faring nok

                                                                                                                                                                  0 0

                                                                                                                                                                  5

                                                                                                                                                                  0

                                                                                                                                                                  6

                                                                                                                                                                  A B C D E

                                                                                                                                                                  Chart1

                                                                                                                                                                  0
                                                                                                                                                                  0
                                                                                                                                                                  5
                                                                                                                                                                  0
                                                                                                                                                                  6

                                                                                                                                                                  Sheet1

                                                                                                                                                                  DTU Compute

                                                                                                                                                                  2122018Introduction to Medical Image Analysis83 DTU Compute Technical University of Denmark

                                                                                                                                                                  What can you do after today Describe the difference between point processing and neighbourhood

                                                                                                                                                                  processing Compute a rank filtered image using the min max median and

                                                                                                                                                                  difference rank filters Compute a mean filtered image Decide if median or average filtering should be used for noise removal Choose the appropriate image border handling based on a given input

                                                                                                                                                                  image Implement and apply template matching Compute the normalised cross correlation and explain why it should be

                                                                                                                                                                  used Apply given image filter kernels to images Use edge filters on images Describe finite difference approximation of image gradients Describe the concept of edge detection

                                                                                                                                                                  DTU Compute

                                                                                                                                                                  2122018Introduction to Medical Image Analysis84 DTU Compute Technical University of Denmark

                                                                                                                                                                  Oslashvelsesrapport over oslashvelse 4 - 02511 Oslashvelser taeligller cirka 30 af karakteren Skal afleveres senest den 7 marts kl 2359 Kan afleveres af 1 eller 2 personer

                                                                                                                                                                  ndash I skal skrive jeres egen oslashvelsesrapportndash Brug mindst et af jeres egne billeder

                                                                                                                                                                  Afleveres som PDF Lad vaeligre med at kopiere opgaveteksten ind i jeres

                                                                                                                                                                  opgave Put Matlab kode i et Appendix og henvis fra teksten Eksempel rapport over oslashvelse findes paring

                                                                                                                                                                  hjemmesiden under eksamen

                                                                                                                                                                  DTU Compute

                                                                                                                                                                  2122018Introduction to Medical Image Analysis85 DTU Compute Technical University of Denmark

                                                                                                                                                                  Exercises

                                                                                                                                                                  • Introduction to Medical Image Analysis
                                                                                                                                                                  • Lecture 4 ndash Neighbourhood Processing
                                                                                                                                                                  • What can you do after today
                                                                                                                                                                  • Point processing
                                                                                                                                                                  • Point processing
                                                                                                                                                                  • Neighbourhood processing
                                                                                                                                                                  • Use of filtering
                                                                                                                                                                  • Salt and pepper noise
                                                                                                                                                                  • Salt and pepper noise
                                                                                                                                                                  • What is so special about noise
                                                                                                                                                                  • Noise ndash go away
                                                                                                                                                                  • What is the median Value
                                                                                                                                                                  • The median value
                                                                                                                                                                  • Noise away ndash the median filter
                                                                                                                                                                  • Noise removal ndash average filter
                                                                                                                                                                  • Noise removal ndash median filter
                                                                                                                                                                  • Image Filtering
                                                                                                                                                                  • Median filter
                                                                                                                                                                  • Rank filters
                                                                                                                                                                  • Median filter
                                                                                                                                                                  • Correlation
                                                                                                                                                                  • Why do we need similarity
                                                                                                                                                                  • Correlation (1D)
                                                                                                                                                                  • Correlation (1D)
                                                                                                                                                                  • Normalisation
                                                                                                                                                                  • Normalisation
                                                                                                                                                                  • Correlation on images
                                                                                                                                                                  • Correlation on images
                                                                                                                                                                  • Correlation on images
                                                                                                                                                                  • Draw your filter
                                                                                                                                                                  • Correlation on images ndash no normalisation
                                                                                                                                                                  • Correlation on images ndash no normalisation 2
                                                                                                                                                                  • Mathematics of 2D Correlation
                                                                                                                                                                  • Mathematics of 2D Correlation
                                                                                                                                                                  • Mathematics of 2D Correlation
                                                                                                                                                                  • Slide Number 40
                                                                                                                                                                  • 2D Kernel Normalisation
                                                                                                                                                                  • Correlation
                                                                                                                                                                  • Smoothing filters
                                                                                                                                                                  • Use of smoothing
                                                                                                                                                                  • Use of smoothing
                                                                                                                                                                  • Mean filter
                                                                                                                                                                  • Border handling
                                                                                                                                                                  • Border handling ndash extend the input
                                                                                                                                                                  • Correlation with zero padding
                                                                                                                                                                  • Border handling ndash extend the input
                                                                                                                                                                  • Template Matching
                                                                                                                                                                  • Template Matching
                                                                                                                                                                  • Template Matching
                                                                                                                                                                  • Template Matching
                                                                                                                                                                  • Problematic Correlation
                                                                                                                                                                  • Normalised Cross Correlation
                                                                                                                                                                  • Length of template
                                                                                                                                                                  • Length of image patch
                                                                                                                                                                  • Normalised Cross Correlation
                                                                                                                                                                  • Normalised Cross Correlation
                                                                                                                                                                  • Normalised Cross Correlation
                                                                                                                                                                  • Edges
                                                                                                                                                                  • Edges
                                                                                                                                                                  • Finite Difference
                                                                                                                                                                  • Edges
                                                                                                                                                                  • Edges in 2D
                                                                                                                                                                  • Edge filter kernel
                                                                                                                                                                  • Prewitt filter
                                                                                                                                                                  • Edge detection
                                                                                                                                                                  • Edge filtering
                                                                                                                                                                  • 02511 - Niveau af dagens emne forelaeligsing
                                                                                                                                                                  • 02512 - Niveau af dagens emne forelaeligsing
                                                                                                                                                                  • 02511 - Mit eget udbytte af dagen
                                                                                                                                                                  • 02512 - Mit eget udbytte af dagen
                                                                                                                                                                  • 02511 - Sidste uges oslashvelser (pixelwise operations)
                                                                                                                                                                  • 02512 - Sidste uges oslashvelser (pixelwise operations)
                                                                                                                                                                  • Denne uges brug af clickers
                                                                                                                                                                  • What can you do after today
                                                                                                                                                                  • Oslashvelsesrapport over oslashvelse 4 - 02511
                                                                                                                                                                  • Exercises
                                                                                                                                                                    A0
                                                                                                                                                                    B0
                                                                                                                                                                    C5
                                                                                                                                                                    D0
                                                                                                                                                                    E6
                                                                                                                                                                    A
                                                                                                                                                                    B
                                                                                                                                                                    C
                                                                                                                                                                    D
                                                                                                                                                                    E
                                                                                                                                                                    A3
                                                                                                                                                                    B0
                                                                                                                                                                    C3
                                                                                                                                                                    D0
                                                                                                                                                                    E0
                                                                                                                                                                    A
                                                                                                                                                                    B
                                                                                                                                                                    C
                                                                                                                                                                    D
                                                                                                                                                                    E
                                                                                                                                                                    A0
                                                                                                                                                                    B0
                                                                                                                                                                    C1
                                                                                                                                                                    D4
                                                                                                                                                                    E1
                                                                                                                                                                    A
                                                                                                                                                                    B
                                                                                                                                                                    C
                                                                                                                                                                    D
                                                                                                                                                                    E
                                                                                                                                                                    A2
                                                                                                                                                                    B1
                                                                                                                                                                    C3
                                                                                                                                                                    D2
                                                                                                                                                                    E0
                                                                                                                                                                    A
                                                                                                                                                                    B
                                                                                                                                                                    C
                                                                                                                                                                    D
                                                                                                                                                                    E
                                                                                                                                                                    A0
                                                                                                                                                                    B0
                                                                                                                                                                    C2
                                                                                                                                                                    D6
                                                                                                                                                                    E0
                                                                                                                                                                    A
                                                                                                                                                                    B
                                                                                                                                                                    C
                                                                                                                                                                    D
                                                                                                                                                                    E
                                                                                                                                                                    A0
                                                                                                                                                                    B0
                                                                                                                                                                    C1
                                                                                                                                                                    D0
                                                                                                                                                                    E0
                                                                                                                                                                    A
                                                                                                                                                                    B
                                                                                                                                                                    C
                                                                                                                                                                    D
                                                                                                                                                                    E
                                                                                                                                                                    A2
                                                                                                                                                                    B3
                                                                                                                                                                    C6
                                                                                                                                                                    D1
                                                                                                                                                                    E0
                                                                                                                                                                    A
                                                                                                                                                                    B
                                                                                                                                                                    C
                                                                                                                                                                    D
                                                                                                                                                                    E
                                                                                                                                                                    A0
                                                                                                                                                                    B8
                                                                                                                                                                    C1
                                                                                                                                                                    D1
                                                                                                                                                                    E0
                                                                                                                                                                    A
                                                                                                                                                                    B
                                                                                                                                                                    C
                                                                                                                                                                    D
                                                                                                                                                                    E

                                                                                                                                                                    DTU Compute

                                                                                                                                                                    2122018Introduction to Medical Image Analysis72 DTU Compute Technical University of Denmark

                                                                                                                                                                    Prewitt filter

                                                                                                                                                                    Original Prewitt Prewitt

                                                                                                                                                                    Hot colormapSmooth 15x15

                                                                                                                                                                    Smooth 15x15

                                                                                                                                                                    Prewitt

                                                                                                                                                                    DTU Compute

                                                                                                                                                                    2122018Introduction to Medical Image Analysis73 DTU Compute Technical University of Denmark

                                                                                                                                                                    Edge detection Edge filter

                                                                                                                                                                    ndash Prewitt for example Thresholding

                                                                                                                                                                    ndash Separate edges from non-edges

                                                                                                                                                                    Output is binary imagendash Edges are white

                                                                                                                                                                    DTU Compute

                                                                                                                                                                    2122018Introduction to Medical Image Analysis74 DTU Compute Technical University of Denmark

                                                                                                                                                                    Edge filtering

                                                                                                                                                                    A) MeanB) Horizontal SobelC) Vertical PrewittD) Horisontal PrewittE) Median

                                                                                                                                                                    Der udfoslashres en filtrering (correlation) med et filter paring billedet Der bruges ikke coefficient normalization Den filtrerede vaeligrdi i den markerede pixel bliver -119 Hvilket et 3x3 filter blev benyttet

                                                                                                                                                                    0

                                                                                                                                                                    8

                                                                                                                                                                    1 10

                                                                                                                                                                    A B C D E

                                                                                                                                                                    Chart1

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                                                                                                                                                                    1
                                                                                                                                                                    1
                                                                                                                                                                    0

                                                                                                                                                                    Sheet1

                                                                                                                                                                    DTU Compute

                                                                                                                                                                    2122018Introduction to Medical Image Analysis76 DTU Compute Technical University of Denmark

                                                                                                                                                                    02511 - Niveau af dagens emne forelaeligsingA) Meget letB) LetC) PassendeD) SvaeligrtE) Meget svaeligrt

                                                                                                                                                                    23

                                                                                                                                                                    6

                                                                                                                                                                    10

                                                                                                                                                                    A B C D E

                                                                                                                                                                    Chart1

                                                                                                                                                                    2
                                                                                                                                                                    3
                                                                                                                                                                    6
                                                                                                                                                                    1
                                                                                                                                                                    0

                                                                                                                                                                    Sheet1

                                                                                                                                                                    DTU Compute

                                                                                                                                                                    2122018Introduction to Medical Image Analysis77 DTU Compute Technical University of Denmark

                                                                                                                                                                    02512 - Niveau af dagens emne forelaeligsingA) Meget letB) LetC) PassendeD) SvaeligrtE) Meget svaeligrt

                                                                                                                                                                    0 0

                                                                                                                                                                    1

                                                                                                                                                                    0 0

                                                                                                                                                                    A B C D E

                                                                                                                                                                    Chart1

                                                                                                                                                                    0
                                                                                                                                                                    0
                                                                                                                                                                    1
                                                                                                                                                                    0
                                                                                                                                                                    0

                                                                                                                                                                    Sheet1

                                                                                                                                                                    DTU Compute

                                                                                                                                                                    2122018Introduction to Medical Image Analysis78 DTU Compute Technical University of Denmark

                                                                                                                                                                    02511 - Mit eget udbytte af dagenA) Jeg har laeligrt meget lidtB) Lidt laeligringC) PassendeD) God laeligringE) Jeg har laeligrt meget

                                                                                                                                                                    0 0

                                                                                                                                                                    2

                                                                                                                                                                    6

                                                                                                                                                                    0

                                                                                                                                                                    A B C D E

                                                                                                                                                                    Chart1

                                                                                                                                                                    0
                                                                                                                                                                    0
                                                                                                                                                                    2
                                                                                                                                                                    6
                                                                                                                                                                    0

                                                                                                                                                                    Sheet1

                                                                                                                                                                    DTU Compute

                                                                                                                                                                    2122018Introduction to Medical Image Analysis79 DTU Compute Technical University of Denmark

                                                                                                                                                                    02512 - Mit eget udbytte af dagenA) Jeg har laeligrt meget lidtB) Lidt laeligringC) PassendeD) God laeligringE) Jeg har laeligrt meget

                                                                                                                                                                    2

                                                                                                                                                                    1

                                                                                                                                                                    3

                                                                                                                                                                    2

                                                                                                                                                                    0

                                                                                                                                                                    A B C D E

                                                                                                                                                                    Chart1

                                                                                                                                                                    2
                                                                                                                                                                    1
                                                                                                                                                                    3
                                                                                                                                                                    2
                                                                                                                                                                    0

                                                                                                                                                                    Sheet1

                                                                                                                                                                    DTU Compute

                                                                                                                                                                    2122018Introduction to Medical Image Analysis80 DTU Compute Technical University of Denmark

                                                                                                                                                                    02511 - Sidste uges oslashvelser (pixelwiseoperations)A) Meget letteB) LetteC) PassendeD) SvaeligreE) Meget svaeligre

                                                                                                                                                                    0 0

                                                                                                                                                                    1

                                                                                                                                                                    4

                                                                                                                                                                    1

                                                                                                                                                                    A B C D E

                                                                                                                                                                    Chart1

                                                                                                                                                                    0
                                                                                                                                                                    0
                                                                                                                                                                    1
                                                                                                                                                                    4
                                                                                                                                                                    1

                                                                                                                                                                    Sheet1

                                                                                                                                                                    DTU Compute

                                                                                                                                                                    2122018Introduction to Medical Image Analysis81 DTU Compute Technical University of Denmark

                                                                                                                                                                    02512 - Sidste uges oslashvelser (pixelwiseoperations)A) Meget letteB) LetteC) PassendeD) SvaeligreE) Meget svaeligre

                                                                                                                                                                    3

                                                                                                                                                                    0

                                                                                                                                                                    3

                                                                                                                                                                    0 0

                                                                                                                                                                    A B C D E

                                                                                                                                                                    Chart1

                                                                                                                                                                    3
                                                                                                                                                                    0
                                                                                                                                                                    3
                                                                                                                                                                    0
                                                                                                                                                                    0

                                                                                                                                                                    Sheet1

                                                                                                                                                                    DTU Compute

                                                                                                                                                                    2122018Introduction to Medical Image Analysis82 DTU Compute Technical University of Denmark

                                                                                                                                                                    Denne uges brug af clickersA) click click click ndash jeg bliver

                                                                                                                                                                    sindssygB) For meget clickC) PassendeD) Jeg vil gerne have lidt mereE) Jeg kan ikrsquo faring nok

                                                                                                                                                                    0 0

                                                                                                                                                                    5

                                                                                                                                                                    0

                                                                                                                                                                    6

                                                                                                                                                                    A B C D E

                                                                                                                                                                    Chart1

                                                                                                                                                                    0
                                                                                                                                                                    0
                                                                                                                                                                    5
                                                                                                                                                                    0
                                                                                                                                                                    6

                                                                                                                                                                    Sheet1

                                                                                                                                                                    DTU Compute

                                                                                                                                                                    2122018Introduction to Medical Image Analysis83 DTU Compute Technical University of Denmark

                                                                                                                                                                    What can you do after today Describe the difference between point processing and neighbourhood

                                                                                                                                                                    processing Compute a rank filtered image using the min max median and

                                                                                                                                                                    difference rank filters Compute a mean filtered image Decide if median or average filtering should be used for noise removal Choose the appropriate image border handling based on a given input

                                                                                                                                                                    image Implement and apply template matching Compute the normalised cross correlation and explain why it should be

                                                                                                                                                                    used Apply given image filter kernels to images Use edge filters on images Describe finite difference approximation of image gradients Describe the concept of edge detection

                                                                                                                                                                    DTU Compute

                                                                                                                                                                    2122018Introduction to Medical Image Analysis84 DTU Compute Technical University of Denmark

                                                                                                                                                                    Oslashvelsesrapport over oslashvelse 4 - 02511 Oslashvelser taeligller cirka 30 af karakteren Skal afleveres senest den 7 marts kl 2359 Kan afleveres af 1 eller 2 personer

                                                                                                                                                                    ndash I skal skrive jeres egen oslashvelsesrapportndash Brug mindst et af jeres egne billeder

                                                                                                                                                                    Afleveres som PDF Lad vaeligre med at kopiere opgaveteksten ind i jeres

                                                                                                                                                                    opgave Put Matlab kode i et Appendix og henvis fra teksten Eksempel rapport over oslashvelse findes paring

                                                                                                                                                                    hjemmesiden under eksamen

                                                                                                                                                                    DTU Compute

                                                                                                                                                                    2122018Introduction to Medical Image Analysis85 DTU Compute Technical University of Denmark

                                                                                                                                                                    Exercises

                                                                                                                                                                    • Introduction to Medical Image Analysis
                                                                                                                                                                    • Lecture 4 ndash Neighbourhood Processing
                                                                                                                                                                    • What can you do after today
                                                                                                                                                                    • Point processing
                                                                                                                                                                    • Point processing
                                                                                                                                                                    • Neighbourhood processing
                                                                                                                                                                    • Use of filtering
                                                                                                                                                                    • Salt and pepper noise
                                                                                                                                                                    • Salt and pepper noise
                                                                                                                                                                    • What is so special about noise
                                                                                                                                                                    • Noise ndash go away
                                                                                                                                                                    • What is the median Value
                                                                                                                                                                    • The median value
                                                                                                                                                                    • Noise away ndash the median filter
                                                                                                                                                                    • Noise removal ndash average filter
                                                                                                                                                                    • Noise removal ndash median filter
                                                                                                                                                                    • Image Filtering
                                                                                                                                                                    • Median filter
                                                                                                                                                                    • Rank filters
                                                                                                                                                                    • Median filter
                                                                                                                                                                    • Correlation
                                                                                                                                                                    • Why do we need similarity
                                                                                                                                                                    • Correlation (1D)
                                                                                                                                                                    • Correlation (1D)
                                                                                                                                                                    • Normalisation
                                                                                                                                                                    • Normalisation
                                                                                                                                                                    • Correlation on images
                                                                                                                                                                    • Correlation on images
                                                                                                                                                                    • Correlation on images
                                                                                                                                                                    • Draw your filter
                                                                                                                                                                    • Correlation on images ndash no normalisation
                                                                                                                                                                    • Correlation on images ndash no normalisation 2
                                                                                                                                                                    • Mathematics of 2D Correlation
                                                                                                                                                                    • Mathematics of 2D Correlation
                                                                                                                                                                    • Mathematics of 2D Correlation
                                                                                                                                                                    • Slide Number 40
                                                                                                                                                                    • 2D Kernel Normalisation
                                                                                                                                                                    • Correlation
                                                                                                                                                                    • Smoothing filters
                                                                                                                                                                    • Use of smoothing
                                                                                                                                                                    • Use of smoothing
                                                                                                                                                                    • Mean filter
                                                                                                                                                                    • Border handling
                                                                                                                                                                    • Border handling ndash extend the input
                                                                                                                                                                    • Correlation with zero padding
                                                                                                                                                                    • Border handling ndash extend the input
                                                                                                                                                                    • Template Matching
                                                                                                                                                                    • Template Matching
                                                                                                                                                                    • Template Matching
                                                                                                                                                                    • Template Matching
                                                                                                                                                                    • Problematic Correlation
                                                                                                                                                                    • Normalised Cross Correlation
                                                                                                                                                                    • Length of template
                                                                                                                                                                    • Length of image patch
                                                                                                                                                                    • Normalised Cross Correlation
                                                                                                                                                                    • Normalised Cross Correlation
                                                                                                                                                                    • Normalised Cross Correlation
                                                                                                                                                                    • Edges
                                                                                                                                                                    • Edges
                                                                                                                                                                    • Finite Difference
                                                                                                                                                                    • Edges
                                                                                                                                                                    • Edges in 2D
                                                                                                                                                                    • Edge filter kernel
                                                                                                                                                                    • Prewitt filter
                                                                                                                                                                    • Edge detection
                                                                                                                                                                    • Edge filtering
                                                                                                                                                                    • 02511 - Niveau af dagens emne forelaeligsing
                                                                                                                                                                    • 02512 - Niveau af dagens emne forelaeligsing
                                                                                                                                                                    • 02511 - Mit eget udbytte af dagen
                                                                                                                                                                    • 02512 - Mit eget udbytte af dagen
                                                                                                                                                                    • 02511 - Sidste uges oslashvelser (pixelwise operations)
                                                                                                                                                                    • 02512 - Sidste uges oslashvelser (pixelwise operations)
                                                                                                                                                                    • Denne uges brug af clickers
                                                                                                                                                                    • What can you do after today
                                                                                                                                                                    • Oslashvelsesrapport over oslashvelse 4 - 02511
                                                                                                                                                                    • Exercises
                                                                                                                                                                      A0
                                                                                                                                                                      B0
                                                                                                                                                                      C5
                                                                                                                                                                      D0
                                                                                                                                                                      E6
                                                                                                                                                                      A
                                                                                                                                                                      B
                                                                                                                                                                      C
                                                                                                                                                                      D
                                                                                                                                                                      E
                                                                                                                                                                      A3
                                                                                                                                                                      B0
                                                                                                                                                                      C3
                                                                                                                                                                      D0
                                                                                                                                                                      E0
                                                                                                                                                                      A
                                                                                                                                                                      B
                                                                                                                                                                      C
                                                                                                                                                                      D
                                                                                                                                                                      E
                                                                                                                                                                      A0
                                                                                                                                                                      B0
                                                                                                                                                                      C1
                                                                                                                                                                      D4
                                                                                                                                                                      E1
                                                                                                                                                                      A
                                                                                                                                                                      B
                                                                                                                                                                      C
                                                                                                                                                                      D
                                                                                                                                                                      E
                                                                                                                                                                      A2
                                                                                                                                                                      B1
                                                                                                                                                                      C3
                                                                                                                                                                      D2
                                                                                                                                                                      E0
                                                                                                                                                                      A
                                                                                                                                                                      B
                                                                                                                                                                      C
                                                                                                                                                                      D
                                                                                                                                                                      E
                                                                                                                                                                      A0
                                                                                                                                                                      B0
                                                                                                                                                                      C2
                                                                                                                                                                      D6
                                                                                                                                                                      E0
                                                                                                                                                                      A
                                                                                                                                                                      B
                                                                                                                                                                      C
                                                                                                                                                                      D
                                                                                                                                                                      E
                                                                                                                                                                      A0
                                                                                                                                                                      B0
                                                                                                                                                                      C1
                                                                                                                                                                      D0
                                                                                                                                                                      E0
                                                                                                                                                                      A
                                                                                                                                                                      B
                                                                                                                                                                      C
                                                                                                                                                                      D
                                                                                                                                                                      E
                                                                                                                                                                      A2
                                                                                                                                                                      B3
                                                                                                                                                                      C6
                                                                                                                                                                      D1
                                                                                                                                                                      E0
                                                                                                                                                                      A
                                                                                                                                                                      B
                                                                                                                                                                      C
                                                                                                                                                                      D
                                                                                                                                                                      E
                                                                                                                                                                      A0
                                                                                                                                                                      B8
                                                                                                                                                                      C1
                                                                                                                                                                      D1
                                                                                                                                                                      E0
                                                                                                                                                                      A
                                                                                                                                                                      B
                                                                                                                                                                      C
                                                                                                                                                                      D
                                                                                                                                                                      E

                                                                                                                                                                      DTU Compute

                                                                                                                                                                      2122018Introduction to Medical Image Analysis73 DTU Compute Technical University of Denmark

                                                                                                                                                                      Edge detection Edge filter

                                                                                                                                                                      ndash Prewitt for example Thresholding

                                                                                                                                                                      ndash Separate edges from non-edges

                                                                                                                                                                      Output is binary imagendash Edges are white

                                                                                                                                                                      DTU Compute

                                                                                                                                                                      2122018Introduction to Medical Image Analysis74 DTU Compute Technical University of Denmark

                                                                                                                                                                      Edge filtering

                                                                                                                                                                      A) MeanB) Horizontal SobelC) Vertical PrewittD) Horisontal PrewittE) Median

                                                                                                                                                                      Der udfoslashres en filtrering (correlation) med et filter paring billedet Der bruges ikke coefficient normalization Den filtrerede vaeligrdi i den markerede pixel bliver -119 Hvilket et 3x3 filter blev benyttet

                                                                                                                                                                      0

                                                                                                                                                                      8

                                                                                                                                                                      1 10

                                                                                                                                                                      A B C D E

                                                                                                                                                                      Chart1

                                                                                                                                                                      0
                                                                                                                                                                      8
                                                                                                                                                                      1
                                                                                                                                                                      1
                                                                                                                                                                      0

                                                                                                                                                                      Sheet1

                                                                                                                                                                      DTU Compute

                                                                                                                                                                      2122018Introduction to Medical Image Analysis76 DTU Compute Technical University of Denmark

                                                                                                                                                                      02511 - Niveau af dagens emne forelaeligsingA) Meget letB) LetC) PassendeD) SvaeligrtE) Meget svaeligrt

                                                                                                                                                                      23

                                                                                                                                                                      6

                                                                                                                                                                      10

                                                                                                                                                                      A B C D E

                                                                                                                                                                      Chart1

                                                                                                                                                                      2
                                                                                                                                                                      3
                                                                                                                                                                      6
                                                                                                                                                                      1
                                                                                                                                                                      0

                                                                                                                                                                      Sheet1

                                                                                                                                                                      DTU Compute

                                                                                                                                                                      2122018Introduction to Medical Image Analysis77 DTU Compute Technical University of Denmark

                                                                                                                                                                      02512 - Niveau af dagens emne forelaeligsingA) Meget letB) LetC) PassendeD) SvaeligrtE) Meget svaeligrt

                                                                                                                                                                      0 0

                                                                                                                                                                      1

                                                                                                                                                                      0 0

                                                                                                                                                                      A B C D E

                                                                                                                                                                      Chart1

                                                                                                                                                                      0
                                                                                                                                                                      0
                                                                                                                                                                      1
                                                                                                                                                                      0
                                                                                                                                                                      0

                                                                                                                                                                      Sheet1

                                                                                                                                                                      DTU Compute

                                                                                                                                                                      2122018Introduction to Medical Image Analysis78 DTU Compute Technical University of Denmark

                                                                                                                                                                      02511 - Mit eget udbytte af dagenA) Jeg har laeligrt meget lidtB) Lidt laeligringC) PassendeD) God laeligringE) Jeg har laeligrt meget

                                                                                                                                                                      0 0

                                                                                                                                                                      2

                                                                                                                                                                      6

                                                                                                                                                                      0

                                                                                                                                                                      A B C D E

                                                                                                                                                                      Chart1

                                                                                                                                                                      0
                                                                                                                                                                      0
                                                                                                                                                                      2
                                                                                                                                                                      6
                                                                                                                                                                      0

                                                                                                                                                                      Sheet1

                                                                                                                                                                      DTU Compute

                                                                                                                                                                      2122018Introduction to Medical Image Analysis79 DTU Compute Technical University of Denmark

                                                                                                                                                                      02512 - Mit eget udbytte af dagenA) Jeg har laeligrt meget lidtB) Lidt laeligringC) PassendeD) God laeligringE) Jeg har laeligrt meget

                                                                                                                                                                      2

                                                                                                                                                                      1

                                                                                                                                                                      3

                                                                                                                                                                      2

                                                                                                                                                                      0

                                                                                                                                                                      A B C D E

                                                                                                                                                                      Chart1

                                                                                                                                                                      2
                                                                                                                                                                      1
                                                                                                                                                                      3
                                                                                                                                                                      2
                                                                                                                                                                      0

                                                                                                                                                                      Sheet1

                                                                                                                                                                      DTU Compute

                                                                                                                                                                      2122018Introduction to Medical Image Analysis80 DTU Compute Technical University of Denmark

                                                                                                                                                                      02511 - Sidste uges oslashvelser (pixelwiseoperations)A) Meget letteB) LetteC) PassendeD) SvaeligreE) Meget svaeligre

                                                                                                                                                                      0 0

                                                                                                                                                                      1

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                                                                                                                                                                      DTU Compute

                                                                                                                                                                      2122018Introduction to Medical Image Analysis81 DTU Compute Technical University of Denmark

                                                                                                                                                                      02512 - Sidste uges oslashvelser (pixelwiseoperations)A) Meget letteB) LetteC) PassendeD) SvaeligreE) Meget svaeligre

                                                                                                                                                                      3

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                                                                                                                                                                      DTU Compute

                                                                                                                                                                      2122018Introduction to Medical Image Analysis82 DTU Compute Technical University of Denmark

                                                                                                                                                                      Denne uges brug af clickersA) click click click ndash jeg bliver

                                                                                                                                                                      sindssygB) For meget clickC) PassendeD) Jeg vil gerne have lidt mereE) Jeg kan ikrsquo faring nok

                                                                                                                                                                      0 0

                                                                                                                                                                      5

                                                                                                                                                                      0

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                                                                                                                                                                      Sheet1

                                                                                                                                                                      DTU Compute

                                                                                                                                                                      2122018Introduction to Medical Image Analysis83 DTU Compute Technical University of Denmark

                                                                                                                                                                      What can you do after today Describe the difference between point processing and neighbourhood

                                                                                                                                                                      processing Compute a rank filtered image using the min max median and

                                                                                                                                                                      difference rank filters Compute a mean filtered image Decide if median or average filtering should be used for noise removal Choose the appropriate image border handling based on a given input

                                                                                                                                                                      image Implement and apply template matching Compute the normalised cross correlation and explain why it should be

                                                                                                                                                                      used Apply given image filter kernels to images Use edge filters on images Describe finite difference approximation of image gradients Describe the concept of edge detection

                                                                                                                                                                      DTU Compute

                                                                                                                                                                      2122018Introduction to Medical Image Analysis84 DTU Compute Technical University of Denmark

                                                                                                                                                                      Oslashvelsesrapport over oslashvelse 4 - 02511 Oslashvelser taeligller cirka 30 af karakteren Skal afleveres senest den 7 marts kl 2359 Kan afleveres af 1 eller 2 personer

                                                                                                                                                                      ndash I skal skrive jeres egen oslashvelsesrapportndash Brug mindst et af jeres egne billeder

                                                                                                                                                                      Afleveres som PDF Lad vaeligre med at kopiere opgaveteksten ind i jeres

                                                                                                                                                                      opgave Put Matlab kode i et Appendix og henvis fra teksten Eksempel rapport over oslashvelse findes paring

                                                                                                                                                                      hjemmesiden under eksamen

                                                                                                                                                                      DTU Compute

                                                                                                                                                                      2122018Introduction to Medical Image Analysis85 DTU Compute Technical University of Denmark

                                                                                                                                                                      Exercises

                                                                                                                                                                      • Introduction to Medical Image Analysis
                                                                                                                                                                      • Lecture 4 ndash Neighbourhood Processing
                                                                                                                                                                      • What can you do after today
                                                                                                                                                                      • Point processing
                                                                                                                                                                      • Point processing
                                                                                                                                                                      • Neighbourhood processing
                                                                                                                                                                      • Use of filtering
                                                                                                                                                                      • Salt and pepper noise
                                                                                                                                                                      • Salt and pepper noise
                                                                                                                                                                      • What is so special about noise
                                                                                                                                                                      • Noise ndash go away
                                                                                                                                                                      • What is the median Value
                                                                                                                                                                      • The median value
                                                                                                                                                                      • Noise away ndash the median filter
                                                                                                                                                                      • Noise removal ndash average filter
                                                                                                                                                                      • Noise removal ndash median filter
                                                                                                                                                                      • Image Filtering
                                                                                                                                                                      • Median filter
                                                                                                                                                                      • Rank filters
                                                                                                                                                                      • Median filter
                                                                                                                                                                      • Correlation
                                                                                                                                                                      • Why do we need similarity
                                                                                                                                                                      • Correlation (1D)
                                                                                                                                                                      • Correlation (1D)
                                                                                                                                                                      • Normalisation
                                                                                                                                                                      • Normalisation
                                                                                                                                                                      • Correlation on images
                                                                                                                                                                      • Correlation on images
                                                                                                                                                                      • Correlation on images
                                                                                                                                                                      • Draw your filter
                                                                                                                                                                      • Correlation on images ndash no normalisation
                                                                                                                                                                      • Correlation on images ndash no normalisation 2
                                                                                                                                                                      • Mathematics of 2D Correlation
                                                                                                                                                                      • Mathematics of 2D Correlation
                                                                                                                                                                      • Mathematics of 2D Correlation
                                                                                                                                                                      • Slide Number 40
                                                                                                                                                                      • 2D Kernel Normalisation
                                                                                                                                                                      • Correlation
                                                                                                                                                                      • Smoothing filters
                                                                                                                                                                      • Use of smoothing
                                                                                                                                                                      • Use of smoothing
                                                                                                                                                                      • Mean filter
                                                                                                                                                                      • Border handling
                                                                                                                                                                      • Border handling ndash extend the input
                                                                                                                                                                      • Correlation with zero padding
                                                                                                                                                                      • Border handling ndash extend the input
                                                                                                                                                                      • Template Matching
                                                                                                                                                                      • Template Matching
                                                                                                                                                                      • Template Matching
                                                                                                                                                                      • Template Matching
                                                                                                                                                                      • Problematic Correlation
                                                                                                                                                                      • Normalised Cross Correlation
                                                                                                                                                                      • Length of template
                                                                                                                                                                      • Length of image patch
                                                                                                                                                                      • Normalised Cross Correlation
                                                                                                                                                                      • Normalised Cross Correlation
                                                                                                                                                                      • Normalised Cross Correlation
                                                                                                                                                                      • Edges
                                                                                                                                                                      • Edges
                                                                                                                                                                      • Finite Difference
                                                                                                                                                                      • Edges
                                                                                                                                                                      • Edges in 2D
                                                                                                                                                                      • Edge filter kernel
                                                                                                                                                                      • Prewitt filter
                                                                                                                                                                      • Edge detection
                                                                                                                                                                      • Edge filtering
                                                                                                                                                                      • 02511 - Niveau af dagens emne forelaeligsing
                                                                                                                                                                      • 02512 - Niveau af dagens emne forelaeligsing
                                                                                                                                                                      • 02511 - Mit eget udbytte af dagen
                                                                                                                                                                      • 02512 - Mit eget udbytte af dagen
                                                                                                                                                                      • 02511 - Sidste uges oslashvelser (pixelwise operations)
                                                                                                                                                                      • 02512 - Sidste uges oslashvelser (pixelwise operations)
                                                                                                                                                                      • Denne uges brug af clickers
                                                                                                                                                                      • What can you do after today
                                                                                                                                                                      • Oslashvelsesrapport over oslashvelse 4 - 02511
                                                                                                                                                                      • Exercises
                                                                                                                                                                        A0
                                                                                                                                                                        B0
                                                                                                                                                                        C5
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                                                                                                                                                                        E6
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                                                                                                                                                                        DTU Compute

                                                                                                                                                                        2122018Introduction to Medical Image Analysis74 DTU Compute Technical University of Denmark

                                                                                                                                                                        Edge filtering

                                                                                                                                                                        A) MeanB) Horizontal SobelC) Vertical PrewittD) Horisontal PrewittE) Median

                                                                                                                                                                        Der udfoslashres en filtrering (correlation) med et filter paring billedet Der bruges ikke coefficient normalization Den filtrerede vaeligrdi i den markerede pixel bliver -119 Hvilket et 3x3 filter blev benyttet

                                                                                                                                                                        0

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                                                                                                                                                                        DTU Compute

                                                                                                                                                                        2122018Introduction to Medical Image Analysis76 DTU Compute Technical University of Denmark

                                                                                                                                                                        02511 - Niveau af dagens emne forelaeligsingA) Meget letB) LetC) PassendeD) SvaeligrtE) Meget svaeligrt

                                                                                                                                                                        23

                                                                                                                                                                        6

                                                                                                                                                                        10

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                                                                                                                                                                        1
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                                                                                                                                                                        DTU Compute

                                                                                                                                                                        2122018Introduction to Medical Image Analysis77 DTU Compute Technical University of Denmark

                                                                                                                                                                        02512 - Niveau af dagens emne forelaeligsingA) Meget letB) LetC) PassendeD) SvaeligrtE) Meget svaeligrt

                                                                                                                                                                        0 0

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                                                                                                                                                                        DTU Compute

                                                                                                                                                                        2122018Introduction to Medical Image Analysis78 DTU Compute Technical University of Denmark

                                                                                                                                                                        02511 - Mit eget udbytte af dagenA) Jeg har laeligrt meget lidtB) Lidt laeligringC) PassendeD) God laeligringE) Jeg har laeligrt meget

                                                                                                                                                                        0 0

                                                                                                                                                                        2

                                                                                                                                                                        6

                                                                                                                                                                        0

                                                                                                                                                                        A B C D E

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                                                                                                                                                                        0
                                                                                                                                                                        2
                                                                                                                                                                        6
                                                                                                                                                                        0

                                                                                                                                                                        Sheet1

                                                                                                                                                                        DTU Compute

                                                                                                                                                                        2122018Introduction to Medical Image Analysis79 DTU Compute Technical University of Denmark

                                                                                                                                                                        02512 - Mit eget udbytte af dagenA) Jeg har laeligrt meget lidtB) Lidt laeligringC) PassendeD) God laeligringE) Jeg har laeligrt meget

                                                                                                                                                                        2

                                                                                                                                                                        1

                                                                                                                                                                        3

                                                                                                                                                                        2

                                                                                                                                                                        0

                                                                                                                                                                        A B C D E

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                                                                                                                                                                        2
                                                                                                                                                                        1
                                                                                                                                                                        3
                                                                                                                                                                        2
                                                                                                                                                                        0

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                                                                                                                                                                        DTU Compute

                                                                                                                                                                        2122018Introduction to Medical Image Analysis80 DTU Compute Technical University of Denmark

                                                                                                                                                                        02511 - Sidste uges oslashvelser (pixelwiseoperations)A) Meget letteB) LetteC) PassendeD) SvaeligreE) Meget svaeligre

                                                                                                                                                                        0 0

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                                                                                                                                                                        DTU Compute

                                                                                                                                                                        2122018Introduction to Medical Image Analysis81 DTU Compute Technical University of Denmark

                                                                                                                                                                        02512 - Sidste uges oslashvelser (pixelwiseoperations)A) Meget letteB) LetteC) PassendeD) SvaeligreE) Meget svaeligre

                                                                                                                                                                        3

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                                                                                                                                                                        0
                                                                                                                                                                        3
                                                                                                                                                                        0
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                                                                                                                                                                        DTU Compute

                                                                                                                                                                        2122018Introduction to Medical Image Analysis82 DTU Compute Technical University of Denmark

                                                                                                                                                                        Denne uges brug af clickersA) click click click ndash jeg bliver

                                                                                                                                                                        sindssygB) For meget clickC) PassendeD) Jeg vil gerne have lidt mereE) Jeg kan ikrsquo faring nok

                                                                                                                                                                        0 0

                                                                                                                                                                        5

                                                                                                                                                                        0

                                                                                                                                                                        6

                                                                                                                                                                        A B C D E

                                                                                                                                                                        Chart1

                                                                                                                                                                        0
                                                                                                                                                                        0
                                                                                                                                                                        5
                                                                                                                                                                        0
                                                                                                                                                                        6

                                                                                                                                                                        Sheet1

                                                                                                                                                                        DTU Compute

                                                                                                                                                                        2122018Introduction to Medical Image Analysis83 DTU Compute Technical University of Denmark

                                                                                                                                                                        What can you do after today Describe the difference between point processing and neighbourhood

                                                                                                                                                                        processing Compute a rank filtered image using the min max median and

                                                                                                                                                                        difference rank filters Compute a mean filtered image Decide if median or average filtering should be used for noise removal Choose the appropriate image border handling based on a given input

                                                                                                                                                                        image Implement and apply template matching Compute the normalised cross correlation and explain why it should be

                                                                                                                                                                        used Apply given image filter kernels to images Use edge filters on images Describe finite difference approximation of image gradients Describe the concept of edge detection

                                                                                                                                                                        DTU Compute

                                                                                                                                                                        2122018Introduction to Medical Image Analysis84 DTU Compute Technical University of Denmark

                                                                                                                                                                        Oslashvelsesrapport over oslashvelse 4 - 02511 Oslashvelser taeligller cirka 30 af karakteren Skal afleveres senest den 7 marts kl 2359 Kan afleveres af 1 eller 2 personer

                                                                                                                                                                        ndash I skal skrive jeres egen oslashvelsesrapportndash Brug mindst et af jeres egne billeder

                                                                                                                                                                        Afleveres som PDF Lad vaeligre med at kopiere opgaveteksten ind i jeres

                                                                                                                                                                        opgave Put Matlab kode i et Appendix og henvis fra teksten Eksempel rapport over oslashvelse findes paring

                                                                                                                                                                        hjemmesiden under eksamen

                                                                                                                                                                        DTU Compute

                                                                                                                                                                        2122018Introduction to Medical Image Analysis85 DTU Compute Technical University of Denmark

                                                                                                                                                                        Exercises

                                                                                                                                                                        • Introduction to Medical Image Analysis
                                                                                                                                                                        • Lecture 4 ndash Neighbourhood Processing
                                                                                                                                                                        • What can you do after today
                                                                                                                                                                        • Point processing
                                                                                                                                                                        • Point processing
                                                                                                                                                                        • Neighbourhood processing
                                                                                                                                                                        • Use of filtering
                                                                                                                                                                        • Salt and pepper noise
                                                                                                                                                                        • Salt and pepper noise
                                                                                                                                                                        • What is so special about noise
                                                                                                                                                                        • Noise ndash go away
                                                                                                                                                                        • What is the median Value
                                                                                                                                                                        • The median value
                                                                                                                                                                        • Noise away ndash the median filter
                                                                                                                                                                        • Noise removal ndash average filter
                                                                                                                                                                        • Noise removal ndash median filter
                                                                                                                                                                        • Image Filtering
                                                                                                                                                                        • Median filter
                                                                                                                                                                        • Rank filters
                                                                                                                                                                        • Median filter
                                                                                                                                                                        • Correlation
                                                                                                                                                                        • Why do we need similarity
                                                                                                                                                                        • Correlation (1D)
                                                                                                                                                                        • Correlation (1D)
                                                                                                                                                                        • Normalisation
                                                                                                                                                                        • Normalisation
                                                                                                                                                                        • Correlation on images
                                                                                                                                                                        • Correlation on images
                                                                                                                                                                        • Correlation on images
                                                                                                                                                                        • Draw your filter
                                                                                                                                                                        • Correlation on images ndash no normalisation
                                                                                                                                                                        • Correlation on images ndash no normalisation 2
                                                                                                                                                                        • Mathematics of 2D Correlation
                                                                                                                                                                        • Mathematics of 2D Correlation
                                                                                                                                                                        • Mathematics of 2D Correlation
                                                                                                                                                                        • Slide Number 40
                                                                                                                                                                        • 2D Kernel Normalisation
                                                                                                                                                                        • Correlation
                                                                                                                                                                        • Smoothing filters
                                                                                                                                                                        • Use of smoothing
                                                                                                                                                                        • Use of smoothing
                                                                                                                                                                        • Mean filter
                                                                                                                                                                        • Border handling
                                                                                                                                                                        • Border handling ndash extend the input
                                                                                                                                                                        • Correlation with zero padding
                                                                                                                                                                        • Border handling ndash extend the input
                                                                                                                                                                        • Template Matching
                                                                                                                                                                        • Template Matching
                                                                                                                                                                        • Template Matching
                                                                                                                                                                        • Template Matching
                                                                                                                                                                        • Problematic Correlation
                                                                                                                                                                        • Normalised Cross Correlation
                                                                                                                                                                        • Length of template
                                                                                                                                                                        • Length of image patch
                                                                                                                                                                        • Normalised Cross Correlation
                                                                                                                                                                        • Normalised Cross Correlation
                                                                                                                                                                        • Normalised Cross Correlation
                                                                                                                                                                        • Edges
                                                                                                                                                                        • Edges
                                                                                                                                                                        • Finite Difference
                                                                                                                                                                        • Edges
                                                                                                                                                                        • Edges in 2D
                                                                                                                                                                        • Edge filter kernel
                                                                                                                                                                        • Prewitt filter
                                                                                                                                                                        • Edge detection
                                                                                                                                                                        • Edge filtering
                                                                                                                                                                        • 02511 - Niveau af dagens emne forelaeligsing
                                                                                                                                                                        • 02512 - Niveau af dagens emne forelaeligsing
                                                                                                                                                                        • 02511 - Mit eget udbytte af dagen
                                                                                                                                                                        • 02512 - Mit eget udbytte af dagen
                                                                                                                                                                        • 02511 - Sidste uges oslashvelser (pixelwise operations)
                                                                                                                                                                        • 02512 - Sidste uges oslashvelser (pixelwise operations)
                                                                                                                                                                        • Denne uges brug af clickers
                                                                                                                                                                        • What can you do after today
                                                                                                                                                                        • Oslashvelsesrapport over oslashvelse 4 - 02511
                                                                                                                                                                        • Exercises
                                                                                                                                                                          A0
                                                                                                                                                                          B0
                                                                                                                                                                          C5
                                                                                                                                                                          D0
                                                                                                                                                                          E6
                                                                                                                                                                          A
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                                                                                                                                                                          D
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                                                                                                                                                                          DTU Compute

                                                                                                                                                                          2122018Introduction to Medical Image Analysis76 DTU Compute Technical University of Denmark

                                                                                                                                                                          02511 - Niveau af dagens emne forelaeligsingA) Meget letB) LetC) PassendeD) SvaeligrtE) Meget svaeligrt

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                                                                                                                                                                          DTU Compute

                                                                                                                                                                          2122018Introduction to Medical Image Analysis77 DTU Compute Technical University of Denmark

                                                                                                                                                                          02512 - Niveau af dagens emne forelaeligsingA) Meget letB) LetC) PassendeD) SvaeligrtE) Meget svaeligrt

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                                                                                                                                                                          DTU Compute

                                                                                                                                                                          2122018Introduction to Medical Image Analysis78 DTU Compute Technical University of Denmark

                                                                                                                                                                          02511 - Mit eget udbytte af dagenA) Jeg har laeligrt meget lidtB) Lidt laeligringC) PassendeD) God laeligringE) Jeg har laeligrt meget

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                                                                                                                                                                          DTU Compute

                                                                                                                                                                          2122018Introduction to Medical Image Analysis79 DTU Compute Technical University of Denmark

                                                                                                                                                                          02512 - Mit eget udbytte af dagenA) Jeg har laeligrt meget lidtB) Lidt laeligringC) PassendeD) God laeligringE) Jeg har laeligrt meget

                                                                                                                                                                          2

                                                                                                                                                                          1

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                                                                                                                                                                          A B C D E

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                                                                                                                                                                          DTU Compute

                                                                                                                                                                          2122018Introduction to Medical Image Analysis80 DTU Compute Technical University of Denmark

                                                                                                                                                                          02511 - Sidste uges oslashvelser (pixelwiseoperations)A) Meget letteB) LetteC) PassendeD) SvaeligreE) Meget svaeligre

                                                                                                                                                                          0 0

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                                                                                                                                                                          DTU Compute

                                                                                                                                                                          2122018Introduction to Medical Image Analysis81 DTU Compute Technical University of Denmark

                                                                                                                                                                          02512 - Sidste uges oslashvelser (pixelwiseoperations)A) Meget letteB) LetteC) PassendeD) SvaeligreE) Meget svaeligre

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                                                                                                                                                                          DTU Compute

                                                                                                                                                                          2122018Introduction to Medical Image Analysis82 DTU Compute Technical University of Denmark

                                                                                                                                                                          Denne uges brug af clickersA) click click click ndash jeg bliver

                                                                                                                                                                          sindssygB) For meget clickC) PassendeD) Jeg vil gerne have lidt mereE) Jeg kan ikrsquo faring nok

                                                                                                                                                                          0 0

                                                                                                                                                                          5

                                                                                                                                                                          0

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                                                                                                                                                                          A B C D E

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                                                                                                                                                                          6

                                                                                                                                                                          Sheet1

                                                                                                                                                                          DTU Compute

                                                                                                                                                                          2122018Introduction to Medical Image Analysis83 DTU Compute Technical University of Denmark

                                                                                                                                                                          What can you do after today Describe the difference between point processing and neighbourhood

                                                                                                                                                                          processing Compute a rank filtered image using the min max median and

                                                                                                                                                                          difference rank filters Compute a mean filtered image Decide if median or average filtering should be used for noise removal Choose the appropriate image border handling based on a given input

                                                                                                                                                                          image Implement and apply template matching Compute the normalised cross correlation and explain why it should be

                                                                                                                                                                          used Apply given image filter kernels to images Use edge filters on images Describe finite difference approximation of image gradients Describe the concept of edge detection

                                                                                                                                                                          DTU Compute

                                                                                                                                                                          2122018Introduction to Medical Image Analysis84 DTU Compute Technical University of Denmark

                                                                                                                                                                          Oslashvelsesrapport over oslashvelse 4 - 02511 Oslashvelser taeligller cirka 30 af karakteren Skal afleveres senest den 7 marts kl 2359 Kan afleveres af 1 eller 2 personer

                                                                                                                                                                          ndash I skal skrive jeres egen oslashvelsesrapportndash Brug mindst et af jeres egne billeder

                                                                                                                                                                          Afleveres som PDF Lad vaeligre med at kopiere opgaveteksten ind i jeres

                                                                                                                                                                          opgave Put Matlab kode i et Appendix og henvis fra teksten Eksempel rapport over oslashvelse findes paring

                                                                                                                                                                          hjemmesiden under eksamen

                                                                                                                                                                          DTU Compute

                                                                                                                                                                          2122018Introduction to Medical Image Analysis85 DTU Compute Technical University of Denmark

                                                                                                                                                                          Exercises

                                                                                                                                                                          • Introduction to Medical Image Analysis
                                                                                                                                                                          • Lecture 4 ndash Neighbourhood Processing
                                                                                                                                                                          • What can you do after today
                                                                                                                                                                          • Point processing
                                                                                                                                                                          • Point processing
                                                                                                                                                                          • Neighbourhood processing
                                                                                                                                                                          • Use of filtering
                                                                                                                                                                          • Salt and pepper noise
                                                                                                                                                                          • Salt and pepper noise
                                                                                                                                                                          • What is so special about noise
                                                                                                                                                                          • Noise ndash go away
                                                                                                                                                                          • What is the median Value
                                                                                                                                                                          • The median value
                                                                                                                                                                          • Noise away ndash the median filter
                                                                                                                                                                          • Noise removal ndash average filter
                                                                                                                                                                          • Noise removal ndash median filter
                                                                                                                                                                          • Image Filtering
                                                                                                                                                                          • Median filter
                                                                                                                                                                          • Rank filters
                                                                                                                                                                          • Median filter
                                                                                                                                                                          • Correlation
                                                                                                                                                                          • Why do we need similarity
                                                                                                                                                                          • Correlation (1D)
                                                                                                                                                                          • Correlation (1D)
                                                                                                                                                                          • Normalisation
                                                                                                                                                                          • Normalisation
                                                                                                                                                                          • Correlation on images
                                                                                                                                                                          • Correlation on images
                                                                                                                                                                          • Correlation on images
                                                                                                                                                                          • Draw your filter
                                                                                                                                                                          • Correlation on images ndash no normalisation
                                                                                                                                                                          • Correlation on images ndash no normalisation 2
                                                                                                                                                                          • Mathematics of 2D Correlation
                                                                                                                                                                          • Mathematics of 2D Correlation
                                                                                                                                                                          • Mathematics of 2D Correlation
                                                                                                                                                                          • Slide Number 40
                                                                                                                                                                          • 2D Kernel Normalisation
                                                                                                                                                                          • Correlation
                                                                                                                                                                          • Smoothing filters
                                                                                                                                                                          • Use of smoothing
                                                                                                                                                                          • Use of smoothing
                                                                                                                                                                          • Mean filter
                                                                                                                                                                          • Border handling
                                                                                                                                                                          • Border handling ndash extend the input
                                                                                                                                                                          • Correlation with zero padding
                                                                                                                                                                          • Border handling ndash extend the input
                                                                                                                                                                          • Template Matching
                                                                                                                                                                          • Template Matching
                                                                                                                                                                          • Template Matching
                                                                                                                                                                          • Template Matching
                                                                                                                                                                          • Problematic Correlation
                                                                                                                                                                          • Normalised Cross Correlation
                                                                                                                                                                          • Length of template
                                                                                                                                                                          • Length of image patch
                                                                                                                                                                          • Normalised Cross Correlation
                                                                                                                                                                          • Normalised Cross Correlation
                                                                                                                                                                          • Normalised Cross Correlation
                                                                                                                                                                          • Edges
                                                                                                                                                                          • Edges
                                                                                                                                                                          • Finite Difference
                                                                                                                                                                          • Edges
                                                                                                                                                                          • Edges in 2D
                                                                                                                                                                          • Edge filter kernel
                                                                                                                                                                          • Prewitt filter
                                                                                                                                                                          • Edge detection
                                                                                                                                                                          • Edge filtering
                                                                                                                                                                          • 02511 - Niveau af dagens emne forelaeligsing
                                                                                                                                                                          • 02512 - Niveau af dagens emne forelaeligsing
                                                                                                                                                                          • 02511 - Mit eget udbytte af dagen
                                                                                                                                                                          • 02512 - Mit eget udbytte af dagen
                                                                                                                                                                          • 02511 - Sidste uges oslashvelser (pixelwise operations)
                                                                                                                                                                          • 02512 - Sidste uges oslashvelser (pixelwise operations)
                                                                                                                                                                          • Denne uges brug af clickers
                                                                                                                                                                          • What can you do after today
                                                                                                                                                                          • Oslashvelsesrapport over oslashvelse 4 - 02511
                                                                                                                                                                          • Exercises
                                                                                                                                                                            A0
                                                                                                                                                                            B0
                                                                                                                                                                            C5
                                                                                                                                                                            D0
                                                                                                                                                                            E6
                                                                                                                                                                            A
                                                                                                                                                                            B
                                                                                                                                                                            C
                                                                                                                                                                            D
                                                                                                                                                                            E
                                                                                                                                                                            A3
                                                                                                                                                                            B0
                                                                                                                                                                            C3
                                                                                                                                                                            D0
                                                                                                                                                                            E0
                                                                                                                                                                            A
                                                                                                                                                                            B
                                                                                                                                                                            C
                                                                                                                                                                            D
                                                                                                                                                                            E
                                                                                                                                                                            A0
                                                                                                                                                                            B0
                                                                                                                                                                            C1
                                                                                                                                                                            D4
                                                                                                                                                                            E1
                                                                                                                                                                            A
                                                                                                                                                                            B
                                                                                                                                                                            C
                                                                                                                                                                            D
                                                                                                                                                                            E
                                                                                                                                                                            A2
                                                                                                                                                                            B1
                                                                                                                                                                            C3
                                                                                                                                                                            D2
                                                                                                                                                                            E0
                                                                                                                                                                            A
                                                                                                                                                                            B
                                                                                                                                                                            C
                                                                                                                                                                            D
                                                                                                                                                                            E
                                                                                                                                                                            A0
                                                                                                                                                                            B0
                                                                                                                                                                            C2
                                                                                                                                                                            D6
                                                                                                                                                                            E0
                                                                                                                                                                            A
                                                                                                                                                                            B
                                                                                                                                                                            C
                                                                                                                                                                            D
                                                                                                                                                                            E
                                                                                                                                                                            A0
                                                                                                                                                                            B0
                                                                                                                                                                            C1
                                                                                                                                                                            D0
                                                                                                                                                                            E0
                                                                                                                                                                            A
                                                                                                                                                                            B
                                                                                                                                                                            C
                                                                                                                                                                            D
                                                                                                                                                                            E
                                                                                                                                                                            A2
                                                                                                                                                                            B3
                                                                                                                                                                            C6
                                                                                                                                                                            D1
                                                                                                                                                                            E0
                                                                                                                                                                            A
                                                                                                                                                                            B
                                                                                                                                                                            C
                                                                                                                                                                            D
                                                                                                                                                                            E
                                                                                                                                                                            A0
                                                                                                                                                                            B8
                                                                                                                                                                            C1
                                                                                                                                                                            D1
                                                                                                                                                                            E0
                                                                                                                                                                            A
                                                                                                                                                                            B
                                                                                                                                                                            C
                                                                                                                                                                            D
                                                                                                                                                                            E

                                                                                                                                                                            Sheet1

                                                                                                                                                                            DTU Compute

                                                                                                                                                                            2122018Introduction to Medical Image Analysis76 DTU Compute Technical University of Denmark

                                                                                                                                                                            02511 - Niveau af dagens emne forelaeligsingA) Meget letB) LetC) PassendeD) SvaeligrtE) Meget svaeligrt

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                                                                                                                                                                            0

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                                                                                                                                                                            DTU Compute

                                                                                                                                                                            2122018Introduction to Medical Image Analysis77 DTU Compute Technical University of Denmark

                                                                                                                                                                            02512 - Niveau af dagens emne forelaeligsingA) Meget letB) LetC) PassendeD) SvaeligrtE) Meget svaeligrt

                                                                                                                                                                            0 0

                                                                                                                                                                            1

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                                                                                                                                                                            0

                                                                                                                                                                            Sheet1

                                                                                                                                                                            DTU Compute

                                                                                                                                                                            2122018Introduction to Medical Image Analysis78 DTU Compute Technical University of Denmark

                                                                                                                                                                            02511 - Mit eget udbytte af dagenA) Jeg har laeligrt meget lidtB) Lidt laeligringC) PassendeD) God laeligringE) Jeg har laeligrt meget

                                                                                                                                                                            0 0

                                                                                                                                                                            2

                                                                                                                                                                            6

                                                                                                                                                                            0

                                                                                                                                                                            A B C D E

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                                                                                                                                                                            0
                                                                                                                                                                            2
                                                                                                                                                                            6
                                                                                                                                                                            0

                                                                                                                                                                            Sheet1

                                                                                                                                                                            DTU Compute

                                                                                                                                                                            2122018Introduction to Medical Image Analysis79 DTU Compute Technical University of Denmark

                                                                                                                                                                            02512 - Mit eget udbytte af dagenA) Jeg har laeligrt meget lidtB) Lidt laeligringC) PassendeD) God laeligringE) Jeg har laeligrt meget

                                                                                                                                                                            2

                                                                                                                                                                            1

                                                                                                                                                                            3

                                                                                                                                                                            2

                                                                                                                                                                            0

                                                                                                                                                                            A B C D E

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                                                                                                                                                                            3
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                                                                                                                                                                            0

                                                                                                                                                                            Sheet1

                                                                                                                                                                            DTU Compute

                                                                                                                                                                            2122018Introduction to Medical Image Analysis80 DTU Compute Technical University of Denmark

                                                                                                                                                                            02511 - Sidste uges oslashvelser (pixelwiseoperations)A) Meget letteB) LetteC) PassendeD) SvaeligreE) Meget svaeligre

                                                                                                                                                                            0 0

                                                                                                                                                                            1

                                                                                                                                                                            4

                                                                                                                                                                            1

                                                                                                                                                                            A B C D E

                                                                                                                                                                            Chart1

                                                                                                                                                                            0
                                                                                                                                                                            0
                                                                                                                                                                            1
                                                                                                                                                                            4
                                                                                                                                                                            1

                                                                                                                                                                            Sheet1

                                                                                                                                                                            DTU Compute

                                                                                                                                                                            2122018Introduction to Medical Image Analysis81 DTU Compute Technical University of Denmark

                                                                                                                                                                            02512 - Sidste uges oslashvelser (pixelwiseoperations)A) Meget letteB) LetteC) PassendeD) SvaeligreE) Meget svaeligre

                                                                                                                                                                            3

                                                                                                                                                                            0

                                                                                                                                                                            3

                                                                                                                                                                            0 0

                                                                                                                                                                            A B C D E

                                                                                                                                                                            Chart1

                                                                                                                                                                            3
                                                                                                                                                                            0
                                                                                                                                                                            3
                                                                                                                                                                            0
                                                                                                                                                                            0

                                                                                                                                                                            Sheet1

                                                                                                                                                                            DTU Compute

                                                                                                                                                                            2122018Introduction to Medical Image Analysis82 DTU Compute Technical University of Denmark

                                                                                                                                                                            Denne uges brug af clickersA) click click click ndash jeg bliver

                                                                                                                                                                            sindssygB) For meget clickC) PassendeD) Jeg vil gerne have lidt mereE) Jeg kan ikrsquo faring nok

                                                                                                                                                                            0 0

                                                                                                                                                                            5

                                                                                                                                                                            0

                                                                                                                                                                            6

                                                                                                                                                                            A B C D E

                                                                                                                                                                            Chart1

                                                                                                                                                                            0
                                                                                                                                                                            0
                                                                                                                                                                            5
                                                                                                                                                                            0
                                                                                                                                                                            6

                                                                                                                                                                            Sheet1

                                                                                                                                                                            DTU Compute

                                                                                                                                                                            2122018Introduction to Medical Image Analysis83 DTU Compute Technical University of Denmark

                                                                                                                                                                            What can you do after today Describe the difference between point processing and neighbourhood

                                                                                                                                                                            processing Compute a rank filtered image using the min max median and

                                                                                                                                                                            difference rank filters Compute a mean filtered image Decide if median or average filtering should be used for noise removal Choose the appropriate image border handling based on a given input

                                                                                                                                                                            image Implement and apply template matching Compute the normalised cross correlation and explain why it should be

                                                                                                                                                                            used Apply given image filter kernels to images Use edge filters on images Describe finite difference approximation of image gradients Describe the concept of edge detection

                                                                                                                                                                            DTU Compute

                                                                                                                                                                            2122018Introduction to Medical Image Analysis84 DTU Compute Technical University of Denmark

                                                                                                                                                                            Oslashvelsesrapport over oslashvelse 4 - 02511 Oslashvelser taeligller cirka 30 af karakteren Skal afleveres senest den 7 marts kl 2359 Kan afleveres af 1 eller 2 personer

                                                                                                                                                                            ndash I skal skrive jeres egen oslashvelsesrapportndash Brug mindst et af jeres egne billeder

                                                                                                                                                                            Afleveres som PDF Lad vaeligre med at kopiere opgaveteksten ind i jeres

                                                                                                                                                                            opgave Put Matlab kode i et Appendix og henvis fra teksten Eksempel rapport over oslashvelse findes paring

                                                                                                                                                                            hjemmesiden under eksamen

                                                                                                                                                                            DTU Compute

                                                                                                                                                                            2122018Introduction to Medical Image Analysis85 DTU Compute Technical University of Denmark

                                                                                                                                                                            Exercises

                                                                                                                                                                            • Introduction to Medical Image Analysis
                                                                                                                                                                            • Lecture 4 ndash Neighbourhood Processing
                                                                                                                                                                            • What can you do after today
                                                                                                                                                                            • Point processing
                                                                                                                                                                            • Point processing
                                                                                                                                                                            • Neighbourhood processing
                                                                                                                                                                            • Use of filtering
                                                                                                                                                                            • Salt and pepper noise
                                                                                                                                                                            • Salt and pepper noise
                                                                                                                                                                            • What is so special about noise
                                                                                                                                                                            • Noise ndash go away
                                                                                                                                                                            • What is the median Value
                                                                                                                                                                            • The median value
                                                                                                                                                                            • Noise away ndash the median filter
                                                                                                                                                                            • Noise removal ndash average filter
                                                                                                                                                                            • Noise removal ndash median filter
                                                                                                                                                                            • Image Filtering
                                                                                                                                                                            • Median filter
                                                                                                                                                                            • Rank filters
                                                                                                                                                                            • Median filter
                                                                                                                                                                            • Correlation
                                                                                                                                                                            • Why do we need similarity
                                                                                                                                                                            • Correlation (1D)
                                                                                                                                                                            • Correlation (1D)
                                                                                                                                                                            • Normalisation
                                                                                                                                                                            • Normalisation
                                                                                                                                                                            • Correlation on images
                                                                                                                                                                            • Correlation on images
                                                                                                                                                                            • Correlation on images
                                                                                                                                                                            • Draw your filter
                                                                                                                                                                            • Correlation on images ndash no normalisation
                                                                                                                                                                            • Correlation on images ndash no normalisation 2
                                                                                                                                                                            • Mathematics of 2D Correlation
                                                                                                                                                                            • Mathematics of 2D Correlation
                                                                                                                                                                            • Mathematics of 2D Correlation
                                                                                                                                                                            • Slide Number 40
                                                                                                                                                                            • 2D Kernel Normalisation
                                                                                                                                                                            • Correlation
                                                                                                                                                                            • Smoothing filters
                                                                                                                                                                            • Use of smoothing
                                                                                                                                                                            • Use of smoothing
                                                                                                                                                                            • Mean filter
                                                                                                                                                                            • Border handling
                                                                                                                                                                            • Border handling ndash extend the input
                                                                                                                                                                            • Correlation with zero padding
                                                                                                                                                                            • Border handling ndash extend the input
                                                                                                                                                                            • Template Matching
                                                                                                                                                                            • Template Matching
                                                                                                                                                                            • Template Matching
                                                                                                                                                                            • Template Matching
                                                                                                                                                                            • Problematic Correlation
                                                                                                                                                                            • Normalised Cross Correlation
                                                                                                                                                                            • Length of template
                                                                                                                                                                            • Length of image patch
                                                                                                                                                                            • Normalised Cross Correlation
                                                                                                                                                                            • Normalised Cross Correlation
                                                                                                                                                                            • Normalised Cross Correlation
                                                                                                                                                                            • Edges
                                                                                                                                                                            • Edges
                                                                                                                                                                            • Finite Difference
                                                                                                                                                                            • Edges
                                                                                                                                                                            • Edges in 2D
                                                                                                                                                                            • Edge filter kernel
                                                                                                                                                                            • Prewitt filter
                                                                                                                                                                            • Edge detection
                                                                                                                                                                            • Edge filtering
                                                                                                                                                                            • 02511 - Niveau af dagens emne forelaeligsing
                                                                                                                                                                            • 02512 - Niveau af dagens emne forelaeligsing
                                                                                                                                                                            • 02511 - Mit eget udbytte af dagen
                                                                                                                                                                            • 02512 - Mit eget udbytte af dagen
                                                                                                                                                                            • 02511 - Sidste uges oslashvelser (pixelwise operations)
                                                                                                                                                                            • 02512 - Sidste uges oslashvelser (pixelwise operations)
                                                                                                                                                                            • Denne uges brug af clickers
                                                                                                                                                                            • What can you do after today
                                                                                                                                                                            • Oslashvelsesrapport over oslashvelse 4 - 02511
                                                                                                                                                                            • Exercises
                                                                                                                                                                              A0
                                                                                                                                                                              B0
                                                                                                                                                                              C5
                                                                                                                                                                              D0
                                                                                                                                                                              E6
                                                                                                                                                                              A
                                                                                                                                                                              B
                                                                                                                                                                              C
                                                                                                                                                                              D
                                                                                                                                                                              E
                                                                                                                                                                              A3
                                                                                                                                                                              B0
                                                                                                                                                                              C3
                                                                                                                                                                              D0
                                                                                                                                                                              E0
                                                                                                                                                                              A
                                                                                                                                                                              B
                                                                                                                                                                              C
                                                                                                                                                                              D
                                                                                                                                                                              E
                                                                                                                                                                              A0
                                                                                                                                                                              B0
                                                                                                                                                                              C1
                                                                                                                                                                              D4
                                                                                                                                                                              E1
                                                                                                                                                                              A
                                                                                                                                                                              B
                                                                                                                                                                              C
                                                                                                                                                                              D
                                                                                                                                                                              E
                                                                                                                                                                              A2
                                                                                                                                                                              B1
                                                                                                                                                                              C3
                                                                                                                                                                              D2
                                                                                                                                                                              E0
                                                                                                                                                                              A
                                                                                                                                                                              B
                                                                                                                                                                              C
                                                                                                                                                                              D
                                                                                                                                                                              E
                                                                                                                                                                              A0
                                                                                                                                                                              B0
                                                                                                                                                                              C2
                                                                                                                                                                              D6
                                                                                                                                                                              E0
                                                                                                                                                                              A
                                                                                                                                                                              B
                                                                                                                                                                              C
                                                                                                                                                                              D
                                                                                                                                                                              E
                                                                                                                                                                              A0
                                                                                                                                                                              B0
                                                                                                                                                                              C1
                                                                                                                                                                              D0
                                                                                                                                                                              E0
                                                                                                                                                                              A
                                                                                                                                                                              B
                                                                                                                                                                              C
                                                                                                                                                                              D
                                                                                                                                                                              E
                                                                                                                                                                              A2
                                                                                                                                                                              B3
                                                                                                                                                                              C6
                                                                                                                                                                              D1
                                                                                                                                                                              E0
                                                                                                                                                                              A
                                                                                                                                                                              B
                                                                                                                                                                              C
                                                                                                                                                                              D
                                                                                                                                                                              E
                                                                                                                                                                              A0
                                                                                                                                                                              B8
                                                                                                                                                                              C1
                                                                                                                                                                              D1
                                                                                                                                                                              E0

                                                                                                                                                                              DTU Compute

                                                                                                                                                                              2122018Introduction to Medical Image Analysis76 DTU Compute Technical University of Denmark

                                                                                                                                                                              02511 - Niveau af dagens emne forelaeligsingA) Meget letB) LetC) PassendeD) SvaeligrtE) Meget svaeligrt

                                                                                                                                                                              23

                                                                                                                                                                              6

                                                                                                                                                                              10

                                                                                                                                                                              A B C D E

                                                                                                                                                                              Chart1

                                                                                                                                                                              2
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                                                                                                                                                                              6
                                                                                                                                                                              1
                                                                                                                                                                              0

                                                                                                                                                                              Sheet1

                                                                                                                                                                              DTU Compute

                                                                                                                                                                              2122018Introduction to Medical Image Analysis77 DTU Compute Technical University of Denmark

                                                                                                                                                                              02512 - Niveau af dagens emne forelaeligsingA) Meget letB) LetC) PassendeD) SvaeligrtE) Meget svaeligrt

                                                                                                                                                                              0 0

                                                                                                                                                                              1

                                                                                                                                                                              0 0

                                                                                                                                                                              A B C D E

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                                                                                                                                                                              DTU Compute

                                                                                                                                                                              2122018Introduction to Medical Image Analysis78 DTU Compute Technical University of Denmark

                                                                                                                                                                              02511 - Mit eget udbytte af dagenA) Jeg har laeligrt meget lidtB) Lidt laeligringC) PassendeD) God laeligringE) Jeg har laeligrt meget

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                                                                                                                                                                              DTU Compute

                                                                                                                                                                              2122018Introduction to Medical Image Analysis79 DTU Compute Technical University of Denmark

                                                                                                                                                                              02512 - Mit eget udbytte af dagenA) Jeg har laeligrt meget lidtB) Lidt laeligringC) PassendeD) God laeligringE) Jeg har laeligrt meget

                                                                                                                                                                              2

                                                                                                                                                                              1

                                                                                                                                                                              3

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                                                                                                                                                                              0

                                                                                                                                                                              A B C D E

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                                                                                                                                                                              3
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                                                                                                                                                                              DTU Compute

                                                                                                                                                                              2122018Introduction to Medical Image Analysis80 DTU Compute Technical University of Denmark

                                                                                                                                                                              02511 - Sidste uges oslashvelser (pixelwiseoperations)A) Meget letteB) LetteC) PassendeD) SvaeligreE) Meget svaeligre

                                                                                                                                                                              0 0

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                                                                                                                                                                              DTU Compute

                                                                                                                                                                              2122018Introduction to Medical Image Analysis81 DTU Compute Technical University of Denmark

                                                                                                                                                                              02512 - Sidste uges oslashvelser (pixelwiseoperations)A) Meget letteB) LetteC) PassendeD) SvaeligreE) Meget svaeligre

                                                                                                                                                                              3

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                                                                                                                                                                              DTU Compute

                                                                                                                                                                              2122018Introduction to Medical Image Analysis82 DTU Compute Technical University of Denmark

                                                                                                                                                                              Denne uges brug af clickersA) click click click ndash jeg bliver

                                                                                                                                                                              sindssygB) For meget clickC) PassendeD) Jeg vil gerne have lidt mereE) Jeg kan ikrsquo faring nok

                                                                                                                                                                              0 0

                                                                                                                                                                              5

                                                                                                                                                                              0

                                                                                                                                                                              6

                                                                                                                                                                              A B C D E

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                                                                                                                                                                              Sheet1

                                                                                                                                                                              DTU Compute

                                                                                                                                                                              2122018Introduction to Medical Image Analysis83 DTU Compute Technical University of Denmark

                                                                                                                                                                              What can you do after today Describe the difference between point processing and neighbourhood

                                                                                                                                                                              processing Compute a rank filtered image using the min max median and

                                                                                                                                                                              difference rank filters Compute a mean filtered image Decide if median or average filtering should be used for noise removal Choose the appropriate image border handling based on a given input

                                                                                                                                                                              image Implement and apply template matching Compute the normalised cross correlation and explain why it should be

                                                                                                                                                                              used Apply given image filter kernels to images Use edge filters on images Describe finite difference approximation of image gradients Describe the concept of edge detection

                                                                                                                                                                              DTU Compute

                                                                                                                                                                              2122018Introduction to Medical Image Analysis84 DTU Compute Technical University of Denmark

                                                                                                                                                                              Oslashvelsesrapport over oslashvelse 4 - 02511 Oslashvelser taeligller cirka 30 af karakteren Skal afleveres senest den 7 marts kl 2359 Kan afleveres af 1 eller 2 personer

                                                                                                                                                                              ndash I skal skrive jeres egen oslashvelsesrapportndash Brug mindst et af jeres egne billeder

                                                                                                                                                                              Afleveres som PDF Lad vaeligre med at kopiere opgaveteksten ind i jeres

                                                                                                                                                                              opgave Put Matlab kode i et Appendix og henvis fra teksten Eksempel rapport over oslashvelse findes paring

                                                                                                                                                                              hjemmesiden under eksamen

                                                                                                                                                                              DTU Compute

                                                                                                                                                                              2122018Introduction to Medical Image Analysis85 DTU Compute Technical University of Denmark

                                                                                                                                                                              Exercises

                                                                                                                                                                              • Introduction to Medical Image Analysis
                                                                                                                                                                              • Lecture 4 ndash Neighbourhood Processing
                                                                                                                                                                              • What can you do after today
                                                                                                                                                                              • Point processing
                                                                                                                                                                              • Point processing
                                                                                                                                                                              • Neighbourhood processing
                                                                                                                                                                              • Use of filtering
                                                                                                                                                                              • Salt and pepper noise
                                                                                                                                                                              • Salt and pepper noise
                                                                                                                                                                              • What is so special about noise
                                                                                                                                                                              • Noise ndash go away
                                                                                                                                                                              • What is the median Value
                                                                                                                                                                              • The median value
                                                                                                                                                                              • Noise away ndash the median filter
                                                                                                                                                                              • Noise removal ndash average filter
                                                                                                                                                                              • Noise removal ndash median filter
                                                                                                                                                                              • Image Filtering
                                                                                                                                                                              • Median filter
                                                                                                                                                                              • Rank filters
                                                                                                                                                                              • Median filter
                                                                                                                                                                              • Correlation
                                                                                                                                                                              • Why do we need similarity
                                                                                                                                                                              • Correlation (1D)
                                                                                                                                                                              • Correlation (1D)
                                                                                                                                                                              • Normalisation
                                                                                                                                                                              • Normalisation
                                                                                                                                                                              • Correlation on images
                                                                                                                                                                              • Correlation on images
                                                                                                                                                                              • Correlation on images
                                                                                                                                                                              • Draw your filter
                                                                                                                                                                              • Correlation on images ndash no normalisation
                                                                                                                                                                              • Correlation on images ndash no normalisation 2
                                                                                                                                                                              • Mathematics of 2D Correlation
                                                                                                                                                                              • Mathematics of 2D Correlation
                                                                                                                                                                              • Mathematics of 2D Correlation
                                                                                                                                                                              • Slide Number 40
                                                                                                                                                                              • 2D Kernel Normalisation
                                                                                                                                                                              • Correlation
                                                                                                                                                                              • Smoothing filters
                                                                                                                                                                              • Use of smoothing
                                                                                                                                                                              • Use of smoothing
                                                                                                                                                                              • Mean filter
                                                                                                                                                                              • Border handling
                                                                                                                                                                              • Border handling ndash extend the input
                                                                                                                                                                              • Correlation with zero padding
                                                                                                                                                                              • Border handling ndash extend the input
                                                                                                                                                                              • Template Matching
                                                                                                                                                                              • Template Matching
                                                                                                                                                                              • Template Matching
                                                                                                                                                                              • Template Matching
                                                                                                                                                                              • Problematic Correlation
                                                                                                                                                                              • Normalised Cross Correlation
                                                                                                                                                                              • Length of template
                                                                                                                                                                              • Length of image patch
                                                                                                                                                                              • Normalised Cross Correlation
                                                                                                                                                                              • Normalised Cross Correlation
                                                                                                                                                                              • Normalised Cross Correlation
                                                                                                                                                                              • Edges
                                                                                                                                                                              • Edges
                                                                                                                                                                              • Finite Difference
                                                                                                                                                                              • Edges
                                                                                                                                                                              • Edges in 2D
                                                                                                                                                                              • Edge filter kernel
                                                                                                                                                                              • Prewitt filter
                                                                                                                                                                              • Edge detection
                                                                                                                                                                              • Edge filtering
                                                                                                                                                                              • 02511 - Niveau af dagens emne forelaeligsing
                                                                                                                                                                              • 02512 - Niveau af dagens emne forelaeligsing
                                                                                                                                                                              • 02511 - Mit eget udbytte af dagen
                                                                                                                                                                              • 02512 - Mit eget udbytte af dagen
                                                                                                                                                                              • 02511 - Sidste uges oslashvelser (pixelwise operations)
                                                                                                                                                                              • 02512 - Sidste uges oslashvelser (pixelwise operations)
                                                                                                                                                                              • Denne uges brug af clickers
                                                                                                                                                                              • What can you do after today
                                                                                                                                                                              • Oslashvelsesrapport over oslashvelse 4 - 02511
                                                                                                                                                                              • Exercises
                                                                                                                                                                                A0
                                                                                                                                                                                B0
                                                                                                                                                                                C5
                                                                                                                                                                                D0
                                                                                                                                                                                E6
                                                                                                                                                                                A
                                                                                                                                                                                B
                                                                                                                                                                                C
                                                                                                                                                                                D
                                                                                                                                                                                E
                                                                                                                                                                                A3
                                                                                                                                                                                B0
                                                                                                                                                                                C3
                                                                                                                                                                                D0
                                                                                                                                                                                E0
                                                                                                                                                                                A
                                                                                                                                                                                B
                                                                                                                                                                                C
                                                                                                                                                                                D
                                                                                                                                                                                E
                                                                                                                                                                                A0
                                                                                                                                                                                B0
                                                                                                                                                                                C1
                                                                                                                                                                                D4
                                                                                                                                                                                E1
                                                                                                                                                                                A
                                                                                                                                                                                B
                                                                                                                                                                                C
                                                                                                                                                                                D
                                                                                                                                                                                E
                                                                                                                                                                                A2
                                                                                                                                                                                B1
                                                                                                                                                                                C3
                                                                                                                                                                                D2
                                                                                                                                                                                E0
                                                                                                                                                                                A
                                                                                                                                                                                B
                                                                                                                                                                                C
                                                                                                                                                                                D
                                                                                                                                                                                E
                                                                                                                                                                                A0
                                                                                                                                                                                B0
                                                                                                                                                                                C2
                                                                                                                                                                                D6
                                                                                                                                                                                E0
                                                                                                                                                                                A
                                                                                                                                                                                B
                                                                                                                                                                                C
                                                                                                                                                                                D
                                                                                                                                                                                E
                                                                                                                                                                                A0
                                                                                                                                                                                B0
                                                                                                                                                                                C1
                                                                                                                                                                                D0
                                                                                                                                                                                E0
                                                                                                                                                                                A
                                                                                                                                                                                B
                                                                                                                                                                                C
                                                                                                                                                                                D
                                                                                                                                                                                E
                                                                                                                                                                                A2
                                                                                                                                                                                B3
                                                                                                                                                                                C6
                                                                                                                                                                                D1
                                                                                                                                                                                E0
                                                                                                                                                                                A
                                                                                                                                                                                B
                                                                                                                                                                                C
                                                                                                                                                                                D
                                                                                                                                                                                E

                                                                                                                                                                                Chart1

                                                                                                                                                                                2
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                                                                                                                                                                                6
                                                                                                                                                                                1
                                                                                                                                                                                0

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                                                                                                                                                                                DTU Compute

                                                                                                                                                                                2122018Introduction to Medical Image Analysis77 DTU Compute Technical University of Denmark

                                                                                                                                                                                02512 - Niveau af dagens emne forelaeligsingA) Meget letB) LetC) PassendeD) SvaeligrtE) Meget svaeligrt

                                                                                                                                                                                0 0

                                                                                                                                                                                1

                                                                                                                                                                                0 0

                                                                                                                                                                                A B C D E

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                                                                                                                                                                                0
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                                                                                                                                                                                Sheet1

                                                                                                                                                                                DTU Compute

                                                                                                                                                                                2122018Introduction to Medical Image Analysis78 DTU Compute Technical University of Denmark

                                                                                                                                                                                02511 - Mit eget udbytte af dagenA) Jeg har laeligrt meget lidtB) Lidt laeligringC) PassendeD) God laeligringE) Jeg har laeligrt meget

                                                                                                                                                                                0 0

                                                                                                                                                                                2

                                                                                                                                                                                6

                                                                                                                                                                                0

                                                                                                                                                                                A B C D E

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                                                                                                                                                                                0
                                                                                                                                                                                2
                                                                                                                                                                                6
                                                                                                                                                                                0

                                                                                                                                                                                Sheet1

                                                                                                                                                                                DTU Compute

                                                                                                                                                                                2122018Introduction to Medical Image Analysis79 DTU Compute Technical University of Denmark

                                                                                                                                                                                02512 - Mit eget udbytte af dagenA) Jeg har laeligrt meget lidtB) Lidt laeligringC) PassendeD) God laeligringE) Jeg har laeligrt meget

                                                                                                                                                                                2

                                                                                                                                                                                1

                                                                                                                                                                                3

                                                                                                                                                                                2

                                                                                                                                                                                0

                                                                                                                                                                                A B C D E

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                                                                                                                                                                                2
                                                                                                                                                                                1
                                                                                                                                                                                3
                                                                                                                                                                                2
                                                                                                                                                                                0

                                                                                                                                                                                Sheet1

                                                                                                                                                                                DTU Compute

                                                                                                                                                                                2122018Introduction to Medical Image Analysis80 DTU Compute Technical University of Denmark

                                                                                                                                                                                02511 - Sidste uges oslashvelser (pixelwiseoperations)A) Meget letteB) LetteC) PassendeD) SvaeligreE) Meget svaeligre

                                                                                                                                                                                0 0

                                                                                                                                                                                1

                                                                                                                                                                                4

                                                                                                                                                                                1

                                                                                                                                                                                A B C D E

                                                                                                                                                                                Chart1

                                                                                                                                                                                0
                                                                                                                                                                                0
                                                                                                                                                                                1
                                                                                                                                                                                4
                                                                                                                                                                                1

                                                                                                                                                                                Sheet1

                                                                                                                                                                                DTU Compute

                                                                                                                                                                                2122018Introduction to Medical Image Analysis81 DTU Compute Technical University of Denmark

                                                                                                                                                                                02512 - Sidste uges oslashvelser (pixelwiseoperations)A) Meget letteB) LetteC) PassendeD) SvaeligreE) Meget svaeligre

                                                                                                                                                                                3

                                                                                                                                                                                0

                                                                                                                                                                                3

                                                                                                                                                                                0 0

                                                                                                                                                                                A B C D E

                                                                                                                                                                                Chart1

                                                                                                                                                                                3
                                                                                                                                                                                0
                                                                                                                                                                                3
                                                                                                                                                                                0
                                                                                                                                                                                0

                                                                                                                                                                                Sheet1

                                                                                                                                                                                DTU Compute

                                                                                                                                                                                2122018Introduction to Medical Image Analysis82 DTU Compute Technical University of Denmark

                                                                                                                                                                                Denne uges brug af clickersA) click click click ndash jeg bliver

                                                                                                                                                                                sindssygB) For meget clickC) PassendeD) Jeg vil gerne have lidt mereE) Jeg kan ikrsquo faring nok

                                                                                                                                                                                0 0

                                                                                                                                                                                5

                                                                                                                                                                                0

                                                                                                                                                                                6

                                                                                                                                                                                A B C D E

                                                                                                                                                                                Chart1

                                                                                                                                                                                0
                                                                                                                                                                                0
                                                                                                                                                                                5
                                                                                                                                                                                0
                                                                                                                                                                                6

                                                                                                                                                                                Sheet1

                                                                                                                                                                                DTU Compute

                                                                                                                                                                                2122018Introduction to Medical Image Analysis83 DTU Compute Technical University of Denmark

                                                                                                                                                                                What can you do after today Describe the difference between point processing and neighbourhood

                                                                                                                                                                                processing Compute a rank filtered image using the min max median and

                                                                                                                                                                                difference rank filters Compute a mean filtered image Decide if median or average filtering should be used for noise removal Choose the appropriate image border handling based on a given input

                                                                                                                                                                                image Implement and apply template matching Compute the normalised cross correlation and explain why it should be

                                                                                                                                                                                used Apply given image filter kernels to images Use edge filters on images Describe finite difference approximation of image gradients Describe the concept of edge detection

                                                                                                                                                                                DTU Compute

                                                                                                                                                                                2122018Introduction to Medical Image Analysis84 DTU Compute Technical University of Denmark

                                                                                                                                                                                Oslashvelsesrapport over oslashvelse 4 - 02511 Oslashvelser taeligller cirka 30 af karakteren Skal afleveres senest den 7 marts kl 2359 Kan afleveres af 1 eller 2 personer

                                                                                                                                                                                ndash I skal skrive jeres egen oslashvelsesrapportndash Brug mindst et af jeres egne billeder

                                                                                                                                                                                Afleveres som PDF Lad vaeligre med at kopiere opgaveteksten ind i jeres

                                                                                                                                                                                opgave Put Matlab kode i et Appendix og henvis fra teksten Eksempel rapport over oslashvelse findes paring

                                                                                                                                                                                hjemmesiden under eksamen

                                                                                                                                                                                DTU Compute

                                                                                                                                                                                2122018Introduction to Medical Image Analysis85 DTU Compute Technical University of Denmark

                                                                                                                                                                                Exercises

                                                                                                                                                                                • Introduction to Medical Image Analysis
                                                                                                                                                                                • Lecture 4 ndash Neighbourhood Processing
                                                                                                                                                                                • What can you do after today
                                                                                                                                                                                • Point processing
                                                                                                                                                                                • Point processing
                                                                                                                                                                                • Neighbourhood processing
                                                                                                                                                                                • Use of filtering
                                                                                                                                                                                • Salt and pepper noise
                                                                                                                                                                                • Salt and pepper noise
                                                                                                                                                                                • What is so special about noise
                                                                                                                                                                                • Noise ndash go away
                                                                                                                                                                                • What is the median Value
                                                                                                                                                                                • The median value
                                                                                                                                                                                • Noise away ndash the median filter
                                                                                                                                                                                • Noise removal ndash average filter
                                                                                                                                                                                • Noise removal ndash median filter
                                                                                                                                                                                • Image Filtering
                                                                                                                                                                                • Median filter
                                                                                                                                                                                • Rank filters
                                                                                                                                                                                • Median filter
                                                                                                                                                                                • Correlation
                                                                                                                                                                                • Why do we need similarity
                                                                                                                                                                                • Correlation (1D)
                                                                                                                                                                                • Correlation (1D)
                                                                                                                                                                                • Normalisation
                                                                                                                                                                                • Normalisation
                                                                                                                                                                                • Correlation on images
                                                                                                                                                                                • Correlation on images
                                                                                                                                                                                • Correlation on images
                                                                                                                                                                                • Draw your filter
                                                                                                                                                                                • Correlation on images ndash no normalisation
                                                                                                                                                                                • Correlation on images ndash no normalisation 2
                                                                                                                                                                                • Mathematics of 2D Correlation
                                                                                                                                                                                • Mathematics of 2D Correlation
                                                                                                                                                                                • Mathematics of 2D Correlation
                                                                                                                                                                                • Slide Number 40
                                                                                                                                                                                • 2D Kernel Normalisation
                                                                                                                                                                                • Correlation
                                                                                                                                                                                • Smoothing filters
                                                                                                                                                                                • Use of smoothing
                                                                                                                                                                                • Use of smoothing
                                                                                                                                                                                • Mean filter
                                                                                                                                                                                • Border handling
                                                                                                                                                                                • Border handling ndash extend the input
                                                                                                                                                                                • Correlation with zero padding
                                                                                                                                                                                • Border handling ndash extend the input
                                                                                                                                                                                • Template Matching
                                                                                                                                                                                • Template Matching
                                                                                                                                                                                • Template Matching
                                                                                                                                                                                • Template Matching
                                                                                                                                                                                • Problematic Correlation
                                                                                                                                                                                • Normalised Cross Correlation
                                                                                                                                                                                • Length of template
                                                                                                                                                                                • Length of image patch
                                                                                                                                                                                • Normalised Cross Correlation
                                                                                                                                                                                • Normalised Cross Correlation
                                                                                                                                                                                • Normalised Cross Correlation
                                                                                                                                                                                • Edges
                                                                                                                                                                                • Edges
                                                                                                                                                                                • Finite Difference
                                                                                                                                                                                • Edges
                                                                                                                                                                                • Edges in 2D
                                                                                                                                                                                • Edge filter kernel
                                                                                                                                                                                • Prewitt filter
                                                                                                                                                                                • Edge detection
                                                                                                                                                                                • Edge filtering
                                                                                                                                                                                • 02511 - Niveau af dagens emne forelaeligsing
                                                                                                                                                                                • 02512 - Niveau af dagens emne forelaeligsing
                                                                                                                                                                                • 02511 - Mit eget udbytte af dagen
                                                                                                                                                                                • 02512 - Mit eget udbytte af dagen
                                                                                                                                                                                • 02511 - Sidste uges oslashvelser (pixelwise operations)
                                                                                                                                                                                • 02512 - Sidste uges oslashvelser (pixelwise operations)
                                                                                                                                                                                • Denne uges brug af clickers
                                                                                                                                                                                • What can you do after today
                                                                                                                                                                                • Oslashvelsesrapport over oslashvelse 4 - 02511
                                                                                                                                                                                • Exercises
                                                                                                                                                                                  A0
                                                                                                                                                                                  B0
                                                                                                                                                                                  C5
                                                                                                                                                                                  D0
                                                                                                                                                                                  E6
                                                                                                                                                                                  A
                                                                                                                                                                                  B
                                                                                                                                                                                  C
                                                                                                                                                                                  D
                                                                                                                                                                                  E
                                                                                                                                                                                  A3
                                                                                                                                                                                  B0
                                                                                                                                                                                  C3
                                                                                                                                                                                  D0
                                                                                                                                                                                  E0
                                                                                                                                                                                  A
                                                                                                                                                                                  B
                                                                                                                                                                                  C
                                                                                                                                                                                  D
                                                                                                                                                                                  E
                                                                                                                                                                                  A0
                                                                                                                                                                                  B0
                                                                                                                                                                                  C1
                                                                                                                                                                                  D4
                                                                                                                                                                                  E1
                                                                                                                                                                                  A
                                                                                                                                                                                  B
                                                                                                                                                                                  C
                                                                                                                                                                                  D
                                                                                                                                                                                  E
                                                                                                                                                                                  A2
                                                                                                                                                                                  B1
                                                                                                                                                                                  C3
                                                                                                                                                                                  D2
                                                                                                                                                                                  E0
                                                                                                                                                                                  A
                                                                                                                                                                                  B
                                                                                                                                                                                  C
                                                                                                                                                                                  D
                                                                                                                                                                                  E
                                                                                                                                                                                  A0
                                                                                                                                                                                  B0
                                                                                                                                                                                  C2
                                                                                                                                                                                  D6
                                                                                                                                                                                  E0
                                                                                                                                                                                  A
                                                                                                                                                                                  B
                                                                                                                                                                                  C
                                                                                                                                                                                  D
                                                                                                                                                                                  E
                                                                                                                                                                                  A0
                                                                                                                                                                                  B0
                                                                                                                                                                                  C1
                                                                                                                                                                                  D0
                                                                                                                                                                                  E0
                                                                                                                                                                                  A
                                                                                                                                                                                  B
                                                                                                                                                                                  C
                                                                                                                                                                                  D
                                                                                                                                                                                  E
                                                                                                                                                                                  A2
                                                                                                                                                                                  B3
                                                                                                                                                                                  C6
                                                                                                                                                                                  D1
                                                                                                                                                                                  E0
                                                                                                                                                                                  A
                                                                                                                                                                                  B
                                                                                                                                                                                  C
                                                                                                                                                                                  D
                                                                                                                                                                                  E

                                                                                                                                                                                  Sheet1

                                                                                                                                                                                  DTU Compute

                                                                                                                                                                                  2122018Introduction to Medical Image Analysis77 DTU Compute Technical University of Denmark

                                                                                                                                                                                  02512 - Niveau af dagens emne forelaeligsingA) Meget letB) LetC) PassendeD) SvaeligrtE) Meget svaeligrt

                                                                                                                                                                                  0 0

                                                                                                                                                                                  1

                                                                                                                                                                                  0 0

                                                                                                                                                                                  A B C D E

                                                                                                                                                                                  Chart1

                                                                                                                                                                                  0
                                                                                                                                                                                  0
                                                                                                                                                                                  1
                                                                                                                                                                                  0
                                                                                                                                                                                  0

                                                                                                                                                                                  Sheet1

                                                                                                                                                                                  DTU Compute

                                                                                                                                                                                  2122018Introduction to Medical Image Analysis78 DTU Compute Technical University of Denmark

                                                                                                                                                                                  02511 - Mit eget udbytte af dagenA) Jeg har laeligrt meget lidtB) Lidt laeligringC) PassendeD) God laeligringE) Jeg har laeligrt meget

                                                                                                                                                                                  0 0

                                                                                                                                                                                  2

                                                                                                                                                                                  6

                                                                                                                                                                                  0

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                                                                                                                                                                                  DTU Compute

                                                                                                                                                                                  2122018Introduction to Medical Image Analysis79 DTU Compute Technical University of Denmark

                                                                                                                                                                                  02512 - Mit eget udbytte af dagenA) Jeg har laeligrt meget lidtB) Lidt laeligringC) PassendeD) God laeligringE) Jeg har laeligrt meget

                                                                                                                                                                                  2

                                                                                                                                                                                  1

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                                                                                                                                                                                  A B C D E

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                                                                                                                                                                                  DTU Compute

                                                                                                                                                                                  2122018Introduction to Medical Image Analysis80 DTU Compute Technical University of Denmark

                                                                                                                                                                                  02511 - Sidste uges oslashvelser (pixelwiseoperations)A) Meget letteB) LetteC) PassendeD) SvaeligreE) Meget svaeligre

                                                                                                                                                                                  0 0

                                                                                                                                                                                  1

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                                                                                                                                                                                  DTU Compute

                                                                                                                                                                                  2122018Introduction to Medical Image Analysis81 DTU Compute Technical University of Denmark

                                                                                                                                                                                  02512 - Sidste uges oslashvelser (pixelwiseoperations)A) Meget letteB) LetteC) PassendeD) SvaeligreE) Meget svaeligre

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                                                                                                                                                                                  DTU Compute

                                                                                                                                                                                  2122018Introduction to Medical Image Analysis82 DTU Compute Technical University of Denmark

                                                                                                                                                                                  Denne uges brug af clickersA) click click click ndash jeg bliver

                                                                                                                                                                                  sindssygB) For meget clickC) PassendeD) Jeg vil gerne have lidt mereE) Jeg kan ikrsquo faring nok

                                                                                                                                                                                  0 0

                                                                                                                                                                                  5

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                                                                                                                                                                                  Sheet1

                                                                                                                                                                                  DTU Compute

                                                                                                                                                                                  2122018Introduction to Medical Image Analysis83 DTU Compute Technical University of Denmark

                                                                                                                                                                                  What can you do after today Describe the difference between point processing and neighbourhood

                                                                                                                                                                                  processing Compute a rank filtered image using the min max median and

                                                                                                                                                                                  difference rank filters Compute a mean filtered image Decide if median or average filtering should be used for noise removal Choose the appropriate image border handling based on a given input

                                                                                                                                                                                  image Implement and apply template matching Compute the normalised cross correlation and explain why it should be

                                                                                                                                                                                  used Apply given image filter kernels to images Use edge filters on images Describe finite difference approximation of image gradients Describe the concept of edge detection

                                                                                                                                                                                  DTU Compute

                                                                                                                                                                                  2122018Introduction to Medical Image Analysis84 DTU Compute Technical University of Denmark

                                                                                                                                                                                  Oslashvelsesrapport over oslashvelse 4 - 02511 Oslashvelser taeligller cirka 30 af karakteren Skal afleveres senest den 7 marts kl 2359 Kan afleveres af 1 eller 2 personer

                                                                                                                                                                                  ndash I skal skrive jeres egen oslashvelsesrapportndash Brug mindst et af jeres egne billeder

                                                                                                                                                                                  Afleveres som PDF Lad vaeligre med at kopiere opgaveteksten ind i jeres

                                                                                                                                                                                  opgave Put Matlab kode i et Appendix og henvis fra teksten Eksempel rapport over oslashvelse findes paring

                                                                                                                                                                                  hjemmesiden under eksamen

                                                                                                                                                                                  DTU Compute

                                                                                                                                                                                  2122018Introduction to Medical Image Analysis85 DTU Compute Technical University of Denmark

                                                                                                                                                                                  Exercises

                                                                                                                                                                                  • Introduction to Medical Image Analysis
                                                                                                                                                                                  • Lecture 4 ndash Neighbourhood Processing
                                                                                                                                                                                  • What can you do after today
                                                                                                                                                                                  • Point processing
                                                                                                                                                                                  • Point processing
                                                                                                                                                                                  • Neighbourhood processing
                                                                                                                                                                                  • Use of filtering
                                                                                                                                                                                  • Salt and pepper noise
                                                                                                                                                                                  • Salt and pepper noise
                                                                                                                                                                                  • What is so special about noise
                                                                                                                                                                                  • Noise ndash go away
                                                                                                                                                                                  • What is the median Value
                                                                                                                                                                                  • The median value
                                                                                                                                                                                  • Noise away ndash the median filter
                                                                                                                                                                                  • Noise removal ndash average filter
                                                                                                                                                                                  • Noise removal ndash median filter
                                                                                                                                                                                  • Image Filtering
                                                                                                                                                                                  • Median filter
                                                                                                                                                                                  • Rank filters
                                                                                                                                                                                  • Median filter
                                                                                                                                                                                  • Correlation
                                                                                                                                                                                  • Why do we need similarity
                                                                                                                                                                                  • Correlation (1D)
                                                                                                                                                                                  • Correlation (1D)
                                                                                                                                                                                  • Normalisation
                                                                                                                                                                                  • Normalisation
                                                                                                                                                                                  • Correlation on images
                                                                                                                                                                                  • Correlation on images
                                                                                                                                                                                  • Correlation on images
                                                                                                                                                                                  • Draw your filter
                                                                                                                                                                                  • Correlation on images ndash no normalisation
                                                                                                                                                                                  • Correlation on images ndash no normalisation 2
                                                                                                                                                                                  • Mathematics of 2D Correlation
                                                                                                                                                                                  • Mathematics of 2D Correlation
                                                                                                                                                                                  • Mathematics of 2D Correlation
                                                                                                                                                                                  • Slide Number 40
                                                                                                                                                                                  • 2D Kernel Normalisation
                                                                                                                                                                                  • Correlation
                                                                                                                                                                                  • Smoothing filters
                                                                                                                                                                                  • Use of smoothing
                                                                                                                                                                                  • Use of smoothing
                                                                                                                                                                                  • Mean filter
                                                                                                                                                                                  • Border handling
                                                                                                                                                                                  • Border handling ndash extend the input
                                                                                                                                                                                  • Correlation with zero padding
                                                                                                                                                                                  • Border handling ndash extend the input
                                                                                                                                                                                  • Template Matching
                                                                                                                                                                                  • Template Matching
                                                                                                                                                                                  • Template Matching
                                                                                                                                                                                  • Template Matching
                                                                                                                                                                                  • Problematic Correlation
                                                                                                                                                                                  • Normalised Cross Correlation
                                                                                                                                                                                  • Length of template
                                                                                                                                                                                  • Length of image patch
                                                                                                                                                                                  • Normalised Cross Correlation
                                                                                                                                                                                  • Normalised Cross Correlation
                                                                                                                                                                                  • Normalised Cross Correlation
                                                                                                                                                                                  • Edges
                                                                                                                                                                                  • Edges
                                                                                                                                                                                  • Finite Difference
                                                                                                                                                                                  • Edges
                                                                                                                                                                                  • Edges in 2D
                                                                                                                                                                                  • Edge filter kernel
                                                                                                                                                                                  • Prewitt filter
                                                                                                                                                                                  • Edge detection
                                                                                                                                                                                  • Edge filtering
                                                                                                                                                                                  • 02511 - Niveau af dagens emne forelaeligsing
                                                                                                                                                                                  • 02512 - Niveau af dagens emne forelaeligsing
                                                                                                                                                                                  • 02511 - Mit eget udbytte af dagen
                                                                                                                                                                                  • 02512 - Mit eget udbytte af dagen
                                                                                                                                                                                  • 02511 - Sidste uges oslashvelser (pixelwise operations)
                                                                                                                                                                                  • 02512 - Sidste uges oslashvelser (pixelwise operations)
                                                                                                                                                                                  • Denne uges brug af clickers
                                                                                                                                                                                  • What can you do after today
                                                                                                                                                                                  • Oslashvelsesrapport over oslashvelse 4 - 02511
                                                                                                                                                                                  • Exercises
                                                                                                                                                                                    A0
                                                                                                                                                                                    B0
                                                                                                                                                                                    C5
                                                                                                                                                                                    D0
                                                                                                                                                                                    E6
                                                                                                                                                                                    A
                                                                                                                                                                                    B
                                                                                                                                                                                    C
                                                                                                                                                                                    D
                                                                                                                                                                                    E
                                                                                                                                                                                    A3
                                                                                                                                                                                    B0
                                                                                                                                                                                    C3
                                                                                                                                                                                    D0
                                                                                                                                                                                    E0
                                                                                                                                                                                    A
                                                                                                                                                                                    B
                                                                                                                                                                                    C
                                                                                                                                                                                    D
                                                                                                                                                                                    E
                                                                                                                                                                                    A0
                                                                                                                                                                                    B0
                                                                                                                                                                                    C1
                                                                                                                                                                                    D4
                                                                                                                                                                                    E1
                                                                                                                                                                                    A
                                                                                                                                                                                    B
                                                                                                                                                                                    C
                                                                                                                                                                                    D
                                                                                                                                                                                    E
                                                                                                                                                                                    A2
                                                                                                                                                                                    B1
                                                                                                                                                                                    C3
                                                                                                                                                                                    D2
                                                                                                                                                                                    E0
                                                                                                                                                                                    A
                                                                                                                                                                                    B
                                                                                                                                                                                    C
                                                                                                                                                                                    D
                                                                                                                                                                                    E
                                                                                                                                                                                    A0
                                                                                                                                                                                    B0
                                                                                                                                                                                    C2
                                                                                                                                                                                    D6
                                                                                                                                                                                    E0
                                                                                                                                                                                    A
                                                                                                                                                                                    B
                                                                                                                                                                                    C
                                                                                                                                                                                    D
                                                                                                                                                                                    E
                                                                                                                                                                                    A0
                                                                                                                                                                                    B0
                                                                                                                                                                                    C1
                                                                                                                                                                                    D0
                                                                                                                                                                                    E0
                                                                                                                                                                                    A
                                                                                                                                                                                    B
                                                                                                                                                                                    C
                                                                                                                                                                                    D
                                                                                                                                                                                    E
                                                                                                                                                                                    A2
                                                                                                                                                                                    B3
                                                                                                                                                                                    C6
                                                                                                                                                                                    D1
                                                                                                                                                                                    E0

                                                                                                                                                                                    DTU Compute

                                                                                                                                                                                    2122018Introduction to Medical Image Analysis77 DTU Compute Technical University of Denmark

                                                                                                                                                                                    02512 - Niveau af dagens emne forelaeligsingA) Meget letB) LetC) PassendeD) SvaeligrtE) Meget svaeligrt

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                                                                                                                                                                                    DTU Compute

                                                                                                                                                                                    2122018Introduction to Medical Image Analysis78 DTU Compute Technical University of Denmark

                                                                                                                                                                                    02511 - Mit eget udbytte af dagenA) Jeg har laeligrt meget lidtB) Lidt laeligringC) PassendeD) God laeligringE) Jeg har laeligrt meget

                                                                                                                                                                                    0 0

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                                                                                                                                                                                    0

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                                                                                                                                                                                    0

                                                                                                                                                                                    Sheet1

                                                                                                                                                                                    DTU Compute

                                                                                                                                                                                    2122018Introduction to Medical Image Analysis79 DTU Compute Technical University of Denmark

                                                                                                                                                                                    02512 - Mit eget udbytte af dagenA) Jeg har laeligrt meget lidtB) Lidt laeligringC) PassendeD) God laeligringE) Jeg har laeligrt meget

                                                                                                                                                                                    2

                                                                                                                                                                                    1

                                                                                                                                                                                    3

                                                                                                                                                                                    2

                                                                                                                                                                                    0

                                                                                                                                                                                    A B C D E

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                                                                                                                                                                                    2
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                                                                                                                                                                                    3
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                                                                                                                                                                                    0

                                                                                                                                                                                    Sheet1

                                                                                                                                                                                    DTU Compute

                                                                                                                                                                                    2122018Introduction to Medical Image Analysis80 DTU Compute Technical University of Denmark

                                                                                                                                                                                    02511 - Sidste uges oslashvelser (pixelwiseoperations)A) Meget letteB) LetteC) PassendeD) SvaeligreE) Meget svaeligre

                                                                                                                                                                                    0 0

                                                                                                                                                                                    1

                                                                                                                                                                                    4

                                                                                                                                                                                    1

                                                                                                                                                                                    A B C D E

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                                                                                                                                                                                    1
                                                                                                                                                                                    4
                                                                                                                                                                                    1

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                                                                                                                                                                                    DTU Compute

                                                                                                                                                                                    2122018Introduction to Medical Image Analysis81 DTU Compute Technical University of Denmark

                                                                                                                                                                                    02512 - Sidste uges oslashvelser (pixelwiseoperations)A) Meget letteB) LetteC) PassendeD) SvaeligreE) Meget svaeligre

                                                                                                                                                                                    3

                                                                                                                                                                                    0

                                                                                                                                                                                    3

                                                                                                                                                                                    0 0

                                                                                                                                                                                    A B C D E

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                                                                                                                                                                                    3
                                                                                                                                                                                    0
                                                                                                                                                                                    0

                                                                                                                                                                                    Sheet1

                                                                                                                                                                                    DTU Compute

                                                                                                                                                                                    2122018Introduction to Medical Image Analysis82 DTU Compute Technical University of Denmark

                                                                                                                                                                                    Denne uges brug af clickersA) click click click ndash jeg bliver

                                                                                                                                                                                    sindssygB) For meget clickC) PassendeD) Jeg vil gerne have lidt mereE) Jeg kan ikrsquo faring nok

                                                                                                                                                                                    0 0

                                                                                                                                                                                    5

                                                                                                                                                                                    0

                                                                                                                                                                                    6

                                                                                                                                                                                    A B C D E

                                                                                                                                                                                    Chart1

                                                                                                                                                                                    0
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                                                                                                                                                                                    5
                                                                                                                                                                                    0
                                                                                                                                                                                    6

                                                                                                                                                                                    Sheet1

                                                                                                                                                                                    DTU Compute

                                                                                                                                                                                    2122018Introduction to Medical Image Analysis83 DTU Compute Technical University of Denmark

                                                                                                                                                                                    What can you do after today Describe the difference between point processing and neighbourhood

                                                                                                                                                                                    processing Compute a rank filtered image using the min max median and

                                                                                                                                                                                    difference rank filters Compute a mean filtered image Decide if median or average filtering should be used for noise removal Choose the appropriate image border handling based on a given input

                                                                                                                                                                                    image Implement and apply template matching Compute the normalised cross correlation and explain why it should be

                                                                                                                                                                                    used Apply given image filter kernels to images Use edge filters on images Describe finite difference approximation of image gradients Describe the concept of edge detection

                                                                                                                                                                                    DTU Compute

                                                                                                                                                                                    2122018Introduction to Medical Image Analysis84 DTU Compute Technical University of Denmark

                                                                                                                                                                                    Oslashvelsesrapport over oslashvelse 4 - 02511 Oslashvelser taeligller cirka 30 af karakteren Skal afleveres senest den 7 marts kl 2359 Kan afleveres af 1 eller 2 personer

                                                                                                                                                                                    ndash I skal skrive jeres egen oslashvelsesrapportndash Brug mindst et af jeres egne billeder

                                                                                                                                                                                    Afleveres som PDF Lad vaeligre med at kopiere opgaveteksten ind i jeres

                                                                                                                                                                                    opgave Put Matlab kode i et Appendix og henvis fra teksten Eksempel rapport over oslashvelse findes paring

                                                                                                                                                                                    hjemmesiden under eksamen

                                                                                                                                                                                    DTU Compute

                                                                                                                                                                                    2122018Introduction to Medical Image Analysis85 DTU Compute Technical University of Denmark

                                                                                                                                                                                    Exercises

                                                                                                                                                                                    • Introduction to Medical Image Analysis
                                                                                                                                                                                    • Lecture 4 ndash Neighbourhood Processing
                                                                                                                                                                                    • What can you do after today
                                                                                                                                                                                    • Point processing
                                                                                                                                                                                    • Point processing
                                                                                                                                                                                    • Neighbourhood processing
                                                                                                                                                                                    • Use of filtering
                                                                                                                                                                                    • Salt and pepper noise
                                                                                                                                                                                    • Salt and pepper noise
                                                                                                                                                                                    • What is so special about noise
                                                                                                                                                                                    • Noise ndash go away
                                                                                                                                                                                    • What is the median Value
                                                                                                                                                                                    • The median value
                                                                                                                                                                                    • Noise away ndash the median filter
                                                                                                                                                                                    • Noise removal ndash average filter
                                                                                                                                                                                    • Noise removal ndash median filter
                                                                                                                                                                                    • Image Filtering
                                                                                                                                                                                    • Median filter
                                                                                                                                                                                    • Rank filters
                                                                                                                                                                                    • Median filter
                                                                                                                                                                                    • Correlation
                                                                                                                                                                                    • Why do we need similarity
                                                                                                                                                                                    • Correlation (1D)
                                                                                                                                                                                    • Correlation (1D)
                                                                                                                                                                                    • Normalisation
                                                                                                                                                                                    • Normalisation
                                                                                                                                                                                    • Correlation on images
                                                                                                                                                                                    • Correlation on images
                                                                                                                                                                                    • Correlation on images
                                                                                                                                                                                    • Draw your filter
                                                                                                                                                                                    • Correlation on images ndash no normalisation
                                                                                                                                                                                    • Correlation on images ndash no normalisation 2
                                                                                                                                                                                    • Mathematics of 2D Correlation
                                                                                                                                                                                    • Mathematics of 2D Correlation
                                                                                                                                                                                    • Mathematics of 2D Correlation
                                                                                                                                                                                    • Slide Number 40
                                                                                                                                                                                    • 2D Kernel Normalisation
                                                                                                                                                                                    • Correlation
                                                                                                                                                                                    • Smoothing filters
                                                                                                                                                                                    • Use of smoothing
                                                                                                                                                                                    • Use of smoothing
                                                                                                                                                                                    • Mean filter
                                                                                                                                                                                    • Border handling
                                                                                                                                                                                    • Border handling ndash extend the input
                                                                                                                                                                                    • Correlation with zero padding
                                                                                                                                                                                    • Border handling ndash extend the input
                                                                                                                                                                                    • Template Matching
                                                                                                                                                                                    • Template Matching
                                                                                                                                                                                    • Template Matching
                                                                                                                                                                                    • Template Matching
                                                                                                                                                                                    • Problematic Correlation
                                                                                                                                                                                    • Normalised Cross Correlation
                                                                                                                                                                                    • Length of template
                                                                                                                                                                                    • Length of image patch
                                                                                                                                                                                    • Normalised Cross Correlation
                                                                                                                                                                                    • Normalised Cross Correlation
                                                                                                                                                                                    • Normalised Cross Correlation
                                                                                                                                                                                    • Edges
                                                                                                                                                                                    • Edges
                                                                                                                                                                                    • Finite Difference
                                                                                                                                                                                    • Edges
                                                                                                                                                                                    • Edges in 2D
                                                                                                                                                                                    • Edge filter kernel
                                                                                                                                                                                    • Prewitt filter
                                                                                                                                                                                    • Edge detection
                                                                                                                                                                                    • Edge filtering
                                                                                                                                                                                    • 02511 - Niveau af dagens emne forelaeligsing
                                                                                                                                                                                    • 02512 - Niveau af dagens emne forelaeligsing
                                                                                                                                                                                    • 02511 - Mit eget udbytte af dagen
                                                                                                                                                                                    • 02512 - Mit eget udbytte af dagen
                                                                                                                                                                                    • 02511 - Sidste uges oslashvelser (pixelwise operations)
                                                                                                                                                                                    • 02512 - Sidste uges oslashvelser (pixelwise operations)
                                                                                                                                                                                    • Denne uges brug af clickers
                                                                                                                                                                                    • What can you do after today
                                                                                                                                                                                    • Oslashvelsesrapport over oslashvelse 4 - 02511
                                                                                                                                                                                    • Exercises
                                                                                                                                                                                      A0
                                                                                                                                                                                      B0
                                                                                                                                                                                      C5
                                                                                                                                                                                      D0
                                                                                                                                                                                      E6
                                                                                                                                                                                      A
                                                                                                                                                                                      B
                                                                                                                                                                                      C
                                                                                                                                                                                      D
                                                                                                                                                                                      E
                                                                                                                                                                                      A3
                                                                                                                                                                                      B0
                                                                                                                                                                                      C3
                                                                                                                                                                                      D0
                                                                                                                                                                                      E0
                                                                                                                                                                                      A
                                                                                                                                                                                      B
                                                                                                                                                                                      C
                                                                                                                                                                                      D
                                                                                                                                                                                      E
                                                                                                                                                                                      A0
                                                                                                                                                                                      B0
                                                                                                                                                                                      C1
                                                                                                                                                                                      D4
                                                                                                                                                                                      E1
                                                                                                                                                                                      A
                                                                                                                                                                                      B
                                                                                                                                                                                      C
                                                                                                                                                                                      D
                                                                                                                                                                                      E
                                                                                                                                                                                      A2
                                                                                                                                                                                      B1
                                                                                                                                                                                      C3
                                                                                                                                                                                      D2
                                                                                                                                                                                      E0
                                                                                                                                                                                      A
                                                                                                                                                                                      B
                                                                                                                                                                                      C
                                                                                                                                                                                      D
                                                                                                                                                                                      E
                                                                                                                                                                                      A0
                                                                                                                                                                                      B0
                                                                                                                                                                                      C2
                                                                                                                                                                                      D6
                                                                                                                                                                                      E0
                                                                                                                                                                                      A
                                                                                                                                                                                      B
                                                                                                                                                                                      C
                                                                                                                                                                                      D
                                                                                                                                                                                      E
                                                                                                                                                                                      A0
                                                                                                                                                                                      B0
                                                                                                                                                                                      C1
                                                                                                                                                                                      D0
                                                                                                                                                                                      E0
                                                                                                                                                                                      A
                                                                                                                                                                                      B
                                                                                                                                                                                      C
                                                                                                                                                                                      D
                                                                                                                                                                                      E

                                                                                                                                                                                      Chart1

                                                                                                                                                                                      0
                                                                                                                                                                                      0
                                                                                                                                                                                      1
                                                                                                                                                                                      0
                                                                                                                                                                                      0

                                                                                                                                                                                      Sheet1

                                                                                                                                                                                      DTU Compute

                                                                                                                                                                                      2122018Introduction to Medical Image Analysis78 DTU Compute Technical University of Denmark

                                                                                                                                                                                      02511 - Mit eget udbytte af dagenA) Jeg har laeligrt meget lidtB) Lidt laeligringC) PassendeD) God laeligringE) Jeg har laeligrt meget

                                                                                                                                                                                      0 0

                                                                                                                                                                                      2

                                                                                                                                                                                      6

                                                                                                                                                                                      0

                                                                                                                                                                                      A B C D E

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                                                                                                                                                                                      DTU Compute

                                                                                                                                                                                      2122018Introduction to Medical Image Analysis79 DTU Compute Technical University of Denmark

                                                                                                                                                                                      02512 - Mit eget udbytte af dagenA) Jeg har laeligrt meget lidtB) Lidt laeligringC) PassendeD) God laeligringE) Jeg har laeligrt meget

                                                                                                                                                                                      2

                                                                                                                                                                                      1

                                                                                                                                                                                      3

                                                                                                                                                                                      2

                                                                                                                                                                                      0

                                                                                                                                                                                      A B C D E

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                                                                                                                                                                                      DTU Compute

                                                                                                                                                                                      2122018Introduction to Medical Image Analysis80 DTU Compute Technical University of Denmark

                                                                                                                                                                                      02511 - Sidste uges oslashvelser (pixelwiseoperations)A) Meget letteB) LetteC) PassendeD) SvaeligreE) Meget svaeligre

                                                                                                                                                                                      0 0

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                                                                                                                                                                                      DTU Compute

                                                                                                                                                                                      2122018Introduction to Medical Image Analysis81 DTU Compute Technical University of Denmark

                                                                                                                                                                                      02512 - Sidste uges oslashvelser (pixelwiseoperations)A) Meget letteB) LetteC) PassendeD) SvaeligreE) Meget svaeligre

                                                                                                                                                                                      3

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                                                                                                                                                                                      0 0

                                                                                                                                                                                      A B C D E

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                                                                                                                                                                                      DTU Compute

                                                                                                                                                                                      2122018Introduction to Medical Image Analysis82 DTU Compute Technical University of Denmark

                                                                                                                                                                                      Denne uges brug af clickersA) click click click ndash jeg bliver

                                                                                                                                                                                      sindssygB) For meget clickC) PassendeD) Jeg vil gerne have lidt mereE) Jeg kan ikrsquo faring nok

                                                                                                                                                                                      0 0

                                                                                                                                                                                      5

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                                                                                                                                                                                      DTU Compute

                                                                                                                                                                                      2122018Introduction to Medical Image Analysis83 DTU Compute Technical University of Denmark

                                                                                                                                                                                      What can you do after today Describe the difference between point processing and neighbourhood

                                                                                                                                                                                      processing Compute a rank filtered image using the min max median and

                                                                                                                                                                                      difference rank filters Compute a mean filtered image Decide if median or average filtering should be used for noise removal Choose the appropriate image border handling based on a given input

                                                                                                                                                                                      image Implement and apply template matching Compute the normalised cross correlation and explain why it should be

                                                                                                                                                                                      used Apply given image filter kernels to images Use edge filters on images Describe finite difference approximation of image gradients Describe the concept of edge detection

                                                                                                                                                                                      DTU Compute

                                                                                                                                                                                      2122018Introduction to Medical Image Analysis84 DTU Compute Technical University of Denmark

                                                                                                                                                                                      Oslashvelsesrapport over oslashvelse 4 - 02511 Oslashvelser taeligller cirka 30 af karakteren Skal afleveres senest den 7 marts kl 2359 Kan afleveres af 1 eller 2 personer

                                                                                                                                                                                      ndash I skal skrive jeres egen oslashvelsesrapportndash Brug mindst et af jeres egne billeder

                                                                                                                                                                                      Afleveres som PDF Lad vaeligre med at kopiere opgaveteksten ind i jeres

                                                                                                                                                                                      opgave Put Matlab kode i et Appendix og henvis fra teksten Eksempel rapport over oslashvelse findes paring

                                                                                                                                                                                      hjemmesiden under eksamen

                                                                                                                                                                                      DTU Compute

                                                                                                                                                                                      2122018Introduction to Medical Image Analysis85 DTU Compute Technical University of Denmark

                                                                                                                                                                                      Exercises

                                                                                                                                                                                      • Introduction to Medical Image Analysis
                                                                                                                                                                                      • Lecture 4 ndash Neighbourhood Processing
                                                                                                                                                                                      • What can you do after today
                                                                                                                                                                                      • Point processing
                                                                                                                                                                                      • Point processing
                                                                                                                                                                                      • Neighbourhood processing
                                                                                                                                                                                      • Use of filtering
                                                                                                                                                                                      • Salt and pepper noise
                                                                                                                                                                                      • Salt and pepper noise
                                                                                                                                                                                      • What is so special about noise
                                                                                                                                                                                      • Noise ndash go away
                                                                                                                                                                                      • What is the median Value
                                                                                                                                                                                      • The median value
                                                                                                                                                                                      • Noise away ndash the median filter
                                                                                                                                                                                      • Noise removal ndash average filter
                                                                                                                                                                                      • Noise removal ndash median filter
                                                                                                                                                                                      • Image Filtering
                                                                                                                                                                                      • Median filter
                                                                                                                                                                                      • Rank filters
                                                                                                                                                                                      • Median filter
                                                                                                                                                                                      • Correlation
                                                                                                                                                                                      • Why do we need similarity
                                                                                                                                                                                      • Correlation (1D)
                                                                                                                                                                                      • Correlation (1D)
                                                                                                                                                                                      • Normalisation
                                                                                                                                                                                      • Normalisation
                                                                                                                                                                                      • Correlation on images
                                                                                                                                                                                      • Correlation on images
                                                                                                                                                                                      • Correlation on images
                                                                                                                                                                                      • Draw your filter
                                                                                                                                                                                      • Correlation on images ndash no normalisation
                                                                                                                                                                                      • Correlation on images ndash no normalisation 2
                                                                                                                                                                                      • Mathematics of 2D Correlation
                                                                                                                                                                                      • Mathematics of 2D Correlation
                                                                                                                                                                                      • Mathematics of 2D Correlation
                                                                                                                                                                                      • Slide Number 40
                                                                                                                                                                                      • 2D Kernel Normalisation
                                                                                                                                                                                      • Correlation
                                                                                                                                                                                      • Smoothing filters
                                                                                                                                                                                      • Use of smoothing
                                                                                                                                                                                      • Use of smoothing
                                                                                                                                                                                      • Mean filter
                                                                                                                                                                                      • Border handling
                                                                                                                                                                                      • Border handling ndash extend the input
                                                                                                                                                                                      • Correlation with zero padding
                                                                                                                                                                                      • Border handling ndash extend the input
                                                                                                                                                                                      • Template Matching
                                                                                                                                                                                      • Template Matching
                                                                                                                                                                                      • Template Matching
                                                                                                                                                                                      • Template Matching
                                                                                                                                                                                      • Problematic Correlation
                                                                                                                                                                                      • Normalised Cross Correlation
                                                                                                                                                                                      • Length of template
                                                                                                                                                                                      • Length of image patch
                                                                                                                                                                                      • Normalised Cross Correlation
                                                                                                                                                                                      • Normalised Cross Correlation
                                                                                                                                                                                      • Normalised Cross Correlation
                                                                                                                                                                                      • Edges
                                                                                                                                                                                      • Edges
                                                                                                                                                                                      • Finite Difference
                                                                                                                                                                                      • Edges
                                                                                                                                                                                      • Edges in 2D
                                                                                                                                                                                      • Edge filter kernel
                                                                                                                                                                                      • Prewitt filter
                                                                                                                                                                                      • Edge detection
                                                                                                                                                                                      • Edge filtering
                                                                                                                                                                                      • 02511 - Niveau af dagens emne forelaeligsing
                                                                                                                                                                                      • 02512 - Niveau af dagens emne forelaeligsing
                                                                                                                                                                                      • 02511 - Mit eget udbytte af dagen
                                                                                                                                                                                      • 02512 - Mit eget udbytte af dagen
                                                                                                                                                                                      • 02511 - Sidste uges oslashvelser (pixelwise operations)
                                                                                                                                                                                      • 02512 - Sidste uges oslashvelser (pixelwise operations)
                                                                                                                                                                                      • Denne uges brug af clickers
                                                                                                                                                                                      • What can you do after today
                                                                                                                                                                                      • Oslashvelsesrapport over oslashvelse 4 - 02511
                                                                                                                                                                                      • Exercises
                                                                                                                                                                                        A0
                                                                                                                                                                                        B0
                                                                                                                                                                                        C5
                                                                                                                                                                                        D0
                                                                                                                                                                                        E6
                                                                                                                                                                                        A
                                                                                                                                                                                        B
                                                                                                                                                                                        C
                                                                                                                                                                                        D
                                                                                                                                                                                        E
                                                                                                                                                                                        A3
                                                                                                                                                                                        B0
                                                                                                                                                                                        C3
                                                                                                                                                                                        D0
                                                                                                                                                                                        E0
                                                                                                                                                                                        A
                                                                                                                                                                                        B
                                                                                                                                                                                        C
                                                                                                                                                                                        D
                                                                                                                                                                                        E
                                                                                                                                                                                        A0
                                                                                                                                                                                        B0
                                                                                                                                                                                        C1
                                                                                                                                                                                        D4
                                                                                                                                                                                        E1
                                                                                                                                                                                        A
                                                                                                                                                                                        B
                                                                                                                                                                                        C
                                                                                                                                                                                        D
                                                                                                                                                                                        E
                                                                                                                                                                                        A2
                                                                                                                                                                                        B1
                                                                                                                                                                                        C3
                                                                                                                                                                                        D2
                                                                                                                                                                                        E0
                                                                                                                                                                                        A
                                                                                                                                                                                        B
                                                                                                                                                                                        C
                                                                                                                                                                                        D
                                                                                                                                                                                        E
                                                                                                                                                                                        A0
                                                                                                                                                                                        B0
                                                                                                                                                                                        C2
                                                                                                                                                                                        D6
                                                                                                                                                                                        E0
                                                                                                                                                                                        A
                                                                                                                                                                                        B
                                                                                                                                                                                        C
                                                                                                                                                                                        D
                                                                                                                                                                                        E
                                                                                                                                                                                        A0
                                                                                                                                                                                        B0
                                                                                                                                                                                        C1
                                                                                                                                                                                        D0
                                                                                                                                                                                        E0
                                                                                                                                                                                        A
                                                                                                                                                                                        B
                                                                                                                                                                                        C
                                                                                                                                                                                        D
                                                                                                                                                                                        E

                                                                                                                                                                                        Sheet1

                                                                                                                                                                                        DTU Compute

                                                                                                                                                                                        2122018Introduction to Medical Image Analysis78 DTU Compute Technical University of Denmark

                                                                                                                                                                                        02511 - Mit eget udbytte af dagenA) Jeg har laeligrt meget lidtB) Lidt laeligringC) PassendeD) God laeligringE) Jeg har laeligrt meget

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                                                                                                                                                                                        Sheet1

                                                                                                                                                                                        DTU Compute

                                                                                                                                                                                        2122018Introduction to Medical Image Analysis79 DTU Compute Technical University of Denmark

                                                                                                                                                                                        02512 - Mit eget udbytte af dagenA) Jeg har laeligrt meget lidtB) Lidt laeligringC) PassendeD) God laeligringE) Jeg har laeligrt meget

                                                                                                                                                                                        2

                                                                                                                                                                                        1

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                                                                                                                                                                                        2

                                                                                                                                                                                        0

                                                                                                                                                                                        A B C D E

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                                                                                                                                                                                        DTU Compute

                                                                                                                                                                                        2122018Introduction to Medical Image Analysis80 DTU Compute Technical University of Denmark

                                                                                                                                                                                        02511 - Sidste uges oslashvelser (pixelwiseoperations)A) Meget letteB) LetteC) PassendeD) SvaeligreE) Meget svaeligre

                                                                                                                                                                                        0 0

                                                                                                                                                                                        1

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                                                                                                                                                                                        1

                                                                                                                                                                                        A B C D E

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                                                                                                                                                                                        1
                                                                                                                                                                                        4
                                                                                                                                                                                        1

                                                                                                                                                                                        Sheet1

                                                                                                                                                                                        DTU Compute

                                                                                                                                                                                        2122018Introduction to Medical Image Analysis81 DTU Compute Technical University of Denmark

                                                                                                                                                                                        02512 - Sidste uges oslashvelser (pixelwiseoperations)A) Meget letteB) LetteC) PassendeD) SvaeligreE) Meget svaeligre

                                                                                                                                                                                        3

                                                                                                                                                                                        0

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                                                                                                                                                                                        3
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                                                                                                                                                                                        0

                                                                                                                                                                                        Sheet1

                                                                                                                                                                                        DTU Compute

                                                                                                                                                                                        2122018Introduction to Medical Image Analysis82 DTU Compute Technical University of Denmark

                                                                                                                                                                                        Denne uges brug af clickersA) click click click ndash jeg bliver

                                                                                                                                                                                        sindssygB) For meget clickC) PassendeD) Jeg vil gerne have lidt mereE) Jeg kan ikrsquo faring nok

                                                                                                                                                                                        0 0

                                                                                                                                                                                        5

                                                                                                                                                                                        0

                                                                                                                                                                                        6

                                                                                                                                                                                        A B C D E

                                                                                                                                                                                        Chart1

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                                                                                                                                                                                        5
                                                                                                                                                                                        0
                                                                                                                                                                                        6

                                                                                                                                                                                        Sheet1

                                                                                                                                                                                        DTU Compute

                                                                                                                                                                                        2122018Introduction to Medical Image Analysis83 DTU Compute Technical University of Denmark

                                                                                                                                                                                        What can you do after today Describe the difference between point processing and neighbourhood

                                                                                                                                                                                        processing Compute a rank filtered image using the min max median and

                                                                                                                                                                                        difference rank filters Compute a mean filtered image Decide if median or average filtering should be used for noise removal Choose the appropriate image border handling based on a given input

                                                                                                                                                                                        image Implement and apply template matching Compute the normalised cross correlation and explain why it should be

                                                                                                                                                                                        used Apply given image filter kernels to images Use edge filters on images Describe finite difference approximation of image gradients Describe the concept of edge detection

                                                                                                                                                                                        DTU Compute

                                                                                                                                                                                        2122018Introduction to Medical Image Analysis84 DTU Compute Technical University of Denmark

                                                                                                                                                                                        Oslashvelsesrapport over oslashvelse 4 - 02511 Oslashvelser taeligller cirka 30 af karakteren Skal afleveres senest den 7 marts kl 2359 Kan afleveres af 1 eller 2 personer

                                                                                                                                                                                        ndash I skal skrive jeres egen oslashvelsesrapportndash Brug mindst et af jeres egne billeder

                                                                                                                                                                                        Afleveres som PDF Lad vaeligre med at kopiere opgaveteksten ind i jeres

                                                                                                                                                                                        opgave Put Matlab kode i et Appendix og henvis fra teksten Eksempel rapport over oslashvelse findes paring

                                                                                                                                                                                        hjemmesiden under eksamen

                                                                                                                                                                                        DTU Compute

                                                                                                                                                                                        2122018Introduction to Medical Image Analysis85 DTU Compute Technical University of Denmark

                                                                                                                                                                                        Exercises

                                                                                                                                                                                        • Introduction to Medical Image Analysis
                                                                                                                                                                                        • Lecture 4 ndash Neighbourhood Processing
                                                                                                                                                                                        • What can you do after today
                                                                                                                                                                                        • Point processing
                                                                                                                                                                                        • Point processing
                                                                                                                                                                                        • Neighbourhood processing
                                                                                                                                                                                        • Use of filtering
                                                                                                                                                                                        • Salt and pepper noise
                                                                                                                                                                                        • Salt and pepper noise
                                                                                                                                                                                        • What is so special about noise
                                                                                                                                                                                        • Noise ndash go away
                                                                                                                                                                                        • What is the median Value
                                                                                                                                                                                        • The median value
                                                                                                                                                                                        • Noise away ndash the median filter
                                                                                                                                                                                        • Noise removal ndash average filter
                                                                                                                                                                                        • Noise removal ndash median filter
                                                                                                                                                                                        • Image Filtering
                                                                                                                                                                                        • Median filter
                                                                                                                                                                                        • Rank filters
                                                                                                                                                                                        • Median filter
                                                                                                                                                                                        • Correlation
                                                                                                                                                                                        • Why do we need similarity
                                                                                                                                                                                        • Correlation (1D)
                                                                                                                                                                                        • Correlation (1D)
                                                                                                                                                                                        • Normalisation
                                                                                                                                                                                        • Normalisation
                                                                                                                                                                                        • Correlation on images
                                                                                                                                                                                        • Correlation on images
                                                                                                                                                                                        • Correlation on images
                                                                                                                                                                                        • Draw your filter
                                                                                                                                                                                        • Correlation on images ndash no normalisation
                                                                                                                                                                                        • Correlation on images ndash no normalisation 2
                                                                                                                                                                                        • Mathematics of 2D Correlation
                                                                                                                                                                                        • Mathematics of 2D Correlation
                                                                                                                                                                                        • Mathematics of 2D Correlation
                                                                                                                                                                                        • Slide Number 40
                                                                                                                                                                                        • 2D Kernel Normalisation
                                                                                                                                                                                        • Correlation
                                                                                                                                                                                        • Smoothing filters
                                                                                                                                                                                        • Use of smoothing
                                                                                                                                                                                        • Use of smoothing
                                                                                                                                                                                        • Mean filter
                                                                                                                                                                                        • Border handling
                                                                                                                                                                                        • Border handling ndash extend the input
                                                                                                                                                                                        • Correlation with zero padding
                                                                                                                                                                                        • Border handling ndash extend the input
                                                                                                                                                                                        • Template Matching
                                                                                                                                                                                        • Template Matching
                                                                                                                                                                                        • Template Matching
                                                                                                                                                                                        • Template Matching
                                                                                                                                                                                        • Problematic Correlation
                                                                                                                                                                                        • Normalised Cross Correlation
                                                                                                                                                                                        • Length of template
                                                                                                                                                                                        • Length of image patch
                                                                                                                                                                                        • Normalised Cross Correlation
                                                                                                                                                                                        • Normalised Cross Correlation
                                                                                                                                                                                        • Normalised Cross Correlation
                                                                                                                                                                                        • Edges
                                                                                                                                                                                        • Edges
                                                                                                                                                                                        • Finite Difference
                                                                                                                                                                                        • Edges
                                                                                                                                                                                        • Edges in 2D
                                                                                                                                                                                        • Edge filter kernel
                                                                                                                                                                                        • Prewitt filter
                                                                                                                                                                                        • Edge detection
                                                                                                                                                                                        • Edge filtering
                                                                                                                                                                                        • 02511 - Niveau af dagens emne forelaeligsing
                                                                                                                                                                                        • 02512 - Niveau af dagens emne forelaeligsing
                                                                                                                                                                                        • 02511 - Mit eget udbytte af dagen
                                                                                                                                                                                        • 02512 - Mit eget udbytte af dagen
                                                                                                                                                                                        • 02511 - Sidste uges oslashvelser (pixelwise operations)
                                                                                                                                                                                        • 02512 - Sidste uges oslashvelser (pixelwise operations)
                                                                                                                                                                                        • Denne uges brug af clickers
                                                                                                                                                                                        • What can you do after today
                                                                                                                                                                                        • Oslashvelsesrapport over oslashvelse 4 - 02511
                                                                                                                                                                                        • Exercises
                                                                                                                                                                                          A0
                                                                                                                                                                                          B0
                                                                                                                                                                                          C5
                                                                                                                                                                                          D0
                                                                                                                                                                                          E6
                                                                                                                                                                                          A
                                                                                                                                                                                          B
                                                                                                                                                                                          C
                                                                                                                                                                                          D
                                                                                                                                                                                          E
                                                                                                                                                                                          A3
                                                                                                                                                                                          B0
                                                                                                                                                                                          C3
                                                                                                                                                                                          D0
                                                                                                                                                                                          E0
                                                                                                                                                                                          A
                                                                                                                                                                                          B
                                                                                                                                                                                          C
                                                                                                                                                                                          D
                                                                                                                                                                                          E
                                                                                                                                                                                          A0
                                                                                                                                                                                          B0
                                                                                                                                                                                          C1
                                                                                                                                                                                          D4
                                                                                                                                                                                          E1
                                                                                                                                                                                          A
                                                                                                                                                                                          B
                                                                                                                                                                                          C
                                                                                                                                                                                          D
                                                                                                                                                                                          E
                                                                                                                                                                                          A2
                                                                                                                                                                                          B1
                                                                                                                                                                                          C3
                                                                                                                                                                                          D2
                                                                                                                                                                                          E0
                                                                                                                                                                                          A
                                                                                                                                                                                          B
                                                                                                                                                                                          C
                                                                                                                                                                                          D
                                                                                                                                                                                          E
                                                                                                                                                                                          A0
                                                                                                                                                                                          B0
                                                                                                                                                                                          C2
                                                                                                                                                                                          D6
                                                                                                                                                                                          E0
                                                                                                                                                                                          A
                                                                                                                                                                                          B
                                                                                                                                                                                          C
                                                                                                                                                                                          D
                                                                                                                                                                                          E
                                                                                                                                                                                          A0
                                                                                                                                                                                          B0
                                                                                                                                                                                          C1
                                                                                                                                                                                          D0
                                                                                                                                                                                          E0

                                                                                                                                                                                          DTU Compute

                                                                                                                                                                                          2122018Introduction to Medical Image Analysis78 DTU Compute Technical University of Denmark

                                                                                                                                                                                          02511 - Mit eget udbytte af dagenA) Jeg har laeligrt meget lidtB) Lidt laeligringC) PassendeD) God laeligringE) Jeg har laeligrt meget

                                                                                                                                                                                          0 0

                                                                                                                                                                                          2

                                                                                                                                                                                          6

                                                                                                                                                                                          0

                                                                                                                                                                                          A B C D E

                                                                                                                                                                                          Chart1

                                                                                                                                                                                          0
                                                                                                                                                                                          0
                                                                                                                                                                                          2
                                                                                                                                                                                          6
                                                                                                                                                                                          0

                                                                                                                                                                                          Sheet1

                                                                                                                                                                                          DTU Compute

                                                                                                                                                                                          2122018Introduction to Medical Image Analysis79 DTU Compute Technical University of Denmark

                                                                                                                                                                                          02512 - Mit eget udbytte af dagenA) Jeg har laeligrt meget lidtB) Lidt laeligringC) PassendeD) God laeligringE) Jeg har laeligrt meget

                                                                                                                                                                                          2

                                                                                                                                                                                          1

                                                                                                                                                                                          3

                                                                                                                                                                                          2

                                                                                                                                                                                          0

                                                                                                                                                                                          A B C D E

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                                                                                                                                                                                          2
                                                                                                                                                                                          1
                                                                                                                                                                                          3
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                                                                                                                                                                                          Sheet1

                                                                                                                                                                                          DTU Compute

                                                                                                                                                                                          2122018Introduction to Medical Image Analysis80 DTU Compute Technical University of Denmark

                                                                                                                                                                                          02511 - Sidste uges oslashvelser (pixelwiseoperations)A) Meget letteB) LetteC) PassendeD) SvaeligreE) Meget svaeligre

                                                                                                                                                                                          0 0

                                                                                                                                                                                          1

                                                                                                                                                                                          4

                                                                                                                                                                                          1

                                                                                                                                                                                          A B C D E

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                                                                                                                                                                                          1

                                                                                                                                                                                          Sheet1

                                                                                                                                                                                          DTU Compute

                                                                                                                                                                                          2122018Introduction to Medical Image Analysis81 DTU Compute Technical University of Denmark

                                                                                                                                                                                          02512 - Sidste uges oslashvelser (pixelwiseoperations)A) Meget letteB) LetteC) PassendeD) SvaeligreE) Meget svaeligre

                                                                                                                                                                                          3

                                                                                                                                                                                          0

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                                                                                                                                                                                          DTU Compute

                                                                                                                                                                                          2122018Introduction to Medical Image Analysis82 DTU Compute Technical University of Denmark

                                                                                                                                                                                          Denne uges brug af clickersA) click click click ndash jeg bliver

                                                                                                                                                                                          sindssygB) For meget clickC) PassendeD) Jeg vil gerne have lidt mereE) Jeg kan ikrsquo faring nok

                                                                                                                                                                                          0 0

                                                                                                                                                                                          5

                                                                                                                                                                                          0

                                                                                                                                                                                          6

                                                                                                                                                                                          A B C D E

                                                                                                                                                                                          Chart1

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                                                                                                                                                                                          6

                                                                                                                                                                                          Sheet1

                                                                                                                                                                                          DTU Compute

                                                                                                                                                                                          2122018Introduction to Medical Image Analysis83 DTU Compute Technical University of Denmark

                                                                                                                                                                                          What can you do after today Describe the difference between point processing and neighbourhood

                                                                                                                                                                                          processing Compute a rank filtered image using the min max median and

                                                                                                                                                                                          difference rank filters Compute a mean filtered image Decide if median or average filtering should be used for noise removal Choose the appropriate image border handling based on a given input

                                                                                                                                                                                          image Implement and apply template matching Compute the normalised cross correlation and explain why it should be

                                                                                                                                                                                          used Apply given image filter kernels to images Use edge filters on images Describe finite difference approximation of image gradients Describe the concept of edge detection

                                                                                                                                                                                          DTU Compute

                                                                                                                                                                                          2122018Introduction to Medical Image Analysis84 DTU Compute Technical University of Denmark

                                                                                                                                                                                          Oslashvelsesrapport over oslashvelse 4 - 02511 Oslashvelser taeligller cirka 30 af karakteren Skal afleveres senest den 7 marts kl 2359 Kan afleveres af 1 eller 2 personer

                                                                                                                                                                                          ndash I skal skrive jeres egen oslashvelsesrapportndash Brug mindst et af jeres egne billeder

                                                                                                                                                                                          Afleveres som PDF Lad vaeligre med at kopiere opgaveteksten ind i jeres

                                                                                                                                                                                          opgave Put Matlab kode i et Appendix og henvis fra teksten Eksempel rapport over oslashvelse findes paring

                                                                                                                                                                                          hjemmesiden under eksamen

                                                                                                                                                                                          DTU Compute

                                                                                                                                                                                          2122018Introduction to Medical Image Analysis85 DTU Compute Technical University of Denmark

                                                                                                                                                                                          Exercises

                                                                                                                                                                                          • Introduction to Medical Image Analysis
                                                                                                                                                                                          • Lecture 4 ndash Neighbourhood Processing
                                                                                                                                                                                          • What can you do after today
                                                                                                                                                                                          • Point processing
                                                                                                                                                                                          • Point processing
                                                                                                                                                                                          • Neighbourhood processing
                                                                                                                                                                                          • Use of filtering
                                                                                                                                                                                          • Salt and pepper noise
                                                                                                                                                                                          • Salt and pepper noise
                                                                                                                                                                                          • What is so special about noise
                                                                                                                                                                                          • Noise ndash go away
                                                                                                                                                                                          • What is the median Value
                                                                                                                                                                                          • The median value
                                                                                                                                                                                          • Noise away ndash the median filter
                                                                                                                                                                                          • Noise removal ndash average filter
                                                                                                                                                                                          • Noise removal ndash median filter
                                                                                                                                                                                          • Image Filtering
                                                                                                                                                                                          • Median filter
                                                                                                                                                                                          • Rank filters
                                                                                                                                                                                          • Median filter
                                                                                                                                                                                          • Correlation
                                                                                                                                                                                          • Why do we need similarity
                                                                                                                                                                                          • Correlation (1D)
                                                                                                                                                                                          • Correlation (1D)
                                                                                                                                                                                          • Normalisation
                                                                                                                                                                                          • Normalisation
                                                                                                                                                                                          • Correlation on images
                                                                                                                                                                                          • Correlation on images
                                                                                                                                                                                          • Correlation on images
                                                                                                                                                                                          • Draw your filter
                                                                                                                                                                                          • Correlation on images ndash no normalisation
                                                                                                                                                                                          • Correlation on images ndash no normalisation 2
                                                                                                                                                                                          • Mathematics of 2D Correlation
                                                                                                                                                                                          • Mathematics of 2D Correlation
                                                                                                                                                                                          • Mathematics of 2D Correlation
                                                                                                                                                                                          • Slide Number 40
                                                                                                                                                                                          • 2D Kernel Normalisation
                                                                                                                                                                                          • Correlation
                                                                                                                                                                                          • Smoothing filters
                                                                                                                                                                                          • Use of smoothing
                                                                                                                                                                                          • Use of smoothing
                                                                                                                                                                                          • Mean filter
                                                                                                                                                                                          • Border handling
                                                                                                                                                                                          • Border handling ndash extend the input
                                                                                                                                                                                          • Correlation with zero padding
                                                                                                                                                                                          • Border handling ndash extend the input
                                                                                                                                                                                          • Template Matching
                                                                                                                                                                                          • Template Matching
                                                                                                                                                                                          • Template Matching
                                                                                                                                                                                          • Template Matching
                                                                                                                                                                                          • Problematic Correlation
                                                                                                                                                                                          • Normalised Cross Correlation
                                                                                                                                                                                          • Length of template
                                                                                                                                                                                          • Length of image patch
                                                                                                                                                                                          • Normalised Cross Correlation
                                                                                                                                                                                          • Normalised Cross Correlation
                                                                                                                                                                                          • Normalised Cross Correlation
                                                                                                                                                                                          • Edges
                                                                                                                                                                                          • Edges
                                                                                                                                                                                          • Finite Difference
                                                                                                                                                                                          • Edges
                                                                                                                                                                                          • Edges in 2D
                                                                                                                                                                                          • Edge filter kernel
                                                                                                                                                                                          • Prewitt filter
                                                                                                                                                                                          • Edge detection
                                                                                                                                                                                          • Edge filtering
                                                                                                                                                                                          • 02511 - Niveau af dagens emne forelaeligsing
                                                                                                                                                                                          • 02512 - Niveau af dagens emne forelaeligsing
                                                                                                                                                                                          • 02511 - Mit eget udbytte af dagen
                                                                                                                                                                                          • 02512 - Mit eget udbytte af dagen
                                                                                                                                                                                          • 02511 - Sidste uges oslashvelser (pixelwise operations)
                                                                                                                                                                                          • 02512 - Sidste uges oslashvelser (pixelwise operations)
                                                                                                                                                                                          • Denne uges brug af clickers
                                                                                                                                                                                          • What can you do after today
                                                                                                                                                                                          • Oslashvelsesrapport over oslashvelse 4 - 02511
                                                                                                                                                                                          • Exercises
                                                                                                                                                                                            A0
                                                                                                                                                                                            B0
                                                                                                                                                                                            C5
                                                                                                                                                                                            D0
                                                                                                                                                                                            E6
                                                                                                                                                                                            A
                                                                                                                                                                                            B
                                                                                                                                                                                            C
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                                                                                                                                                                                            E
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                                                                                                                                                                                            D0
                                                                                                                                                                                            E0
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                                                                                                                                                                                            B
                                                                                                                                                                                            C
                                                                                                                                                                                            D
                                                                                                                                                                                            E
                                                                                                                                                                                            A0
                                                                                                                                                                                            B0
                                                                                                                                                                                            C1
                                                                                                                                                                                            D4
                                                                                                                                                                                            E1
                                                                                                                                                                                            A
                                                                                                                                                                                            B
                                                                                                                                                                                            C
                                                                                                                                                                                            D
                                                                                                                                                                                            E
                                                                                                                                                                                            A2
                                                                                                                                                                                            B1
                                                                                                                                                                                            C3
                                                                                                                                                                                            D2
                                                                                                                                                                                            E0
                                                                                                                                                                                            A
                                                                                                                                                                                            B
                                                                                                                                                                                            C
                                                                                                                                                                                            D
                                                                                                                                                                                            E
                                                                                                                                                                                            A0
                                                                                                                                                                                            B0
                                                                                                                                                                                            C2
                                                                                                                                                                                            D6
                                                                                                                                                                                            E0
                                                                                                                                                                                            A
                                                                                                                                                                                            B
                                                                                                                                                                                            C
                                                                                                                                                                                            D
                                                                                                                                                                                            E

                                                                                                                                                                                            Chart1

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                                                                                                                                                                                            DTU Compute

                                                                                                                                                                                            2122018Introduction to Medical Image Analysis79 DTU Compute Technical University of Denmark

                                                                                                                                                                                            02512 - Mit eget udbytte af dagenA) Jeg har laeligrt meget lidtB) Lidt laeligringC) PassendeD) God laeligringE) Jeg har laeligrt meget

                                                                                                                                                                                            2

                                                                                                                                                                                            1

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                                                                                                                                                                                            A B C D E

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                                                                                                                                                                                            DTU Compute

                                                                                                                                                                                            2122018Introduction to Medical Image Analysis80 DTU Compute Technical University of Denmark

                                                                                                                                                                                            02511 - Sidste uges oslashvelser (pixelwiseoperations)A) Meget letteB) LetteC) PassendeD) SvaeligreE) Meget svaeligre

                                                                                                                                                                                            0 0

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                                                                                                                                                                                            DTU Compute

                                                                                                                                                                                            2122018Introduction to Medical Image Analysis81 DTU Compute Technical University of Denmark

                                                                                                                                                                                            02512 - Sidste uges oslashvelser (pixelwiseoperations)A) Meget letteB) LetteC) PassendeD) SvaeligreE) Meget svaeligre

                                                                                                                                                                                            3

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                                                                                                                                                                                            DTU Compute

                                                                                                                                                                                            2122018Introduction to Medical Image Analysis82 DTU Compute Technical University of Denmark

                                                                                                                                                                                            Denne uges brug af clickersA) click click click ndash jeg bliver

                                                                                                                                                                                            sindssygB) For meget clickC) PassendeD) Jeg vil gerne have lidt mereE) Jeg kan ikrsquo faring nok

                                                                                                                                                                                            0 0

                                                                                                                                                                                            5

                                                                                                                                                                                            0

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                                                                                                                                                                                            A B C D E

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                                                                                                                                                                                            6

                                                                                                                                                                                            Sheet1

                                                                                                                                                                                            DTU Compute

                                                                                                                                                                                            2122018Introduction to Medical Image Analysis83 DTU Compute Technical University of Denmark

                                                                                                                                                                                            What can you do after today Describe the difference between point processing and neighbourhood

                                                                                                                                                                                            processing Compute a rank filtered image using the min max median and

                                                                                                                                                                                            difference rank filters Compute a mean filtered image Decide if median or average filtering should be used for noise removal Choose the appropriate image border handling based on a given input

                                                                                                                                                                                            image Implement and apply template matching Compute the normalised cross correlation and explain why it should be

                                                                                                                                                                                            used Apply given image filter kernels to images Use edge filters on images Describe finite difference approximation of image gradients Describe the concept of edge detection

                                                                                                                                                                                            DTU Compute

                                                                                                                                                                                            2122018Introduction to Medical Image Analysis84 DTU Compute Technical University of Denmark

                                                                                                                                                                                            Oslashvelsesrapport over oslashvelse 4 - 02511 Oslashvelser taeligller cirka 30 af karakteren Skal afleveres senest den 7 marts kl 2359 Kan afleveres af 1 eller 2 personer

                                                                                                                                                                                            ndash I skal skrive jeres egen oslashvelsesrapportndash Brug mindst et af jeres egne billeder

                                                                                                                                                                                            Afleveres som PDF Lad vaeligre med at kopiere opgaveteksten ind i jeres

                                                                                                                                                                                            opgave Put Matlab kode i et Appendix og henvis fra teksten Eksempel rapport over oslashvelse findes paring

                                                                                                                                                                                            hjemmesiden under eksamen

                                                                                                                                                                                            DTU Compute

                                                                                                                                                                                            2122018Introduction to Medical Image Analysis85 DTU Compute Technical University of Denmark

                                                                                                                                                                                            Exercises

                                                                                                                                                                                            • Introduction to Medical Image Analysis
                                                                                                                                                                                            • Lecture 4 ndash Neighbourhood Processing
                                                                                                                                                                                            • What can you do after today
                                                                                                                                                                                            • Point processing
                                                                                                                                                                                            • Point processing
                                                                                                                                                                                            • Neighbourhood processing
                                                                                                                                                                                            • Use of filtering
                                                                                                                                                                                            • Salt and pepper noise
                                                                                                                                                                                            • Salt and pepper noise
                                                                                                                                                                                            • What is so special about noise
                                                                                                                                                                                            • Noise ndash go away
                                                                                                                                                                                            • What is the median Value
                                                                                                                                                                                            • The median value
                                                                                                                                                                                            • Noise away ndash the median filter
                                                                                                                                                                                            • Noise removal ndash average filter
                                                                                                                                                                                            • Noise removal ndash median filter
                                                                                                                                                                                            • Image Filtering
                                                                                                                                                                                            • Median filter
                                                                                                                                                                                            • Rank filters
                                                                                                                                                                                            • Median filter
                                                                                                                                                                                            • Correlation
                                                                                                                                                                                            • Why do we need similarity
                                                                                                                                                                                            • Correlation (1D)
                                                                                                                                                                                            • Correlation (1D)
                                                                                                                                                                                            • Normalisation
                                                                                                                                                                                            • Normalisation
                                                                                                                                                                                            • Correlation on images
                                                                                                                                                                                            • Correlation on images
                                                                                                                                                                                            • Correlation on images
                                                                                                                                                                                            • Draw your filter
                                                                                                                                                                                            • Correlation on images ndash no normalisation
                                                                                                                                                                                            • Correlation on images ndash no normalisation 2
                                                                                                                                                                                            • Mathematics of 2D Correlation
                                                                                                                                                                                            • Mathematics of 2D Correlation
                                                                                                                                                                                            • Mathematics of 2D Correlation
                                                                                                                                                                                            • Slide Number 40
                                                                                                                                                                                            • 2D Kernel Normalisation
                                                                                                                                                                                            • Correlation
                                                                                                                                                                                            • Smoothing filters
                                                                                                                                                                                            • Use of smoothing
                                                                                                                                                                                            • Use of smoothing
                                                                                                                                                                                            • Mean filter
                                                                                                                                                                                            • Border handling
                                                                                                                                                                                            • Border handling ndash extend the input
                                                                                                                                                                                            • Correlation with zero padding
                                                                                                                                                                                            • Border handling ndash extend the input
                                                                                                                                                                                            • Template Matching
                                                                                                                                                                                            • Template Matching
                                                                                                                                                                                            • Template Matching
                                                                                                                                                                                            • Template Matching
                                                                                                                                                                                            • Problematic Correlation
                                                                                                                                                                                            • Normalised Cross Correlation
                                                                                                                                                                                            • Length of template
                                                                                                                                                                                            • Length of image patch
                                                                                                                                                                                            • Normalised Cross Correlation
                                                                                                                                                                                            • Normalised Cross Correlation
                                                                                                                                                                                            • Normalised Cross Correlation
                                                                                                                                                                                            • Edges
                                                                                                                                                                                            • Edges
                                                                                                                                                                                            • Finite Difference
                                                                                                                                                                                            • Edges
                                                                                                                                                                                            • Edges in 2D
                                                                                                                                                                                            • Edge filter kernel
                                                                                                                                                                                            • Prewitt filter
                                                                                                                                                                                            • Edge detection
                                                                                                                                                                                            • Edge filtering
                                                                                                                                                                                            • 02511 - Niveau af dagens emne forelaeligsing
                                                                                                                                                                                            • 02512 - Niveau af dagens emne forelaeligsing
                                                                                                                                                                                            • 02511 - Mit eget udbytte af dagen
                                                                                                                                                                                            • 02512 - Mit eget udbytte af dagen
                                                                                                                                                                                            • 02511 - Sidste uges oslashvelser (pixelwise operations)
                                                                                                                                                                                            • 02512 - Sidste uges oslashvelser (pixelwise operations)
                                                                                                                                                                                            • Denne uges brug af clickers
                                                                                                                                                                                            • What can you do after today
                                                                                                                                                                                            • Oslashvelsesrapport over oslashvelse 4 - 02511
                                                                                                                                                                                            • Exercises
                                                                                                                                                                                              A0
                                                                                                                                                                                              B0
                                                                                                                                                                                              C5
                                                                                                                                                                                              D0
                                                                                                                                                                                              E6
                                                                                                                                                                                              A
                                                                                                                                                                                              B
                                                                                                                                                                                              C
                                                                                                                                                                                              D
                                                                                                                                                                                              E
                                                                                                                                                                                              A3
                                                                                                                                                                                              B0
                                                                                                                                                                                              C3
                                                                                                                                                                                              D0
                                                                                                                                                                                              E0
                                                                                                                                                                                              A
                                                                                                                                                                                              B
                                                                                                                                                                                              C
                                                                                                                                                                                              D
                                                                                                                                                                                              E
                                                                                                                                                                                              A0
                                                                                                                                                                                              B0
                                                                                                                                                                                              C1
                                                                                                                                                                                              D4
                                                                                                                                                                                              E1
                                                                                                                                                                                              A
                                                                                                                                                                                              B
                                                                                                                                                                                              C
                                                                                                                                                                                              D
                                                                                                                                                                                              E
                                                                                                                                                                                              A2
                                                                                                                                                                                              B1
                                                                                                                                                                                              C3
                                                                                                                                                                                              D2
                                                                                                                                                                                              E0
                                                                                                                                                                                              A
                                                                                                                                                                                              B
                                                                                                                                                                                              C
                                                                                                                                                                                              D
                                                                                                                                                                                              E
                                                                                                                                                                                              A0
                                                                                                                                                                                              B0
                                                                                                                                                                                              C2
                                                                                                                                                                                              D6
                                                                                                                                                                                              E0
                                                                                                                                                                                              A
                                                                                                                                                                                              B
                                                                                                                                                                                              C
                                                                                                                                                                                              D
                                                                                                                                                                                              E

                                                                                                                                                                                              Sheet1

                                                                                                                                                                                              DTU Compute

                                                                                                                                                                                              2122018Introduction to Medical Image Analysis79 DTU Compute Technical University of Denmark

                                                                                                                                                                                              02512 - Mit eget udbytte af dagenA) Jeg har laeligrt meget lidtB) Lidt laeligringC) PassendeD) God laeligringE) Jeg har laeligrt meget

                                                                                                                                                                                              2

                                                                                                                                                                                              1

                                                                                                                                                                                              3

                                                                                                                                                                                              2

                                                                                                                                                                                              0

                                                                                                                                                                                              A B C D E

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                                                                                                                                                                                              DTU Compute

                                                                                                                                                                                              2122018Introduction to Medical Image Analysis80 DTU Compute Technical University of Denmark

                                                                                                                                                                                              02511 - Sidste uges oslashvelser (pixelwiseoperations)A) Meget letteB) LetteC) PassendeD) SvaeligreE) Meget svaeligre

                                                                                                                                                                                              0 0

                                                                                                                                                                                              1

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                                                                                                                                                                                              1

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                                                                                                                                                                                              DTU Compute

                                                                                                                                                                                              2122018Introduction to Medical Image Analysis81 DTU Compute Technical University of Denmark

                                                                                                                                                                                              02512 - Sidste uges oslashvelser (pixelwiseoperations)A) Meget letteB) LetteC) PassendeD) SvaeligreE) Meget svaeligre

                                                                                                                                                                                              3

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                                                                                                                                                                                              Sheet1

                                                                                                                                                                                              DTU Compute

                                                                                                                                                                                              2122018Introduction to Medical Image Analysis82 DTU Compute Technical University of Denmark

                                                                                                                                                                                              Denne uges brug af clickersA) click click click ndash jeg bliver

                                                                                                                                                                                              sindssygB) For meget clickC) PassendeD) Jeg vil gerne have lidt mereE) Jeg kan ikrsquo faring nok

                                                                                                                                                                                              0 0

                                                                                                                                                                                              5

                                                                                                                                                                                              0

                                                                                                                                                                                              6

                                                                                                                                                                                              A B C D E

                                                                                                                                                                                              Chart1

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                                                                                                                                                                                              6

                                                                                                                                                                                              Sheet1

                                                                                                                                                                                              DTU Compute

                                                                                                                                                                                              2122018Introduction to Medical Image Analysis83 DTU Compute Technical University of Denmark

                                                                                                                                                                                              What can you do after today Describe the difference between point processing and neighbourhood

                                                                                                                                                                                              processing Compute a rank filtered image using the min max median and

                                                                                                                                                                                              difference rank filters Compute a mean filtered image Decide if median or average filtering should be used for noise removal Choose the appropriate image border handling based on a given input

                                                                                                                                                                                              image Implement and apply template matching Compute the normalised cross correlation and explain why it should be

                                                                                                                                                                                              used Apply given image filter kernels to images Use edge filters on images Describe finite difference approximation of image gradients Describe the concept of edge detection

                                                                                                                                                                                              DTU Compute

                                                                                                                                                                                              2122018Introduction to Medical Image Analysis84 DTU Compute Technical University of Denmark

                                                                                                                                                                                              Oslashvelsesrapport over oslashvelse 4 - 02511 Oslashvelser taeligller cirka 30 af karakteren Skal afleveres senest den 7 marts kl 2359 Kan afleveres af 1 eller 2 personer

                                                                                                                                                                                              ndash I skal skrive jeres egen oslashvelsesrapportndash Brug mindst et af jeres egne billeder

                                                                                                                                                                                              Afleveres som PDF Lad vaeligre med at kopiere opgaveteksten ind i jeres

                                                                                                                                                                                              opgave Put Matlab kode i et Appendix og henvis fra teksten Eksempel rapport over oslashvelse findes paring

                                                                                                                                                                                              hjemmesiden under eksamen

                                                                                                                                                                                              DTU Compute

                                                                                                                                                                                              2122018Introduction to Medical Image Analysis85 DTU Compute Technical University of Denmark

                                                                                                                                                                                              Exercises

                                                                                                                                                                                              • Introduction to Medical Image Analysis
                                                                                                                                                                                              • Lecture 4 ndash Neighbourhood Processing
                                                                                                                                                                                              • What can you do after today
                                                                                                                                                                                              • Point processing
                                                                                                                                                                                              • Point processing
                                                                                                                                                                                              • Neighbourhood processing
                                                                                                                                                                                              • Use of filtering
                                                                                                                                                                                              • Salt and pepper noise
                                                                                                                                                                                              • Salt and pepper noise
                                                                                                                                                                                              • What is so special about noise
                                                                                                                                                                                              • Noise ndash go away
                                                                                                                                                                                              • What is the median Value
                                                                                                                                                                                              • The median value
                                                                                                                                                                                              • Noise away ndash the median filter
                                                                                                                                                                                              • Noise removal ndash average filter
                                                                                                                                                                                              • Noise removal ndash median filter
                                                                                                                                                                                              • Image Filtering
                                                                                                                                                                                              • Median filter
                                                                                                                                                                                              • Rank filters
                                                                                                                                                                                              • Median filter
                                                                                                                                                                                              • Correlation
                                                                                                                                                                                              • Why do we need similarity
                                                                                                                                                                                              • Correlation (1D)
                                                                                                                                                                                              • Correlation (1D)
                                                                                                                                                                                              • Normalisation
                                                                                                                                                                                              • Normalisation
                                                                                                                                                                                              • Correlation on images
                                                                                                                                                                                              • Correlation on images
                                                                                                                                                                                              • Correlation on images
                                                                                                                                                                                              • Draw your filter
                                                                                                                                                                                              • Correlation on images ndash no normalisation
                                                                                                                                                                                              • Correlation on images ndash no normalisation 2
                                                                                                                                                                                              • Mathematics of 2D Correlation
                                                                                                                                                                                              • Mathematics of 2D Correlation
                                                                                                                                                                                              • Mathematics of 2D Correlation
                                                                                                                                                                                              • Slide Number 40
                                                                                                                                                                                              • 2D Kernel Normalisation
                                                                                                                                                                                              • Correlation
                                                                                                                                                                                              • Smoothing filters
                                                                                                                                                                                              • Use of smoothing
                                                                                                                                                                                              • Use of smoothing
                                                                                                                                                                                              • Mean filter
                                                                                                                                                                                              • Border handling
                                                                                                                                                                                              • Border handling ndash extend the input
                                                                                                                                                                                              • Correlation with zero padding
                                                                                                                                                                                              • Border handling ndash extend the input
                                                                                                                                                                                              • Template Matching
                                                                                                                                                                                              • Template Matching
                                                                                                                                                                                              • Template Matching
                                                                                                                                                                                              • Template Matching
                                                                                                                                                                                              • Problematic Correlation
                                                                                                                                                                                              • Normalised Cross Correlation
                                                                                                                                                                                              • Length of template
                                                                                                                                                                                              • Length of image patch
                                                                                                                                                                                              • Normalised Cross Correlation
                                                                                                                                                                                              • Normalised Cross Correlation
                                                                                                                                                                                              • Normalised Cross Correlation
                                                                                                                                                                                              • Edges
                                                                                                                                                                                              • Edges
                                                                                                                                                                                              • Finite Difference
                                                                                                                                                                                              • Edges
                                                                                                                                                                                              • Edges in 2D
                                                                                                                                                                                              • Edge filter kernel
                                                                                                                                                                                              • Prewitt filter
                                                                                                                                                                                              • Edge detection
                                                                                                                                                                                              • Edge filtering
                                                                                                                                                                                              • 02511 - Niveau af dagens emne forelaeligsing
                                                                                                                                                                                              • 02512 - Niveau af dagens emne forelaeligsing
                                                                                                                                                                                              • 02511 - Mit eget udbytte af dagen
                                                                                                                                                                                              • 02512 - Mit eget udbytte af dagen
                                                                                                                                                                                              • 02511 - Sidste uges oslashvelser (pixelwise operations)
                                                                                                                                                                                              • 02512 - Sidste uges oslashvelser (pixelwise operations)
                                                                                                                                                                                              • Denne uges brug af clickers
                                                                                                                                                                                              • What can you do after today
                                                                                                                                                                                              • Oslashvelsesrapport over oslashvelse 4 - 02511
                                                                                                                                                                                              • Exercises
                                                                                                                                                                                                A0
                                                                                                                                                                                                B0
                                                                                                                                                                                                C5
                                                                                                                                                                                                D0
                                                                                                                                                                                                E6
                                                                                                                                                                                                A
                                                                                                                                                                                                B
                                                                                                                                                                                                C
                                                                                                                                                                                                D
                                                                                                                                                                                                E
                                                                                                                                                                                                A3
                                                                                                                                                                                                B0
                                                                                                                                                                                                C3
                                                                                                                                                                                                D0
                                                                                                                                                                                                E0
                                                                                                                                                                                                A
                                                                                                                                                                                                B
                                                                                                                                                                                                C
                                                                                                                                                                                                D
                                                                                                                                                                                                E
                                                                                                                                                                                                A0
                                                                                                                                                                                                B0
                                                                                                                                                                                                C1
                                                                                                                                                                                                D4
                                                                                                                                                                                                E1
                                                                                                                                                                                                A
                                                                                                                                                                                                B
                                                                                                                                                                                                C
                                                                                                                                                                                                D
                                                                                                                                                                                                E
                                                                                                                                                                                                A2
                                                                                                                                                                                                B1
                                                                                                                                                                                                C3
                                                                                                                                                                                                D2
                                                                                                                                                                                                E0
                                                                                                                                                                                                A
                                                                                                                                                                                                B
                                                                                                                                                                                                C
                                                                                                                                                                                                D
                                                                                                                                                                                                E
                                                                                                                                                                                                A0
                                                                                                                                                                                                B0
                                                                                                                                                                                                C2
                                                                                                                                                                                                D6
                                                                                                                                                                                                E0

                                                                                                                                                                                                DTU Compute

                                                                                                                                                                                                2122018Introduction to Medical Image Analysis79 DTU Compute Technical University of Denmark

                                                                                                                                                                                                02512 - Mit eget udbytte af dagenA) Jeg har laeligrt meget lidtB) Lidt laeligringC) PassendeD) God laeligringE) Jeg har laeligrt meget

                                                                                                                                                                                                2

                                                                                                                                                                                                1

                                                                                                                                                                                                3

                                                                                                                                                                                                2

                                                                                                                                                                                                0

                                                                                                                                                                                                A B C D E

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                                                                                                                                                                                                DTU Compute

                                                                                                                                                                                                2122018Introduction to Medical Image Analysis80 DTU Compute Technical University of Denmark

                                                                                                                                                                                                02511 - Sidste uges oslashvelser (pixelwiseoperations)A) Meget letteB) LetteC) PassendeD) SvaeligreE) Meget svaeligre

                                                                                                                                                                                                0 0

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                                                                                                                                                                                                DTU Compute

                                                                                                                                                                                                2122018Introduction to Medical Image Analysis81 DTU Compute Technical University of Denmark

                                                                                                                                                                                                02512 - Sidste uges oslashvelser (pixelwiseoperations)A) Meget letteB) LetteC) PassendeD) SvaeligreE) Meget svaeligre

                                                                                                                                                                                                3

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                                                                                                                                                                                                Sheet1

                                                                                                                                                                                                DTU Compute

                                                                                                                                                                                                2122018Introduction to Medical Image Analysis82 DTU Compute Technical University of Denmark

                                                                                                                                                                                                Denne uges brug af clickersA) click click click ndash jeg bliver

                                                                                                                                                                                                sindssygB) For meget clickC) PassendeD) Jeg vil gerne have lidt mereE) Jeg kan ikrsquo faring nok

                                                                                                                                                                                                0 0

                                                                                                                                                                                                5

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                                                                                                                                                                                                6

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                                                                                                                                                                                                Chart1

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                                                                                                                                                                                                6

                                                                                                                                                                                                Sheet1

                                                                                                                                                                                                DTU Compute

                                                                                                                                                                                                2122018Introduction to Medical Image Analysis83 DTU Compute Technical University of Denmark

                                                                                                                                                                                                What can you do after today Describe the difference between point processing and neighbourhood

                                                                                                                                                                                                processing Compute a rank filtered image using the min max median and

                                                                                                                                                                                                difference rank filters Compute a mean filtered image Decide if median or average filtering should be used for noise removal Choose the appropriate image border handling based on a given input

                                                                                                                                                                                                image Implement and apply template matching Compute the normalised cross correlation and explain why it should be

                                                                                                                                                                                                used Apply given image filter kernels to images Use edge filters on images Describe finite difference approximation of image gradients Describe the concept of edge detection

                                                                                                                                                                                                DTU Compute

                                                                                                                                                                                                2122018Introduction to Medical Image Analysis84 DTU Compute Technical University of Denmark

                                                                                                                                                                                                Oslashvelsesrapport over oslashvelse 4 - 02511 Oslashvelser taeligller cirka 30 af karakteren Skal afleveres senest den 7 marts kl 2359 Kan afleveres af 1 eller 2 personer

                                                                                                                                                                                                ndash I skal skrive jeres egen oslashvelsesrapportndash Brug mindst et af jeres egne billeder

                                                                                                                                                                                                Afleveres som PDF Lad vaeligre med at kopiere opgaveteksten ind i jeres

                                                                                                                                                                                                opgave Put Matlab kode i et Appendix og henvis fra teksten Eksempel rapport over oslashvelse findes paring

                                                                                                                                                                                                hjemmesiden under eksamen

                                                                                                                                                                                                DTU Compute

                                                                                                                                                                                                2122018Introduction to Medical Image Analysis85 DTU Compute Technical University of Denmark

                                                                                                                                                                                                Exercises

                                                                                                                                                                                                • Introduction to Medical Image Analysis
                                                                                                                                                                                                • Lecture 4 ndash Neighbourhood Processing
                                                                                                                                                                                                • What can you do after today
                                                                                                                                                                                                • Point processing
                                                                                                                                                                                                • Point processing
                                                                                                                                                                                                • Neighbourhood processing
                                                                                                                                                                                                • Use of filtering
                                                                                                                                                                                                • Salt and pepper noise
                                                                                                                                                                                                • Salt and pepper noise
                                                                                                                                                                                                • What is so special about noise
                                                                                                                                                                                                • Noise ndash go away
                                                                                                                                                                                                • What is the median Value
                                                                                                                                                                                                • The median value
                                                                                                                                                                                                • Noise away ndash the median filter
                                                                                                                                                                                                • Noise removal ndash average filter
                                                                                                                                                                                                • Noise removal ndash median filter
                                                                                                                                                                                                • Image Filtering
                                                                                                                                                                                                • Median filter
                                                                                                                                                                                                • Rank filters
                                                                                                                                                                                                • Median filter
                                                                                                                                                                                                • Correlation
                                                                                                                                                                                                • Why do we need similarity
                                                                                                                                                                                                • Correlation (1D)
                                                                                                                                                                                                • Correlation (1D)
                                                                                                                                                                                                • Normalisation
                                                                                                                                                                                                • Normalisation
                                                                                                                                                                                                • Correlation on images
                                                                                                                                                                                                • Correlation on images
                                                                                                                                                                                                • Correlation on images
                                                                                                                                                                                                • Draw your filter
                                                                                                                                                                                                • Correlation on images ndash no normalisation
                                                                                                                                                                                                • Correlation on images ndash no normalisation 2
                                                                                                                                                                                                • Mathematics of 2D Correlation
                                                                                                                                                                                                • Mathematics of 2D Correlation
                                                                                                                                                                                                • Mathematics of 2D Correlation
                                                                                                                                                                                                • Slide Number 40
                                                                                                                                                                                                • 2D Kernel Normalisation
                                                                                                                                                                                                • Correlation
                                                                                                                                                                                                • Smoothing filters
                                                                                                                                                                                                • Use of smoothing
                                                                                                                                                                                                • Use of smoothing
                                                                                                                                                                                                • Mean filter
                                                                                                                                                                                                • Border handling
                                                                                                                                                                                                • Border handling ndash extend the input
                                                                                                                                                                                                • Correlation with zero padding
                                                                                                                                                                                                • Border handling ndash extend the input
                                                                                                                                                                                                • Template Matching
                                                                                                                                                                                                • Template Matching
                                                                                                                                                                                                • Template Matching
                                                                                                                                                                                                • Template Matching
                                                                                                                                                                                                • Problematic Correlation
                                                                                                                                                                                                • Normalised Cross Correlation
                                                                                                                                                                                                • Length of template
                                                                                                                                                                                                • Length of image patch
                                                                                                                                                                                                • Normalised Cross Correlation
                                                                                                                                                                                                • Normalised Cross Correlation
                                                                                                                                                                                                • Normalised Cross Correlation
                                                                                                                                                                                                • Edges
                                                                                                                                                                                                • Edges
                                                                                                                                                                                                • Finite Difference
                                                                                                                                                                                                • Edges
                                                                                                                                                                                                • Edges in 2D
                                                                                                                                                                                                • Edge filter kernel
                                                                                                                                                                                                • Prewitt filter
                                                                                                                                                                                                • Edge detection
                                                                                                                                                                                                • Edge filtering
                                                                                                                                                                                                • 02511 - Niveau af dagens emne forelaeligsing
                                                                                                                                                                                                • 02512 - Niveau af dagens emne forelaeligsing
                                                                                                                                                                                                • 02511 - Mit eget udbytte af dagen
                                                                                                                                                                                                • 02512 - Mit eget udbytte af dagen
                                                                                                                                                                                                • 02511 - Sidste uges oslashvelser (pixelwise operations)
                                                                                                                                                                                                • 02512 - Sidste uges oslashvelser (pixelwise operations)
                                                                                                                                                                                                • Denne uges brug af clickers
                                                                                                                                                                                                • What can you do after today
                                                                                                                                                                                                • Oslashvelsesrapport over oslashvelse 4 - 02511
                                                                                                                                                                                                • Exercises
                                                                                                                                                                                                  A0
                                                                                                                                                                                                  B0
                                                                                                                                                                                                  C5
                                                                                                                                                                                                  D0
                                                                                                                                                                                                  E6
                                                                                                                                                                                                  A
                                                                                                                                                                                                  B
                                                                                                                                                                                                  C
                                                                                                                                                                                                  D
                                                                                                                                                                                                  E
                                                                                                                                                                                                  A3
                                                                                                                                                                                                  B0
                                                                                                                                                                                                  C3
                                                                                                                                                                                                  D0
                                                                                                                                                                                                  E0
                                                                                                                                                                                                  A
                                                                                                                                                                                                  B
                                                                                                                                                                                                  C
                                                                                                                                                                                                  D
                                                                                                                                                                                                  E
                                                                                                                                                                                                  A0
                                                                                                                                                                                                  B0
                                                                                                                                                                                                  C1
                                                                                                                                                                                                  D4
                                                                                                                                                                                                  E1
                                                                                                                                                                                                  A
                                                                                                                                                                                                  B
                                                                                                                                                                                                  C
                                                                                                                                                                                                  D
                                                                                                                                                                                                  E
                                                                                                                                                                                                  A2
                                                                                                                                                                                                  B1
                                                                                                                                                                                                  C3
                                                                                                                                                                                                  D2
                                                                                                                                                                                                  E0
                                                                                                                                                                                                  A
                                                                                                                                                                                                  B
                                                                                                                                                                                                  C
                                                                                                                                                                                                  D
                                                                                                                                                                                                  E

                                                                                                                                                                                                  Chart1

                                                                                                                                                                                                  2
                                                                                                                                                                                                  1
                                                                                                                                                                                                  3
                                                                                                                                                                                                  2
                                                                                                                                                                                                  0

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                                                                                                                                                                                                  DTU Compute

                                                                                                                                                                                                  2122018Introduction to Medical Image Analysis80 DTU Compute Technical University of Denmark

                                                                                                                                                                                                  02511 - Sidste uges oslashvelser (pixelwiseoperations)A) Meget letteB) LetteC) PassendeD) SvaeligreE) Meget svaeligre

                                                                                                                                                                                                  0 0

                                                                                                                                                                                                  1

                                                                                                                                                                                                  4

                                                                                                                                                                                                  1

                                                                                                                                                                                                  A B C D E

                                                                                                                                                                                                  Chart1

                                                                                                                                                                                                  0
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                                                                                                                                                                                                  1
                                                                                                                                                                                                  4
                                                                                                                                                                                                  1

                                                                                                                                                                                                  Sheet1

                                                                                                                                                                                                  DTU Compute

                                                                                                                                                                                                  2122018Introduction to Medical Image Analysis81 DTU Compute Technical University of Denmark

                                                                                                                                                                                                  02512 - Sidste uges oslashvelser (pixelwiseoperations)A) Meget letteB) LetteC) PassendeD) SvaeligreE) Meget svaeligre

                                                                                                                                                                                                  3

                                                                                                                                                                                                  0

                                                                                                                                                                                                  3

                                                                                                                                                                                                  0 0

                                                                                                                                                                                                  A B C D E

                                                                                                                                                                                                  Chart1

                                                                                                                                                                                                  3
                                                                                                                                                                                                  0
                                                                                                                                                                                                  3
                                                                                                                                                                                                  0
                                                                                                                                                                                                  0

                                                                                                                                                                                                  Sheet1

                                                                                                                                                                                                  DTU Compute

                                                                                                                                                                                                  2122018Introduction to Medical Image Analysis82 DTU Compute Technical University of Denmark

                                                                                                                                                                                                  Denne uges brug af clickersA) click click click ndash jeg bliver

                                                                                                                                                                                                  sindssygB) For meget clickC) PassendeD) Jeg vil gerne have lidt mereE) Jeg kan ikrsquo faring nok

                                                                                                                                                                                                  0 0

                                                                                                                                                                                                  5

                                                                                                                                                                                                  0

                                                                                                                                                                                                  6

                                                                                                                                                                                                  A B C D E

                                                                                                                                                                                                  Chart1

                                                                                                                                                                                                  0
                                                                                                                                                                                                  0
                                                                                                                                                                                                  5
                                                                                                                                                                                                  0
                                                                                                                                                                                                  6

                                                                                                                                                                                                  Sheet1

                                                                                                                                                                                                  DTU Compute

                                                                                                                                                                                                  2122018Introduction to Medical Image Analysis83 DTU Compute Technical University of Denmark

                                                                                                                                                                                                  What can you do after today Describe the difference between point processing and neighbourhood

                                                                                                                                                                                                  processing Compute a rank filtered image using the min max median and

                                                                                                                                                                                                  difference rank filters Compute a mean filtered image Decide if median or average filtering should be used for noise removal Choose the appropriate image border handling based on a given input

                                                                                                                                                                                                  image Implement and apply template matching Compute the normalised cross correlation and explain why it should be

                                                                                                                                                                                                  used Apply given image filter kernels to images Use edge filters on images Describe finite difference approximation of image gradients Describe the concept of edge detection

                                                                                                                                                                                                  DTU Compute

                                                                                                                                                                                                  2122018Introduction to Medical Image Analysis84 DTU Compute Technical University of Denmark

                                                                                                                                                                                                  Oslashvelsesrapport over oslashvelse 4 - 02511 Oslashvelser taeligller cirka 30 af karakteren Skal afleveres senest den 7 marts kl 2359 Kan afleveres af 1 eller 2 personer

                                                                                                                                                                                                  ndash I skal skrive jeres egen oslashvelsesrapportndash Brug mindst et af jeres egne billeder

                                                                                                                                                                                                  Afleveres som PDF Lad vaeligre med at kopiere opgaveteksten ind i jeres

                                                                                                                                                                                                  opgave Put Matlab kode i et Appendix og henvis fra teksten Eksempel rapport over oslashvelse findes paring

                                                                                                                                                                                                  hjemmesiden under eksamen

                                                                                                                                                                                                  DTU Compute

                                                                                                                                                                                                  2122018Introduction to Medical Image Analysis85 DTU Compute Technical University of Denmark

                                                                                                                                                                                                  Exercises

                                                                                                                                                                                                  • Introduction to Medical Image Analysis
                                                                                                                                                                                                  • Lecture 4 ndash Neighbourhood Processing
                                                                                                                                                                                                  • What can you do after today
                                                                                                                                                                                                  • Point processing
                                                                                                                                                                                                  • Point processing
                                                                                                                                                                                                  • Neighbourhood processing
                                                                                                                                                                                                  • Use of filtering
                                                                                                                                                                                                  • Salt and pepper noise
                                                                                                                                                                                                  • Salt and pepper noise
                                                                                                                                                                                                  • What is so special about noise
                                                                                                                                                                                                  • Noise ndash go away
                                                                                                                                                                                                  • What is the median Value
                                                                                                                                                                                                  • The median value
                                                                                                                                                                                                  • Noise away ndash the median filter
                                                                                                                                                                                                  • Noise removal ndash average filter
                                                                                                                                                                                                  • Noise removal ndash median filter
                                                                                                                                                                                                  • Image Filtering
                                                                                                                                                                                                  • Median filter
                                                                                                                                                                                                  • Rank filters
                                                                                                                                                                                                  • Median filter
                                                                                                                                                                                                  • Correlation
                                                                                                                                                                                                  • Why do we need similarity
                                                                                                                                                                                                  • Correlation (1D)
                                                                                                                                                                                                  • Correlation (1D)
                                                                                                                                                                                                  • Normalisation
                                                                                                                                                                                                  • Normalisation
                                                                                                                                                                                                  • Correlation on images
                                                                                                                                                                                                  • Correlation on images
                                                                                                                                                                                                  • Correlation on images
                                                                                                                                                                                                  • Draw your filter
                                                                                                                                                                                                  • Correlation on images ndash no normalisation
                                                                                                                                                                                                  • Correlation on images ndash no normalisation 2
                                                                                                                                                                                                  • Mathematics of 2D Correlation
                                                                                                                                                                                                  • Mathematics of 2D Correlation
                                                                                                                                                                                                  • Mathematics of 2D Correlation
                                                                                                                                                                                                  • Slide Number 40
                                                                                                                                                                                                  • 2D Kernel Normalisation
                                                                                                                                                                                                  • Correlation
                                                                                                                                                                                                  • Smoothing filters
                                                                                                                                                                                                  • Use of smoothing
                                                                                                                                                                                                  • Use of smoothing
                                                                                                                                                                                                  • Mean filter
                                                                                                                                                                                                  • Border handling
                                                                                                                                                                                                  • Border handling ndash extend the input
                                                                                                                                                                                                  • Correlation with zero padding
                                                                                                                                                                                                  • Border handling ndash extend the input
                                                                                                                                                                                                  • Template Matching
                                                                                                                                                                                                  • Template Matching
                                                                                                                                                                                                  • Template Matching
                                                                                                                                                                                                  • Template Matching
                                                                                                                                                                                                  • Problematic Correlation
                                                                                                                                                                                                  • Normalised Cross Correlation
                                                                                                                                                                                                  • Length of template
                                                                                                                                                                                                  • Length of image patch
                                                                                                                                                                                                  • Normalised Cross Correlation
                                                                                                                                                                                                  • Normalised Cross Correlation
                                                                                                                                                                                                  • Normalised Cross Correlation
                                                                                                                                                                                                  • Edges
                                                                                                                                                                                                  • Edges
                                                                                                                                                                                                  • Finite Difference
                                                                                                                                                                                                  • Edges
                                                                                                                                                                                                  • Edges in 2D
                                                                                                                                                                                                  • Edge filter kernel
                                                                                                                                                                                                  • Prewitt filter
                                                                                                                                                                                                  • Edge detection
                                                                                                                                                                                                  • Edge filtering
                                                                                                                                                                                                  • 02511 - Niveau af dagens emne forelaeligsing
                                                                                                                                                                                                  • 02512 - Niveau af dagens emne forelaeligsing
                                                                                                                                                                                                  • 02511 - Mit eget udbytte af dagen
                                                                                                                                                                                                  • 02512 - Mit eget udbytte af dagen
                                                                                                                                                                                                  • 02511 - Sidste uges oslashvelser (pixelwise operations)
                                                                                                                                                                                                  • 02512 - Sidste uges oslashvelser (pixelwise operations)
                                                                                                                                                                                                  • Denne uges brug af clickers
                                                                                                                                                                                                  • What can you do after today
                                                                                                                                                                                                  • Oslashvelsesrapport over oslashvelse 4 - 02511
                                                                                                                                                                                                  • Exercises
                                                                                                                                                                                                    A0
                                                                                                                                                                                                    B0
                                                                                                                                                                                                    C5
                                                                                                                                                                                                    D0
                                                                                                                                                                                                    E6
                                                                                                                                                                                                    A
                                                                                                                                                                                                    B
                                                                                                                                                                                                    C
                                                                                                                                                                                                    D
                                                                                                                                                                                                    E
                                                                                                                                                                                                    A3
                                                                                                                                                                                                    B0
                                                                                                                                                                                                    C3
                                                                                                                                                                                                    D0
                                                                                                                                                                                                    E0
                                                                                                                                                                                                    A
                                                                                                                                                                                                    B
                                                                                                                                                                                                    C
                                                                                                                                                                                                    D
                                                                                                                                                                                                    E
                                                                                                                                                                                                    A0
                                                                                                                                                                                                    B0
                                                                                                                                                                                                    C1
                                                                                                                                                                                                    D4
                                                                                                                                                                                                    E1
                                                                                                                                                                                                    A
                                                                                                                                                                                                    B
                                                                                                                                                                                                    C
                                                                                                                                                                                                    D
                                                                                                                                                                                                    E
                                                                                                                                                                                                    A2
                                                                                                                                                                                                    B1
                                                                                                                                                                                                    C3
                                                                                                                                                                                                    D2
                                                                                                                                                                                                    E0
                                                                                                                                                                                                    A
                                                                                                                                                                                                    B
                                                                                                                                                                                                    C
                                                                                                                                                                                                    D
                                                                                                                                                                                                    E

                                                                                                                                                                                                    Sheet1

                                                                                                                                                                                                    DTU Compute

                                                                                                                                                                                                    2122018Introduction to Medical Image Analysis80 DTU Compute Technical University of Denmark

                                                                                                                                                                                                    02511 - Sidste uges oslashvelser (pixelwiseoperations)A) Meget letteB) LetteC) PassendeD) SvaeligreE) Meget svaeligre

                                                                                                                                                                                                    0 0

                                                                                                                                                                                                    1

                                                                                                                                                                                                    4

                                                                                                                                                                                                    1

                                                                                                                                                                                                    A B C D E

                                                                                                                                                                                                    Chart1

                                                                                                                                                                                                    0
                                                                                                                                                                                                    0
                                                                                                                                                                                                    1
                                                                                                                                                                                                    4
                                                                                                                                                                                                    1

                                                                                                                                                                                                    Sheet1

                                                                                                                                                                                                    DTU Compute

                                                                                                                                                                                                    2122018Introduction to Medical Image Analysis81 DTU Compute Technical University of Denmark

                                                                                                                                                                                                    02512 - Sidste uges oslashvelser (pixelwiseoperations)A) Meget letteB) LetteC) PassendeD) SvaeligreE) Meget svaeligre

                                                                                                                                                                                                    3

                                                                                                                                                                                                    0

                                                                                                                                                                                                    3

                                                                                                                                                                                                    0 0

                                                                                                                                                                                                    A B C D E

                                                                                                                                                                                                    Chart1

                                                                                                                                                                                                    3
                                                                                                                                                                                                    0
                                                                                                                                                                                                    3
                                                                                                                                                                                                    0
                                                                                                                                                                                                    0

                                                                                                                                                                                                    Sheet1

                                                                                                                                                                                                    DTU Compute

                                                                                                                                                                                                    2122018Introduction to Medical Image Analysis82 DTU Compute Technical University of Denmark

                                                                                                                                                                                                    Denne uges brug af clickersA) click click click ndash jeg bliver

                                                                                                                                                                                                    sindssygB) For meget clickC) PassendeD) Jeg vil gerne have lidt mereE) Jeg kan ikrsquo faring nok

                                                                                                                                                                                                    0 0

                                                                                                                                                                                                    5

                                                                                                                                                                                                    0

                                                                                                                                                                                                    6

                                                                                                                                                                                                    A B C D E

                                                                                                                                                                                                    Chart1

                                                                                                                                                                                                    0
                                                                                                                                                                                                    0
                                                                                                                                                                                                    5
                                                                                                                                                                                                    0
                                                                                                                                                                                                    6

                                                                                                                                                                                                    Sheet1

                                                                                                                                                                                                    DTU Compute

                                                                                                                                                                                                    2122018Introduction to Medical Image Analysis83 DTU Compute Technical University of Denmark

                                                                                                                                                                                                    What can you do after today Describe the difference between point processing and neighbourhood

                                                                                                                                                                                                    processing Compute a rank filtered image using the min max median and

                                                                                                                                                                                                    difference rank filters Compute a mean filtered image Decide if median or average filtering should be used for noise removal Choose the appropriate image border handling based on a given input

                                                                                                                                                                                                    image Implement and apply template matching Compute the normalised cross correlation and explain why it should be

                                                                                                                                                                                                    used Apply given image filter kernels to images Use edge filters on images Describe finite difference approximation of image gradients Describe the concept of edge detection

                                                                                                                                                                                                    DTU Compute

                                                                                                                                                                                                    2122018Introduction to Medical Image Analysis84 DTU Compute Technical University of Denmark

                                                                                                                                                                                                    Oslashvelsesrapport over oslashvelse 4 - 02511 Oslashvelser taeligller cirka 30 af karakteren Skal afleveres senest den 7 marts kl 2359 Kan afleveres af 1 eller 2 personer

                                                                                                                                                                                                    ndash I skal skrive jeres egen oslashvelsesrapportndash Brug mindst et af jeres egne billeder

                                                                                                                                                                                                    Afleveres som PDF Lad vaeligre med at kopiere opgaveteksten ind i jeres

                                                                                                                                                                                                    opgave Put Matlab kode i et Appendix og henvis fra teksten Eksempel rapport over oslashvelse findes paring

                                                                                                                                                                                                    hjemmesiden under eksamen

                                                                                                                                                                                                    DTU Compute

                                                                                                                                                                                                    2122018Introduction to Medical Image Analysis85 DTU Compute Technical University of Denmark

                                                                                                                                                                                                    Exercises

                                                                                                                                                                                                    • Introduction to Medical Image Analysis
                                                                                                                                                                                                    • Lecture 4 ndash Neighbourhood Processing
                                                                                                                                                                                                    • What can you do after today
                                                                                                                                                                                                    • Point processing
                                                                                                                                                                                                    • Point processing
                                                                                                                                                                                                    • Neighbourhood processing
                                                                                                                                                                                                    • Use of filtering
                                                                                                                                                                                                    • Salt and pepper noise
                                                                                                                                                                                                    • Salt and pepper noise
                                                                                                                                                                                                    • What is so special about noise
                                                                                                                                                                                                    • Noise ndash go away
                                                                                                                                                                                                    • What is the median Value
                                                                                                                                                                                                    • The median value
                                                                                                                                                                                                    • Noise away ndash the median filter
                                                                                                                                                                                                    • Noise removal ndash average filter
                                                                                                                                                                                                    • Noise removal ndash median filter
                                                                                                                                                                                                    • Image Filtering
                                                                                                                                                                                                    • Median filter
                                                                                                                                                                                                    • Rank filters
                                                                                                                                                                                                    • Median filter
                                                                                                                                                                                                    • Correlation
                                                                                                                                                                                                    • Why do we need similarity
                                                                                                                                                                                                    • Correlation (1D)
                                                                                                                                                                                                    • Correlation (1D)
                                                                                                                                                                                                    • Normalisation
                                                                                                                                                                                                    • Normalisation
                                                                                                                                                                                                    • Correlation on images
                                                                                                                                                                                                    • Correlation on images
                                                                                                                                                                                                    • Correlation on images
                                                                                                                                                                                                    • Draw your filter
                                                                                                                                                                                                    • Correlation on images ndash no normalisation
                                                                                                                                                                                                    • Correlation on images ndash no normalisation 2
                                                                                                                                                                                                    • Mathematics of 2D Correlation
                                                                                                                                                                                                    • Mathematics of 2D Correlation
                                                                                                                                                                                                    • Mathematics of 2D Correlation
                                                                                                                                                                                                    • Slide Number 40
                                                                                                                                                                                                    • 2D Kernel Normalisation
                                                                                                                                                                                                    • Correlation
                                                                                                                                                                                                    • Smoothing filters
                                                                                                                                                                                                    • Use of smoothing
                                                                                                                                                                                                    • Use of smoothing
                                                                                                                                                                                                    • Mean filter
                                                                                                                                                                                                    • Border handling
                                                                                                                                                                                                    • Border handling ndash extend the input
                                                                                                                                                                                                    • Correlation with zero padding
                                                                                                                                                                                                    • Border handling ndash extend the input
                                                                                                                                                                                                    • Template Matching
                                                                                                                                                                                                    • Template Matching
                                                                                                                                                                                                    • Template Matching
                                                                                                                                                                                                    • Template Matching
                                                                                                                                                                                                    • Problematic Correlation
                                                                                                                                                                                                    • Normalised Cross Correlation
                                                                                                                                                                                                    • Length of template
                                                                                                                                                                                                    • Length of image patch
                                                                                                                                                                                                    • Normalised Cross Correlation
                                                                                                                                                                                                    • Normalised Cross Correlation
                                                                                                                                                                                                    • Normalised Cross Correlation
                                                                                                                                                                                                    • Edges
                                                                                                                                                                                                    • Edges
                                                                                                                                                                                                    • Finite Difference
                                                                                                                                                                                                    • Edges
                                                                                                                                                                                                    • Edges in 2D
                                                                                                                                                                                                    • Edge filter kernel
                                                                                                                                                                                                    • Prewitt filter
                                                                                                                                                                                                    • Edge detection
                                                                                                                                                                                                    • Edge filtering
                                                                                                                                                                                                    • 02511 - Niveau af dagens emne forelaeligsing
                                                                                                                                                                                                    • 02512 - Niveau af dagens emne forelaeligsing
                                                                                                                                                                                                    • 02511 - Mit eget udbytte af dagen
                                                                                                                                                                                                    • 02512 - Mit eget udbytte af dagen
                                                                                                                                                                                                    • 02511 - Sidste uges oslashvelser (pixelwise operations)
                                                                                                                                                                                                    • 02512 - Sidste uges oslashvelser (pixelwise operations)
                                                                                                                                                                                                    • Denne uges brug af clickers
                                                                                                                                                                                                    • What can you do after today
                                                                                                                                                                                                    • Oslashvelsesrapport over oslashvelse 4 - 02511
                                                                                                                                                                                                    • Exercises
                                                                                                                                                                                                      A0
                                                                                                                                                                                                      B0
                                                                                                                                                                                                      C5
                                                                                                                                                                                                      D0
                                                                                                                                                                                                      E6
                                                                                                                                                                                                      A
                                                                                                                                                                                                      B
                                                                                                                                                                                                      C
                                                                                                                                                                                                      D
                                                                                                                                                                                                      E
                                                                                                                                                                                                      A3
                                                                                                                                                                                                      B0
                                                                                                                                                                                                      C3
                                                                                                                                                                                                      D0
                                                                                                                                                                                                      E0
                                                                                                                                                                                                      A
                                                                                                                                                                                                      B
                                                                                                                                                                                                      C
                                                                                                                                                                                                      D
                                                                                                                                                                                                      E
                                                                                                                                                                                                      A0
                                                                                                                                                                                                      B0
                                                                                                                                                                                                      C1
                                                                                                                                                                                                      D4
                                                                                                                                                                                                      E1
                                                                                                                                                                                                      A
                                                                                                                                                                                                      B
                                                                                                                                                                                                      C
                                                                                                                                                                                                      D
                                                                                                                                                                                                      E
                                                                                                                                                                                                      A2
                                                                                                                                                                                                      B1
                                                                                                                                                                                                      C3
                                                                                                                                                                                                      D2
                                                                                                                                                                                                      E0

                                                                                                                                                                                                      DTU Compute

                                                                                                                                                                                                      2122018Introduction to Medical Image Analysis80 DTU Compute Technical University of Denmark

                                                                                                                                                                                                      02511 - Sidste uges oslashvelser (pixelwiseoperations)A) Meget letteB) LetteC) PassendeD) SvaeligreE) Meget svaeligre

                                                                                                                                                                                                      0 0

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                                                                                                                                                                                                      4

                                                                                                                                                                                                      1

                                                                                                                                                                                                      A B C D E

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                                                                                                                                                                                                      4
                                                                                                                                                                                                      1

                                                                                                                                                                                                      Sheet1

                                                                                                                                                                                                      DTU Compute

                                                                                                                                                                                                      2122018Introduction to Medical Image Analysis81 DTU Compute Technical University of Denmark

                                                                                                                                                                                                      02512 - Sidste uges oslashvelser (pixelwiseoperations)A) Meget letteB) LetteC) PassendeD) SvaeligreE) Meget svaeligre

                                                                                                                                                                                                      3

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                                                                                                                                                                                                      Sheet1

                                                                                                                                                                                                      DTU Compute

                                                                                                                                                                                                      2122018Introduction to Medical Image Analysis82 DTU Compute Technical University of Denmark

                                                                                                                                                                                                      Denne uges brug af clickersA) click click click ndash jeg bliver

                                                                                                                                                                                                      sindssygB) For meget clickC) PassendeD) Jeg vil gerne have lidt mereE) Jeg kan ikrsquo faring nok

                                                                                                                                                                                                      0 0

                                                                                                                                                                                                      5

                                                                                                                                                                                                      0

                                                                                                                                                                                                      6

                                                                                                                                                                                                      A B C D E

                                                                                                                                                                                                      Chart1

                                                                                                                                                                                                      0
                                                                                                                                                                                                      0
                                                                                                                                                                                                      5
                                                                                                                                                                                                      0
                                                                                                                                                                                                      6

                                                                                                                                                                                                      Sheet1

                                                                                                                                                                                                      DTU Compute

                                                                                                                                                                                                      2122018Introduction to Medical Image Analysis83 DTU Compute Technical University of Denmark

                                                                                                                                                                                                      What can you do after today Describe the difference between point processing and neighbourhood

                                                                                                                                                                                                      processing Compute a rank filtered image using the min max median and

                                                                                                                                                                                                      difference rank filters Compute a mean filtered image Decide if median or average filtering should be used for noise removal Choose the appropriate image border handling based on a given input

                                                                                                                                                                                                      image Implement and apply template matching Compute the normalised cross correlation and explain why it should be

                                                                                                                                                                                                      used Apply given image filter kernels to images Use edge filters on images Describe finite difference approximation of image gradients Describe the concept of edge detection

                                                                                                                                                                                                      DTU Compute

                                                                                                                                                                                                      2122018Introduction to Medical Image Analysis84 DTU Compute Technical University of Denmark

                                                                                                                                                                                                      Oslashvelsesrapport over oslashvelse 4 - 02511 Oslashvelser taeligller cirka 30 af karakteren Skal afleveres senest den 7 marts kl 2359 Kan afleveres af 1 eller 2 personer

                                                                                                                                                                                                      ndash I skal skrive jeres egen oslashvelsesrapportndash Brug mindst et af jeres egne billeder

                                                                                                                                                                                                      Afleveres som PDF Lad vaeligre med at kopiere opgaveteksten ind i jeres

                                                                                                                                                                                                      opgave Put Matlab kode i et Appendix og henvis fra teksten Eksempel rapport over oslashvelse findes paring

                                                                                                                                                                                                      hjemmesiden under eksamen

                                                                                                                                                                                                      DTU Compute

                                                                                                                                                                                                      2122018Introduction to Medical Image Analysis85 DTU Compute Technical University of Denmark

                                                                                                                                                                                                      Exercises

                                                                                                                                                                                                      • Introduction to Medical Image Analysis
                                                                                                                                                                                                      • Lecture 4 ndash Neighbourhood Processing
                                                                                                                                                                                                      • What can you do after today
                                                                                                                                                                                                      • Point processing
                                                                                                                                                                                                      • Point processing
                                                                                                                                                                                                      • Neighbourhood processing
                                                                                                                                                                                                      • Use of filtering
                                                                                                                                                                                                      • Salt and pepper noise
                                                                                                                                                                                                      • Salt and pepper noise
                                                                                                                                                                                                      • What is so special about noise
                                                                                                                                                                                                      • Noise ndash go away
                                                                                                                                                                                                      • What is the median Value
                                                                                                                                                                                                      • The median value
                                                                                                                                                                                                      • Noise away ndash the median filter
                                                                                                                                                                                                      • Noise removal ndash average filter
                                                                                                                                                                                                      • Noise removal ndash median filter
                                                                                                                                                                                                      • Image Filtering
                                                                                                                                                                                                      • Median filter
                                                                                                                                                                                                      • Rank filters
                                                                                                                                                                                                      • Median filter
                                                                                                                                                                                                      • Correlation
                                                                                                                                                                                                      • Why do we need similarity
                                                                                                                                                                                                      • Correlation (1D)
                                                                                                                                                                                                      • Correlation (1D)
                                                                                                                                                                                                      • Normalisation
                                                                                                                                                                                                      • Normalisation
                                                                                                                                                                                                      • Correlation on images
                                                                                                                                                                                                      • Correlation on images
                                                                                                                                                                                                      • Correlation on images
                                                                                                                                                                                                      • Draw your filter
                                                                                                                                                                                                      • Correlation on images ndash no normalisation
                                                                                                                                                                                                      • Correlation on images ndash no normalisation 2
                                                                                                                                                                                                      • Mathematics of 2D Correlation
                                                                                                                                                                                                      • Mathematics of 2D Correlation
                                                                                                                                                                                                      • Mathematics of 2D Correlation
                                                                                                                                                                                                      • Slide Number 40
                                                                                                                                                                                                      • 2D Kernel Normalisation
                                                                                                                                                                                                      • Correlation
                                                                                                                                                                                                      • Smoothing filters
                                                                                                                                                                                                      • Use of smoothing
                                                                                                                                                                                                      • Use of smoothing
                                                                                                                                                                                                      • Mean filter
                                                                                                                                                                                                      • Border handling
                                                                                                                                                                                                      • Border handling ndash extend the input
                                                                                                                                                                                                      • Correlation with zero padding
                                                                                                                                                                                                      • Border handling ndash extend the input
                                                                                                                                                                                                      • Template Matching
                                                                                                                                                                                                      • Template Matching
                                                                                                                                                                                                      • Template Matching
                                                                                                                                                                                                      • Template Matching
                                                                                                                                                                                                      • Problematic Correlation
                                                                                                                                                                                                      • Normalised Cross Correlation
                                                                                                                                                                                                      • Length of template
                                                                                                                                                                                                      • Length of image patch
                                                                                                                                                                                                      • Normalised Cross Correlation
                                                                                                                                                                                                      • Normalised Cross Correlation
                                                                                                                                                                                                      • Normalised Cross Correlation
                                                                                                                                                                                                      • Edges
                                                                                                                                                                                                      • Edges
                                                                                                                                                                                                      • Finite Difference
                                                                                                                                                                                                      • Edges
                                                                                                                                                                                                      • Edges in 2D
                                                                                                                                                                                                      • Edge filter kernel
                                                                                                                                                                                                      • Prewitt filter
                                                                                                                                                                                                      • Edge detection
                                                                                                                                                                                                      • Edge filtering
                                                                                                                                                                                                      • 02511 - Niveau af dagens emne forelaeligsing
                                                                                                                                                                                                      • 02512 - Niveau af dagens emne forelaeligsing
                                                                                                                                                                                                      • 02511 - Mit eget udbytte af dagen
                                                                                                                                                                                                      • 02512 - Mit eget udbytte af dagen
                                                                                                                                                                                                      • 02511 - Sidste uges oslashvelser (pixelwise operations)
                                                                                                                                                                                                      • 02512 - Sidste uges oslashvelser (pixelwise operations)
                                                                                                                                                                                                      • Denne uges brug af clickers
                                                                                                                                                                                                      • What can you do after today
                                                                                                                                                                                                      • Oslashvelsesrapport over oslashvelse 4 - 02511
                                                                                                                                                                                                      • Exercises
                                                                                                                                                                                                        A0
                                                                                                                                                                                                        B0
                                                                                                                                                                                                        C5
                                                                                                                                                                                                        D0
                                                                                                                                                                                                        E6
                                                                                                                                                                                                        A
                                                                                                                                                                                                        B
                                                                                                                                                                                                        C
                                                                                                                                                                                                        D
                                                                                                                                                                                                        E
                                                                                                                                                                                                        A3
                                                                                                                                                                                                        B0
                                                                                                                                                                                                        C3
                                                                                                                                                                                                        D0
                                                                                                                                                                                                        E0
                                                                                                                                                                                                        A
                                                                                                                                                                                                        B
                                                                                                                                                                                                        C
                                                                                                                                                                                                        D
                                                                                                                                                                                                        E
                                                                                                                                                                                                        A0
                                                                                                                                                                                                        B0
                                                                                                                                                                                                        C1
                                                                                                                                                                                                        D4
                                                                                                                                                                                                        E1
                                                                                                                                                                                                        A
                                                                                                                                                                                                        B
                                                                                                                                                                                                        C
                                                                                                                                                                                                        D
                                                                                                                                                                                                        E

                                                                                                                                                                                                        Chart1

                                                                                                                                                                                                        0
                                                                                                                                                                                                        0
                                                                                                                                                                                                        1
                                                                                                                                                                                                        4
                                                                                                                                                                                                        1

                                                                                                                                                                                                        Sheet1

                                                                                                                                                                                                        DTU Compute

                                                                                                                                                                                                        2122018Introduction to Medical Image Analysis81 DTU Compute Technical University of Denmark

                                                                                                                                                                                                        02512 - Sidste uges oslashvelser (pixelwiseoperations)A) Meget letteB) LetteC) PassendeD) SvaeligreE) Meget svaeligre

                                                                                                                                                                                                        3

                                                                                                                                                                                                        0

                                                                                                                                                                                                        3

                                                                                                                                                                                                        0 0

                                                                                                                                                                                                        A B C D E

                                                                                                                                                                                                        Chart1

                                                                                                                                                                                                        3
                                                                                                                                                                                                        0
                                                                                                                                                                                                        3
                                                                                                                                                                                                        0
                                                                                                                                                                                                        0

                                                                                                                                                                                                        Sheet1

                                                                                                                                                                                                        DTU Compute

                                                                                                                                                                                                        2122018Introduction to Medical Image Analysis82 DTU Compute Technical University of Denmark

                                                                                                                                                                                                        Denne uges brug af clickersA) click click click ndash jeg bliver

                                                                                                                                                                                                        sindssygB) For meget clickC) PassendeD) Jeg vil gerne have lidt mereE) Jeg kan ikrsquo faring nok

                                                                                                                                                                                                        0 0

                                                                                                                                                                                                        5

                                                                                                                                                                                                        0

                                                                                                                                                                                                        6

                                                                                                                                                                                                        A B C D E

                                                                                                                                                                                                        Chart1

                                                                                                                                                                                                        0
                                                                                                                                                                                                        0
                                                                                                                                                                                                        5
                                                                                                                                                                                                        0
                                                                                                                                                                                                        6

                                                                                                                                                                                                        Sheet1

                                                                                                                                                                                                        DTU Compute

                                                                                                                                                                                                        2122018Introduction to Medical Image Analysis83 DTU Compute Technical University of Denmark

                                                                                                                                                                                                        What can you do after today Describe the difference between point processing and neighbourhood

                                                                                                                                                                                                        processing Compute a rank filtered image using the min max median and

                                                                                                                                                                                                        difference rank filters Compute a mean filtered image Decide if median or average filtering should be used for noise removal Choose the appropriate image border handling based on a given input

                                                                                                                                                                                                        image Implement and apply template matching Compute the normalised cross correlation and explain why it should be

                                                                                                                                                                                                        used Apply given image filter kernels to images Use edge filters on images Describe finite difference approximation of image gradients Describe the concept of edge detection

                                                                                                                                                                                                        DTU Compute

                                                                                                                                                                                                        2122018Introduction to Medical Image Analysis84 DTU Compute Technical University of Denmark

                                                                                                                                                                                                        Oslashvelsesrapport over oslashvelse 4 - 02511 Oslashvelser taeligller cirka 30 af karakteren Skal afleveres senest den 7 marts kl 2359 Kan afleveres af 1 eller 2 personer

                                                                                                                                                                                                        ndash I skal skrive jeres egen oslashvelsesrapportndash Brug mindst et af jeres egne billeder

                                                                                                                                                                                                        Afleveres som PDF Lad vaeligre med at kopiere opgaveteksten ind i jeres

                                                                                                                                                                                                        opgave Put Matlab kode i et Appendix og henvis fra teksten Eksempel rapport over oslashvelse findes paring

                                                                                                                                                                                                        hjemmesiden under eksamen

                                                                                                                                                                                                        DTU Compute

                                                                                                                                                                                                        2122018Introduction to Medical Image Analysis85 DTU Compute Technical University of Denmark

                                                                                                                                                                                                        Exercises

                                                                                                                                                                                                        • Introduction to Medical Image Analysis
                                                                                                                                                                                                        • Lecture 4 ndash Neighbourhood Processing
                                                                                                                                                                                                        • What can you do after today
                                                                                                                                                                                                        • Point processing
                                                                                                                                                                                                        • Point processing
                                                                                                                                                                                                        • Neighbourhood processing
                                                                                                                                                                                                        • Use of filtering
                                                                                                                                                                                                        • Salt and pepper noise
                                                                                                                                                                                                        • Salt and pepper noise
                                                                                                                                                                                                        • What is so special about noise
                                                                                                                                                                                                        • Noise ndash go away
                                                                                                                                                                                                        • What is the median Value
                                                                                                                                                                                                        • The median value
                                                                                                                                                                                                        • Noise away ndash the median filter
                                                                                                                                                                                                        • Noise removal ndash average filter
                                                                                                                                                                                                        • Noise removal ndash median filter
                                                                                                                                                                                                        • Image Filtering
                                                                                                                                                                                                        • Median filter
                                                                                                                                                                                                        • Rank filters
                                                                                                                                                                                                        • Median filter
                                                                                                                                                                                                        • Correlation
                                                                                                                                                                                                        • Why do we need similarity
                                                                                                                                                                                                        • Correlation (1D)
                                                                                                                                                                                                        • Correlation (1D)
                                                                                                                                                                                                        • Normalisation
                                                                                                                                                                                                        • Normalisation
                                                                                                                                                                                                        • Correlation on images
                                                                                                                                                                                                        • Correlation on images
                                                                                                                                                                                                        • Correlation on images
                                                                                                                                                                                                        • Draw your filter
                                                                                                                                                                                                        • Correlation on images ndash no normalisation
                                                                                                                                                                                                        • Correlation on images ndash no normalisation 2
                                                                                                                                                                                                        • Mathematics of 2D Correlation
                                                                                                                                                                                                        • Mathematics of 2D Correlation
                                                                                                                                                                                                        • Mathematics of 2D Correlation
                                                                                                                                                                                                        • Slide Number 40
                                                                                                                                                                                                        • 2D Kernel Normalisation
                                                                                                                                                                                                        • Correlation
                                                                                                                                                                                                        • Smoothing filters
                                                                                                                                                                                                        • Use of smoothing
                                                                                                                                                                                                        • Use of smoothing
                                                                                                                                                                                                        • Mean filter
                                                                                                                                                                                                        • Border handling
                                                                                                                                                                                                        • Border handling ndash extend the input
                                                                                                                                                                                                        • Correlation with zero padding
                                                                                                                                                                                                        • Border handling ndash extend the input
                                                                                                                                                                                                        • Template Matching
                                                                                                                                                                                                        • Template Matching
                                                                                                                                                                                                        • Template Matching
                                                                                                                                                                                                        • Template Matching
                                                                                                                                                                                                        • Problematic Correlation
                                                                                                                                                                                                        • Normalised Cross Correlation
                                                                                                                                                                                                        • Length of template
                                                                                                                                                                                                        • Length of image patch
                                                                                                                                                                                                        • Normalised Cross Correlation
                                                                                                                                                                                                        • Normalised Cross Correlation
                                                                                                                                                                                                        • Normalised Cross Correlation
                                                                                                                                                                                                        • Edges
                                                                                                                                                                                                        • Edges
                                                                                                                                                                                                        • Finite Difference
                                                                                                                                                                                                        • Edges
                                                                                                                                                                                                        • Edges in 2D
                                                                                                                                                                                                        • Edge filter kernel
                                                                                                                                                                                                        • Prewitt filter
                                                                                                                                                                                                        • Edge detection
                                                                                                                                                                                                        • Edge filtering
                                                                                                                                                                                                        • 02511 - Niveau af dagens emne forelaeligsing
                                                                                                                                                                                                        • 02512 - Niveau af dagens emne forelaeligsing
                                                                                                                                                                                                        • 02511 - Mit eget udbytte af dagen
                                                                                                                                                                                                        • 02512 - Mit eget udbytte af dagen
                                                                                                                                                                                                        • 02511 - Sidste uges oslashvelser (pixelwise operations)
                                                                                                                                                                                                        • 02512 - Sidste uges oslashvelser (pixelwise operations)
                                                                                                                                                                                                        • Denne uges brug af clickers
                                                                                                                                                                                                        • What can you do after today
                                                                                                                                                                                                        • Oslashvelsesrapport over oslashvelse 4 - 02511
                                                                                                                                                                                                        • Exercises
                                                                                                                                                                                                          A0
                                                                                                                                                                                                          B0
                                                                                                                                                                                                          C5
                                                                                                                                                                                                          D0
                                                                                                                                                                                                          E6
                                                                                                                                                                                                          A
                                                                                                                                                                                                          B
                                                                                                                                                                                                          C
                                                                                                                                                                                                          D
                                                                                                                                                                                                          E
                                                                                                                                                                                                          A3
                                                                                                                                                                                                          B0
                                                                                                                                                                                                          C3
                                                                                                                                                                                                          D0
                                                                                                                                                                                                          E0
                                                                                                                                                                                                          A
                                                                                                                                                                                                          B
                                                                                                                                                                                                          C
                                                                                                                                                                                                          D
                                                                                                                                                                                                          E
                                                                                                                                                                                                          A0
                                                                                                                                                                                                          B0
                                                                                                                                                                                                          C1
                                                                                                                                                                                                          D4
                                                                                                                                                                                                          E1
                                                                                                                                                                                                          A
                                                                                                                                                                                                          B
                                                                                                                                                                                                          C
                                                                                                                                                                                                          D
                                                                                                                                                                                                          E

                                                                                                                                                                                                          Sheet1

                                                                                                                                                                                                          DTU Compute

                                                                                                                                                                                                          2122018Introduction to Medical Image Analysis81 DTU Compute Technical University of Denmark

                                                                                                                                                                                                          02512 - Sidste uges oslashvelser (pixelwiseoperations)A) Meget letteB) LetteC) PassendeD) SvaeligreE) Meget svaeligre

                                                                                                                                                                                                          3

                                                                                                                                                                                                          0

                                                                                                                                                                                                          3

                                                                                                                                                                                                          0 0

                                                                                                                                                                                                          A B C D E

                                                                                                                                                                                                          Chart1

                                                                                                                                                                                                          3
                                                                                                                                                                                                          0
                                                                                                                                                                                                          3
                                                                                                                                                                                                          0
                                                                                                                                                                                                          0

                                                                                                                                                                                                          Sheet1

                                                                                                                                                                                                          DTU Compute

                                                                                                                                                                                                          2122018Introduction to Medical Image Analysis82 DTU Compute Technical University of Denmark

                                                                                                                                                                                                          Denne uges brug af clickersA) click click click ndash jeg bliver

                                                                                                                                                                                                          sindssygB) For meget clickC) PassendeD) Jeg vil gerne have lidt mereE) Jeg kan ikrsquo faring nok

                                                                                                                                                                                                          0 0

                                                                                                                                                                                                          5

                                                                                                                                                                                                          0

                                                                                                                                                                                                          6

                                                                                                                                                                                                          A B C D E

                                                                                                                                                                                                          Chart1

                                                                                                                                                                                                          0
                                                                                                                                                                                                          0
                                                                                                                                                                                                          5
                                                                                                                                                                                                          0
                                                                                                                                                                                                          6

                                                                                                                                                                                                          Sheet1

                                                                                                                                                                                                          DTU Compute

                                                                                                                                                                                                          2122018Introduction to Medical Image Analysis83 DTU Compute Technical University of Denmark

                                                                                                                                                                                                          What can you do after today Describe the difference between point processing and neighbourhood

                                                                                                                                                                                                          processing Compute a rank filtered image using the min max median and

                                                                                                                                                                                                          difference rank filters Compute a mean filtered image Decide if median or average filtering should be used for noise removal Choose the appropriate image border handling based on a given input

                                                                                                                                                                                                          image Implement and apply template matching Compute the normalised cross correlation and explain why it should be

                                                                                                                                                                                                          used Apply given image filter kernels to images Use edge filters on images Describe finite difference approximation of image gradients Describe the concept of edge detection

                                                                                                                                                                                                          DTU Compute

                                                                                                                                                                                                          2122018Introduction to Medical Image Analysis84 DTU Compute Technical University of Denmark

                                                                                                                                                                                                          Oslashvelsesrapport over oslashvelse 4 - 02511 Oslashvelser taeligller cirka 30 af karakteren Skal afleveres senest den 7 marts kl 2359 Kan afleveres af 1 eller 2 personer

                                                                                                                                                                                                          ndash I skal skrive jeres egen oslashvelsesrapportndash Brug mindst et af jeres egne billeder

                                                                                                                                                                                                          Afleveres som PDF Lad vaeligre med at kopiere opgaveteksten ind i jeres

                                                                                                                                                                                                          opgave Put Matlab kode i et Appendix og henvis fra teksten Eksempel rapport over oslashvelse findes paring

                                                                                                                                                                                                          hjemmesiden under eksamen

                                                                                                                                                                                                          DTU Compute

                                                                                                                                                                                                          2122018Introduction to Medical Image Analysis85 DTU Compute Technical University of Denmark

                                                                                                                                                                                                          Exercises

                                                                                                                                                                                                          • Introduction to Medical Image Analysis
                                                                                                                                                                                                          • Lecture 4 ndash Neighbourhood Processing
                                                                                                                                                                                                          • What can you do after today
                                                                                                                                                                                                          • Point processing
                                                                                                                                                                                                          • Point processing
                                                                                                                                                                                                          • Neighbourhood processing
                                                                                                                                                                                                          • Use of filtering
                                                                                                                                                                                                          • Salt and pepper noise
                                                                                                                                                                                                          • Salt and pepper noise
                                                                                                                                                                                                          • What is so special about noise
                                                                                                                                                                                                          • Noise ndash go away
                                                                                                                                                                                                          • What is the median Value
                                                                                                                                                                                                          • The median value
                                                                                                                                                                                                          • Noise away ndash the median filter
                                                                                                                                                                                                          • Noise removal ndash average filter
                                                                                                                                                                                                          • Noise removal ndash median filter
                                                                                                                                                                                                          • Image Filtering
                                                                                                                                                                                                          • Median filter
                                                                                                                                                                                                          • Rank filters
                                                                                                                                                                                                          • Median filter
                                                                                                                                                                                                          • Correlation
                                                                                                                                                                                                          • Why do we need similarity
                                                                                                                                                                                                          • Correlation (1D)
                                                                                                                                                                                                          • Correlation (1D)
                                                                                                                                                                                                          • Normalisation
                                                                                                                                                                                                          • Normalisation
                                                                                                                                                                                                          • Correlation on images
                                                                                                                                                                                                          • Correlation on images
                                                                                                                                                                                                          • Correlation on images
                                                                                                                                                                                                          • Draw your filter
                                                                                                                                                                                                          • Correlation on images ndash no normalisation
                                                                                                                                                                                                          • Correlation on images ndash no normalisation 2
                                                                                                                                                                                                          • Mathematics of 2D Correlation
                                                                                                                                                                                                          • Mathematics of 2D Correlation
                                                                                                                                                                                                          • Mathematics of 2D Correlation
                                                                                                                                                                                                          • Slide Number 40
                                                                                                                                                                                                          • 2D Kernel Normalisation
                                                                                                                                                                                                          • Correlation
                                                                                                                                                                                                          • Smoothing filters
                                                                                                                                                                                                          • Use of smoothing
                                                                                                                                                                                                          • Use of smoothing
                                                                                                                                                                                                          • Mean filter
                                                                                                                                                                                                          • Border handling
                                                                                                                                                                                                          • Border handling ndash extend the input
                                                                                                                                                                                                          • Correlation with zero padding
                                                                                                                                                                                                          • Border handling ndash extend the input
                                                                                                                                                                                                          • Template Matching
                                                                                                                                                                                                          • Template Matching
                                                                                                                                                                                                          • Template Matching
                                                                                                                                                                                                          • Template Matching
                                                                                                                                                                                                          • Problematic Correlation
                                                                                                                                                                                                          • Normalised Cross Correlation
                                                                                                                                                                                                          • Length of template
                                                                                                                                                                                                          • Length of image patch
                                                                                                                                                                                                          • Normalised Cross Correlation
                                                                                                                                                                                                          • Normalised Cross Correlation
                                                                                                                                                                                                          • Normalised Cross Correlation
                                                                                                                                                                                                          • Edges
                                                                                                                                                                                                          • Edges
                                                                                                                                                                                                          • Finite Difference
                                                                                                                                                                                                          • Edges
                                                                                                                                                                                                          • Edges in 2D
                                                                                                                                                                                                          • Edge filter kernel
                                                                                                                                                                                                          • Prewitt filter
                                                                                                                                                                                                          • Edge detection
                                                                                                                                                                                                          • Edge filtering
                                                                                                                                                                                                          • 02511 - Niveau af dagens emne forelaeligsing
                                                                                                                                                                                                          • 02512 - Niveau af dagens emne forelaeligsing
                                                                                                                                                                                                          • 02511 - Mit eget udbytte af dagen
                                                                                                                                                                                                          • 02512 - Mit eget udbytte af dagen
                                                                                                                                                                                                          • 02511 - Sidste uges oslashvelser (pixelwise operations)
                                                                                                                                                                                                          • 02512 - Sidste uges oslashvelser (pixelwise operations)
                                                                                                                                                                                                          • Denne uges brug af clickers
                                                                                                                                                                                                          • What can you do after today
                                                                                                                                                                                                          • Oslashvelsesrapport over oslashvelse 4 - 02511
                                                                                                                                                                                                          • Exercises
                                                                                                                                                                                                            A0
                                                                                                                                                                                                            B0
                                                                                                                                                                                                            C5
                                                                                                                                                                                                            D0
                                                                                                                                                                                                            E6
                                                                                                                                                                                                            A
                                                                                                                                                                                                            B
                                                                                                                                                                                                            C
                                                                                                                                                                                                            D
                                                                                                                                                                                                            E
                                                                                                                                                                                                            A3
                                                                                                                                                                                                            B0
                                                                                                                                                                                                            C3
                                                                                                                                                                                                            D0
                                                                                                                                                                                                            E0
                                                                                                                                                                                                            A
                                                                                                                                                                                                            B
                                                                                                                                                                                                            C
                                                                                                                                                                                                            D
                                                                                                                                                                                                            E
                                                                                                                                                                                                            A0
                                                                                                                                                                                                            B0
                                                                                                                                                                                                            C1
                                                                                                                                                                                                            D4
                                                                                                                                                                                                            E1

                                                                                                                                                                                                            DTU Compute

                                                                                                                                                                                                            2122018Introduction to Medical Image Analysis81 DTU Compute Technical University of Denmark

                                                                                                                                                                                                            02512 - Sidste uges oslashvelser (pixelwiseoperations)A) Meget letteB) LetteC) PassendeD) SvaeligreE) Meget svaeligre

                                                                                                                                                                                                            3

                                                                                                                                                                                                            0

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                                                                                                                                                                                                            A B C D E

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                                                                                                                                                                                                            Sheet1

                                                                                                                                                                                                            DTU Compute

                                                                                                                                                                                                            2122018Introduction to Medical Image Analysis82 DTU Compute Technical University of Denmark

                                                                                                                                                                                                            Denne uges brug af clickersA) click click click ndash jeg bliver

                                                                                                                                                                                                            sindssygB) For meget clickC) PassendeD) Jeg vil gerne have lidt mereE) Jeg kan ikrsquo faring nok

                                                                                                                                                                                                            0 0

                                                                                                                                                                                                            5

                                                                                                                                                                                                            0

                                                                                                                                                                                                            6

                                                                                                                                                                                                            A B C D E

                                                                                                                                                                                                            Chart1

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                                                                                                                                                                                                            5
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                                                                                                                                                                                                            Sheet1

                                                                                                                                                                                                            DTU Compute

                                                                                                                                                                                                            2122018Introduction to Medical Image Analysis83 DTU Compute Technical University of Denmark

                                                                                                                                                                                                            What can you do after today Describe the difference between point processing and neighbourhood

                                                                                                                                                                                                            processing Compute a rank filtered image using the min max median and

                                                                                                                                                                                                            difference rank filters Compute a mean filtered image Decide if median or average filtering should be used for noise removal Choose the appropriate image border handling based on a given input

                                                                                                                                                                                                            image Implement and apply template matching Compute the normalised cross correlation and explain why it should be

                                                                                                                                                                                                            used Apply given image filter kernels to images Use edge filters on images Describe finite difference approximation of image gradients Describe the concept of edge detection

                                                                                                                                                                                                            DTU Compute

                                                                                                                                                                                                            2122018Introduction to Medical Image Analysis84 DTU Compute Technical University of Denmark

                                                                                                                                                                                                            Oslashvelsesrapport over oslashvelse 4 - 02511 Oslashvelser taeligller cirka 30 af karakteren Skal afleveres senest den 7 marts kl 2359 Kan afleveres af 1 eller 2 personer

                                                                                                                                                                                                            ndash I skal skrive jeres egen oslashvelsesrapportndash Brug mindst et af jeres egne billeder

                                                                                                                                                                                                            Afleveres som PDF Lad vaeligre med at kopiere opgaveteksten ind i jeres

                                                                                                                                                                                                            opgave Put Matlab kode i et Appendix og henvis fra teksten Eksempel rapport over oslashvelse findes paring

                                                                                                                                                                                                            hjemmesiden under eksamen

                                                                                                                                                                                                            DTU Compute

                                                                                                                                                                                                            2122018Introduction to Medical Image Analysis85 DTU Compute Technical University of Denmark

                                                                                                                                                                                                            Exercises

                                                                                                                                                                                                            • Introduction to Medical Image Analysis
                                                                                                                                                                                                            • Lecture 4 ndash Neighbourhood Processing
                                                                                                                                                                                                            • What can you do after today
                                                                                                                                                                                                            • Point processing
                                                                                                                                                                                                            • Point processing
                                                                                                                                                                                                            • Neighbourhood processing
                                                                                                                                                                                                            • Use of filtering
                                                                                                                                                                                                            • Salt and pepper noise
                                                                                                                                                                                                            • Salt and pepper noise
                                                                                                                                                                                                            • What is so special about noise
                                                                                                                                                                                                            • Noise ndash go away
                                                                                                                                                                                                            • What is the median Value
                                                                                                                                                                                                            • The median value
                                                                                                                                                                                                            • Noise away ndash the median filter
                                                                                                                                                                                                            • Noise removal ndash average filter
                                                                                                                                                                                                            • Noise removal ndash median filter
                                                                                                                                                                                                            • Image Filtering
                                                                                                                                                                                                            • Median filter
                                                                                                                                                                                                            • Rank filters
                                                                                                                                                                                                            • Median filter
                                                                                                                                                                                                            • Correlation
                                                                                                                                                                                                            • Why do we need similarity
                                                                                                                                                                                                            • Correlation (1D)
                                                                                                                                                                                                            • Correlation (1D)
                                                                                                                                                                                                            • Normalisation
                                                                                                                                                                                                            • Normalisation
                                                                                                                                                                                                            • Correlation on images
                                                                                                                                                                                                            • Correlation on images
                                                                                                                                                                                                            • Correlation on images
                                                                                                                                                                                                            • Draw your filter
                                                                                                                                                                                                            • Correlation on images ndash no normalisation
                                                                                                                                                                                                            • Correlation on images ndash no normalisation 2
                                                                                                                                                                                                            • Mathematics of 2D Correlation
                                                                                                                                                                                                            • Mathematics of 2D Correlation
                                                                                                                                                                                                            • Mathematics of 2D Correlation
                                                                                                                                                                                                            • Slide Number 40
                                                                                                                                                                                                            • 2D Kernel Normalisation
                                                                                                                                                                                                            • Correlation
                                                                                                                                                                                                            • Smoothing filters
                                                                                                                                                                                                            • Use of smoothing
                                                                                                                                                                                                            • Use of smoothing
                                                                                                                                                                                                            • Mean filter
                                                                                                                                                                                                            • Border handling
                                                                                                                                                                                                            • Border handling ndash extend the input
                                                                                                                                                                                                            • Correlation with zero padding
                                                                                                                                                                                                            • Border handling ndash extend the input
                                                                                                                                                                                                            • Template Matching
                                                                                                                                                                                                            • Template Matching
                                                                                                                                                                                                            • Template Matching
                                                                                                                                                                                                            • Template Matching
                                                                                                                                                                                                            • Problematic Correlation
                                                                                                                                                                                                            • Normalised Cross Correlation
                                                                                                                                                                                                            • Length of template
                                                                                                                                                                                                            • Length of image patch
                                                                                                                                                                                                            • Normalised Cross Correlation
                                                                                                                                                                                                            • Normalised Cross Correlation
                                                                                                                                                                                                            • Normalised Cross Correlation
                                                                                                                                                                                                            • Edges
                                                                                                                                                                                                            • Edges
                                                                                                                                                                                                            • Finite Difference
                                                                                                                                                                                                            • Edges
                                                                                                                                                                                                            • Edges in 2D
                                                                                                                                                                                                            • Edge filter kernel
                                                                                                                                                                                                            • Prewitt filter
                                                                                                                                                                                                            • Edge detection
                                                                                                                                                                                                            • Edge filtering
                                                                                                                                                                                                            • 02511 - Niveau af dagens emne forelaeligsing
                                                                                                                                                                                                            • 02512 - Niveau af dagens emne forelaeligsing
                                                                                                                                                                                                            • 02511 - Mit eget udbytte af dagen
                                                                                                                                                                                                            • 02512 - Mit eget udbytte af dagen
                                                                                                                                                                                                            • 02511 - Sidste uges oslashvelser (pixelwise operations)
                                                                                                                                                                                                            • 02512 - Sidste uges oslashvelser (pixelwise operations)
                                                                                                                                                                                                            • Denne uges brug af clickers
                                                                                                                                                                                                            • What can you do after today
                                                                                                                                                                                                            • Oslashvelsesrapport over oslashvelse 4 - 02511
                                                                                                                                                                                                            • Exercises
                                                                                                                                                                                                              A0
                                                                                                                                                                                                              B0
                                                                                                                                                                                                              C5
                                                                                                                                                                                                              D0
                                                                                                                                                                                                              E6
                                                                                                                                                                                                              A
                                                                                                                                                                                                              B
                                                                                                                                                                                                              C
                                                                                                                                                                                                              D
                                                                                                                                                                                                              E
                                                                                                                                                                                                              A3
                                                                                                                                                                                                              B0
                                                                                                                                                                                                              C3
                                                                                                                                                                                                              D0
                                                                                                                                                                                                              E0
                                                                                                                                                                                                              A
                                                                                                                                                                                                              B
                                                                                                                                                                                                              C
                                                                                                                                                                                                              D
                                                                                                                                                                                                              E

                                                                                                                                                                                                              Chart1

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                                                                                                                                                                                                              DTU Compute

                                                                                                                                                                                                              2122018Introduction to Medical Image Analysis82 DTU Compute Technical University of Denmark

                                                                                                                                                                                                              Denne uges brug af clickersA) click click click ndash jeg bliver

                                                                                                                                                                                                              sindssygB) For meget clickC) PassendeD) Jeg vil gerne have lidt mereE) Jeg kan ikrsquo faring nok

                                                                                                                                                                                                              0 0

                                                                                                                                                                                                              5

                                                                                                                                                                                                              0

                                                                                                                                                                                                              6

                                                                                                                                                                                                              A B C D E

                                                                                                                                                                                                              Chart1

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                                                                                                                                                                                                              Sheet1

                                                                                                                                                                                                              DTU Compute

                                                                                                                                                                                                              2122018Introduction to Medical Image Analysis83 DTU Compute Technical University of Denmark

                                                                                                                                                                                                              What can you do after today Describe the difference between point processing and neighbourhood

                                                                                                                                                                                                              processing Compute a rank filtered image using the min max median and

                                                                                                                                                                                                              difference rank filters Compute a mean filtered image Decide if median or average filtering should be used for noise removal Choose the appropriate image border handling based on a given input

                                                                                                                                                                                                              image Implement and apply template matching Compute the normalised cross correlation and explain why it should be

                                                                                                                                                                                                              used Apply given image filter kernels to images Use edge filters on images Describe finite difference approximation of image gradients Describe the concept of edge detection

                                                                                                                                                                                                              DTU Compute

                                                                                                                                                                                                              2122018Introduction to Medical Image Analysis84 DTU Compute Technical University of Denmark

                                                                                                                                                                                                              Oslashvelsesrapport over oslashvelse 4 - 02511 Oslashvelser taeligller cirka 30 af karakteren Skal afleveres senest den 7 marts kl 2359 Kan afleveres af 1 eller 2 personer

                                                                                                                                                                                                              ndash I skal skrive jeres egen oslashvelsesrapportndash Brug mindst et af jeres egne billeder

                                                                                                                                                                                                              Afleveres som PDF Lad vaeligre med at kopiere opgaveteksten ind i jeres

                                                                                                                                                                                                              opgave Put Matlab kode i et Appendix og henvis fra teksten Eksempel rapport over oslashvelse findes paring

                                                                                                                                                                                                              hjemmesiden under eksamen

                                                                                                                                                                                                              DTU Compute

                                                                                                                                                                                                              2122018Introduction to Medical Image Analysis85 DTU Compute Technical University of Denmark

                                                                                                                                                                                                              Exercises

                                                                                                                                                                                                              • Introduction to Medical Image Analysis
                                                                                                                                                                                                              • Lecture 4 ndash Neighbourhood Processing
                                                                                                                                                                                                              • What can you do after today
                                                                                                                                                                                                              • Point processing
                                                                                                                                                                                                              • Point processing
                                                                                                                                                                                                              • Neighbourhood processing
                                                                                                                                                                                                              • Use of filtering
                                                                                                                                                                                                              • Salt and pepper noise
                                                                                                                                                                                                              • Salt and pepper noise
                                                                                                                                                                                                              • What is so special about noise
                                                                                                                                                                                                              • Noise ndash go away
                                                                                                                                                                                                              • What is the median Value
                                                                                                                                                                                                              • The median value
                                                                                                                                                                                                              • Noise away ndash the median filter
                                                                                                                                                                                                              • Noise removal ndash average filter
                                                                                                                                                                                                              • Noise removal ndash median filter
                                                                                                                                                                                                              • Image Filtering
                                                                                                                                                                                                              • Median filter
                                                                                                                                                                                                              • Rank filters
                                                                                                                                                                                                              • Median filter
                                                                                                                                                                                                              • Correlation
                                                                                                                                                                                                              • Why do we need similarity
                                                                                                                                                                                                              • Correlation (1D)
                                                                                                                                                                                                              • Correlation (1D)
                                                                                                                                                                                                              • Normalisation
                                                                                                                                                                                                              • Normalisation
                                                                                                                                                                                                              • Correlation on images
                                                                                                                                                                                                              • Correlation on images
                                                                                                                                                                                                              • Correlation on images
                                                                                                                                                                                                              • Draw your filter
                                                                                                                                                                                                              • Correlation on images ndash no normalisation
                                                                                                                                                                                                              • Correlation on images ndash no normalisation 2
                                                                                                                                                                                                              • Mathematics of 2D Correlation
                                                                                                                                                                                                              • Mathematics of 2D Correlation
                                                                                                                                                                                                              • Mathematics of 2D Correlation
                                                                                                                                                                                                              • Slide Number 40
                                                                                                                                                                                                              • 2D Kernel Normalisation
                                                                                                                                                                                                              • Correlation
                                                                                                                                                                                                              • Smoothing filters
                                                                                                                                                                                                              • Use of smoothing
                                                                                                                                                                                                              • Use of smoothing
                                                                                                                                                                                                              • Mean filter
                                                                                                                                                                                                              • Border handling
                                                                                                                                                                                                              • Border handling ndash extend the input
                                                                                                                                                                                                              • Correlation with zero padding
                                                                                                                                                                                                              • Border handling ndash extend the input
                                                                                                                                                                                                              • Template Matching
                                                                                                                                                                                                              • Template Matching
                                                                                                                                                                                                              • Template Matching
                                                                                                                                                                                                              • Template Matching
                                                                                                                                                                                                              • Problematic Correlation
                                                                                                                                                                                                              • Normalised Cross Correlation
                                                                                                                                                                                                              • Length of template
                                                                                                                                                                                                              • Length of image patch
                                                                                                                                                                                                              • Normalised Cross Correlation
                                                                                                                                                                                                              • Normalised Cross Correlation
                                                                                                                                                                                                              • Normalised Cross Correlation
                                                                                                                                                                                                              • Edges
                                                                                                                                                                                                              • Edges
                                                                                                                                                                                                              • Finite Difference
                                                                                                                                                                                                              • Edges
                                                                                                                                                                                                              • Edges in 2D
                                                                                                                                                                                                              • Edge filter kernel
                                                                                                                                                                                                              • Prewitt filter
                                                                                                                                                                                                              • Edge detection
                                                                                                                                                                                                              • Edge filtering
                                                                                                                                                                                                              • 02511 - Niveau af dagens emne forelaeligsing
                                                                                                                                                                                                              • 02512 - Niveau af dagens emne forelaeligsing
                                                                                                                                                                                                              • 02511 - Mit eget udbytte af dagen
                                                                                                                                                                                                              • 02512 - Mit eget udbytte af dagen
                                                                                                                                                                                                              • 02511 - Sidste uges oslashvelser (pixelwise operations)
                                                                                                                                                                                                              • 02512 - Sidste uges oslashvelser (pixelwise operations)
                                                                                                                                                                                                              • Denne uges brug af clickers
                                                                                                                                                                                                              • What can you do after today
                                                                                                                                                                                                              • Oslashvelsesrapport over oslashvelse 4 - 02511
                                                                                                                                                                                                              • Exercises
                                                                                                                                                                                                                A0
                                                                                                                                                                                                                B0
                                                                                                                                                                                                                C5
                                                                                                                                                                                                                D0
                                                                                                                                                                                                                E6
                                                                                                                                                                                                                A
                                                                                                                                                                                                                B
                                                                                                                                                                                                                C
                                                                                                                                                                                                                D
                                                                                                                                                                                                                E
                                                                                                                                                                                                                A3
                                                                                                                                                                                                                B0
                                                                                                                                                                                                                C3
                                                                                                                                                                                                                D0
                                                                                                                                                                                                                E0
                                                                                                                                                                                                                A
                                                                                                                                                                                                                B
                                                                                                                                                                                                                C
                                                                                                                                                                                                                D
                                                                                                                                                                                                                E

                                                                                                                                                                                                                Sheet1

                                                                                                                                                                                                                DTU Compute

                                                                                                                                                                                                                2122018Introduction to Medical Image Analysis82 DTU Compute Technical University of Denmark

                                                                                                                                                                                                                Denne uges brug af clickersA) click click click ndash jeg bliver

                                                                                                                                                                                                                sindssygB) For meget clickC) PassendeD) Jeg vil gerne have lidt mereE) Jeg kan ikrsquo faring nok

                                                                                                                                                                                                                0 0

                                                                                                                                                                                                                5

                                                                                                                                                                                                                0

                                                                                                                                                                                                                6

                                                                                                                                                                                                                A B C D E

                                                                                                                                                                                                                Chart1

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                                                                                                                                                                                                                5
                                                                                                                                                                                                                0
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                                                                                                                                                                                                                Sheet1

                                                                                                                                                                                                                DTU Compute

                                                                                                                                                                                                                2122018Introduction to Medical Image Analysis83 DTU Compute Technical University of Denmark

                                                                                                                                                                                                                What can you do after today Describe the difference between point processing and neighbourhood

                                                                                                                                                                                                                processing Compute a rank filtered image using the min max median and

                                                                                                                                                                                                                difference rank filters Compute a mean filtered image Decide if median or average filtering should be used for noise removal Choose the appropriate image border handling based on a given input

                                                                                                                                                                                                                image Implement and apply template matching Compute the normalised cross correlation and explain why it should be

                                                                                                                                                                                                                used Apply given image filter kernels to images Use edge filters on images Describe finite difference approximation of image gradients Describe the concept of edge detection

                                                                                                                                                                                                                DTU Compute

                                                                                                                                                                                                                2122018Introduction to Medical Image Analysis84 DTU Compute Technical University of Denmark

                                                                                                                                                                                                                Oslashvelsesrapport over oslashvelse 4 - 02511 Oslashvelser taeligller cirka 30 af karakteren Skal afleveres senest den 7 marts kl 2359 Kan afleveres af 1 eller 2 personer

                                                                                                                                                                                                                ndash I skal skrive jeres egen oslashvelsesrapportndash Brug mindst et af jeres egne billeder

                                                                                                                                                                                                                Afleveres som PDF Lad vaeligre med at kopiere opgaveteksten ind i jeres

                                                                                                                                                                                                                opgave Put Matlab kode i et Appendix og henvis fra teksten Eksempel rapport over oslashvelse findes paring

                                                                                                                                                                                                                hjemmesiden under eksamen

                                                                                                                                                                                                                DTU Compute

                                                                                                                                                                                                                2122018Introduction to Medical Image Analysis85 DTU Compute Technical University of Denmark

                                                                                                                                                                                                                Exercises

                                                                                                                                                                                                                • Introduction to Medical Image Analysis
                                                                                                                                                                                                                • Lecture 4 ndash Neighbourhood Processing
                                                                                                                                                                                                                • What can you do after today
                                                                                                                                                                                                                • Point processing
                                                                                                                                                                                                                • Point processing
                                                                                                                                                                                                                • Neighbourhood processing
                                                                                                                                                                                                                • Use of filtering
                                                                                                                                                                                                                • Salt and pepper noise
                                                                                                                                                                                                                • Salt and pepper noise
                                                                                                                                                                                                                • What is so special about noise
                                                                                                                                                                                                                • Noise ndash go away
                                                                                                                                                                                                                • What is the median Value
                                                                                                                                                                                                                • The median value
                                                                                                                                                                                                                • Noise away ndash the median filter
                                                                                                                                                                                                                • Noise removal ndash average filter
                                                                                                                                                                                                                • Noise removal ndash median filter
                                                                                                                                                                                                                • Image Filtering
                                                                                                                                                                                                                • Median filter
                                                                                                                                                                                                                • Rank filters
                                                                                                                                                                                                                • Median filter
                                                                                                                                                                                                                • Correlation
                                                                                                                                                                                                                • Why do we need similarity
                                                                                                                                                                                                                • Correlation (1D)
                                                                                                                                                                                                                • Correlation (1D)
                                                                                                                                                                                                                • Normalisation
                                                                                                                                                                                                                • Normalisation
                                                                                                                                                                                                                • Correlation on images
                                                                                                                                                                                                                • Correlation on images
                                                                                                                                                                                                                • Correlation on images
                                                                                                                                                                                                                • Draw your filter
                                                                                                                                                                                                                • Correlation on images ndash no normalisation
                                                                                                                                                                                                                • Correlation on images ndash no normalisation 2
                                                                                                                                                                                                                • Mathematics of 2D Correlation
                                                                                                                                                                                                                • Mathematics of 2D Correlation
                                                                                                                                                                                                                • Mathematics of 2D Correlation
                                                                                                                                                                                                                • Slide Number 40
                                                                                                                                                                                                                • 2D Kernel Normalisation
                                                                                                                                                                                                                • Correlation
                                                                                                                                                                                                                • Smoothing filters
                                                                                                                                                                                                                • Use of smoothing
                                                                                                                                                                                                                • Use of smoothing
                                                                                                                                                                                                                • Mean filter
                                                                                                                                                                                                                • Border handling
                                                                                                                                                                                                                • Border handling ndash extend the input
                                                                                                                                                                                                                • Correlation with zero padding
                                                                                                                                                                                                                • Border handling ndash extend the input
                                                                                                                                                                                                                • Template Matching
                                                                                                                                                                                                                • Template Matching
                                                                                                                                                                                                                • Template Matching
                                                                                                                                                                                                                • Template Matching
                                                                                                                                                                                                                • Problematic Correlation
                                                                                                                                                                                                                • Normalised Cross Correlation
                                                                                                                                                                                                                • Length of template
                                                                                                                                                                                                                • Length of image patch
                                                                                                                                                                                                                • Normalised Cross Correlation
                                                                                                                                                                                                                • Normalised Cross Correlation
                                                                                                                                                                                                                • Normalised Cross Correlation
                                                                                                                                                                                                                • Edges
                                                                                                                                                                                                                • Edges
                                                                                                                                                                                                                • Finite Difference
                                                                                                                                                                                                                • Edges
                                                                                                                                                                                                                • Edges in 2D
                                                                                                                                                                                                                • Edge filter kernel
                                                                                                                                                                                                                • Prewitt filter
                                                                                                                                                                                                                • Edge detection
                                                                                                                                                                                                                • Edge filtering
                                                                                                                                                                                                                • 02511 - Niveau af dagens emne forelaeligsing
                                                                                                                                                                                                                • 02512 - Niveau af dagens emne forelaeligsing
                                                                                                                                                                                                                • 02511 - Mit eget udbytte af dagen
                                                                                                                                                                                                                • 02512 - Mit eget udbytte af dagen
                                                                                                                                                                                                                • 02511 - Sidste uges oslashvelser (pixelwise operations)
                                                                                                                                                                                                                • 02512 - Sidste uges oslashvelser (pixelwise operations)
                                                                                                                                                                                                                • Denne uges brug af clickers
                                                                                                                                                                                                                • What can you do after today
                                                                                                                                                                                                                • Oslashvelsesrapport over oslashvelse 4 - 02511
                                                                                                                                                                                                                • Exercises
                                                                                                                                                                                                                  A0
                                                                                                                                                                                                                  B0
                                                                                                                                                                                                                  C5
                                                                                                                                                                                                                  D0
                                                                                                                                                                                                                  E6
                                                                                                                                                                                                                  A
                                                                                                                                                                                                                  B
                                                                                                                                                                                                                  C
                                                                                                                                                                                                                  D
                                                                                                                                                                                                                  E
                                                                                                                                                                                                                  A3
                                                                                                                                                                                                                  B0
                                                                                                                                                                                                                  C3
                                                                                                                                                                                                                  D0
                                                                                                                                                                                                                  E0

                                                                                                                                                                                                                  DTU Compute

                                                                                                                                                                                                                  2122018Introduction to Medical Image Analysis82 DTU Compute Technical University of Denmark

                                                                                                                                                                                                                  Denne uges brug af clickersA) click click click ndash jeg bliver

                                                                                                                                                                                                                  sindssygB) For meget clickC) PassendeD) Jeg vil gerne have lidt mereE) Jeg kan ikrsquo faring nok

                                                                                                                                                                                                                  0 0

                                                                                                                                                                                                                  5

                                                                                                                                                                                                                  0

                                                                                                                                                                                                                  6

                                                                                                                                                                                                                  A B C D E

                                                                                                                                                                                                                  Chart1

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                                                                                                                                                                                                                  5
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                                                                                                                                                                                                                  Sheet1

                                                                                                                                                                                                                  DTU Compute

                                                                                                                                                                                                                  2122018Introduction to Medical Image Analysis83 DTU Compute Technical University of Denmark

                                                                                                                                                                                                                  What can you do after today Describe the difference between point processing and neighbourhood

                                                                                                                                                                                                                  processing Compute a rank filtered image using the min max median and

                                                                                                                                                                                                                  difference rank filters Compute a mean filtered image Decide if median or average filtering should be used for noise removal Choose the appropriate image border handling based on a given input

                                                                                                                                                                                                                  image Implement and apply template matching Compute the normalised cross correlation and explain why it should be

                                                                                                                                                                                                                  used Apply given image filter kernels to images Use edge filters on images Describe finite difference approximation of image gradients Describe the concept of edge detection

                                                                                                                                                                                                                  DTU Compute

                                                                                                                                                                                                                  2122018Introduction to Medical Image Analysis84 DTU Compute Technical University of Denmark

                                                                                                                                                                                                                  Oslashvelsesrapport over oslashvelse 4 - 02511 Oslashvelser taeligller cirka 30 af karakteren Skal afleveres senest den 7 marts kl 2359 Kan afleveres af 1 eller 2 personer

                                                                                                                                                                                                                  ndash I skal skrive jeres egen oslashvelsesrapportndash Brug mindst et af jeres egne billeder

                                                                                                                                                                                                                  Afleveres som PDF Lad vaeligre med at kopiere opgaveteksten ind i jeres

                                                                                                                                                                                                                  opgave Put Matlab kode i et Appendix og henvis fra teksten Eksempel rapport over oslashvelse findes paring

                                                                                                                                                                                                                  hjemmesiden under eksamen

                                                                                                                                                                                                                  DTU Compute

                                                                                                                                                                                                                  2122018Introduction to Medical Image Analysis85 DTU Compute Technical University of Denmark

                                                                                                                                                                                                                  Exercises

                                                                                                                                                                                                                  • Introduction to Medical Image Analysis
                                                                                                                                                                                                                  • Lecture 4 ndash Neighbourhood Processing
                                                                                                                                                                                                                  • What can you do after today
                                                                                                                                                                                                                  • Point processing
                                                                                                                                                                                                                  • Point processing
                                                                                                                                                                                                                  • Neighbourhood processing
                                                                                                                                                                                                                  • Use of filtering
                                                                                                                                                                                                                  • Salt and pepper noise
                                                                                                                                                                                                                  • Salt and pepper noise
                                                                                                                                                                                                                  • What is so special about noise
                                                                                                                                                                                                                  • Noise ndash go away
                                                                                                                                                                                                                  • What is the median Value
                                                                                                                                                                                                                  • The median value
                                                                                                                                                                                                                  • Noise away ndash the median filter
                                                                                                                                                                                                                  • Noise removal ndash average filter
                                                                                                                                                                                                                  • Noise removal ndash median filter
                                                                                                                                                                                                                  • Image Filtering
                                                                                                                                                                                                                  • Median filter
                                                                                                                                                                                                                  • Rank filters
                                                                                                                                                                                                                  • Median filter
                                                                                                                                                                                                                  • Correlation
                                                                                                                                                                                                                  • Why do we need similarity
                                                                                                                                                                                                                  • Correlation (1D)
                                                                                                                                                                                                                  • Correlation (1D)
                                                                                                                                                                                                                  • Normalisation
                                                                                                                                                                                                                  • Normalisation
                                                                                                                                                                                                                  • Correlation on images
                                                                                                                                                                                                                  • Correlation on images
                                                                                                                                                                                                                  • Correlation on images
                                                                                                                                                                                                                  • Draw your filter
                                                                                                                                                                                                                  • Correlation on images ndash no normalisation
                                                                                                                                                                                                                  • Correlation on images ndash no normalisation 2
                                                                                                                                                                                                                  • Mathematics of 2D Correlation
                                                                                                                                                                                                                  • Mathematics of 2D Correlation
                                                                                                                                                                                                                  • Mathematics of 2D Correlation
                                                                                                                                                                                                                  • Slide Number 40
                                                                                                                                                                                                                  • 2D Kernel Normalisation
                                                                                                                                                                                                                  • Correlation
                                                                                                                                                                                                                  • Smoothing filters
                                                                                                                                                                                                                  • Use of smoothing
                                                                                                                                                                                                                  • Use of smoothing
                                                                                                                                                                                                                  • Mean filter
                                                                                                                                                                                                                  • Border handling
                                                                                                                                                                                                                  • Border handling ndash extend the input
                                                                                                                                                                                                                  • Correlation with zero padding
                                                                                                                                                                                                                  • Border handling ndash extend the input
                                                                                                                                                                                                                  • Template Matching
                                                                                                                                                                                                                  • Template Matching
                                                                                                                                                                                                                  • Template Matching
                                                                                                                                                                                                                  • Template Matching
                                                                                                                                                                                                                  • Problematic Correlation
                                                                                                                                                                                                                  • Normalised Cross Correlation
                                                                                                                                                                                                                  • Length of template
                                                                                                                                                                                                                  • Length of image patch
                                                                                                                                                                                                                  • Normalised Cross Correlation
                                                                                                                                                                                                                  • Normalised Cross Correlation
                                                                                                                                                                                                                  • Normalised Cross Correlation
                                                                                                                                                                                                                  • Edges
                                                                                                                                                                                                                  • Edges
                                                                                                                                                                                                                  • Finite Difference
                                                                                                                                                                                                                  • Edges
                                                                                                                                                                                                                  • Edges in 2D
                                                                                                                                                                                                                  • Edge filter kernel
                                                                                                                                                                                                                  • Prewitt filter
                                                                                                                                                                                                                  • Edge detection
                                                                                                                                                                                                                  • Edge filtering
                                                                                                                                                                                                                  • 02511 - Niveau af dagens emne forelaeligsing
                                                                                                                                                                                                                  • 02512 - Niveau af dagens emne forelaeligsing
                                                                                                                                                                                                                  • 02511 - Mit eget udbytte af dagen
                                                                                                                                                                                                                  • 02512 - Mit eget udbytte af dagen
                                                                                                                                                                                                                  • 02511 - Sidste uges oslashvelser (pixelwise operations)
                                                                                                                                                                                                                  • 02512 - Sidste uges oslashvelser (pixelwise operations)
                                                                                                                                                                                                                  • Denne uges brug af clickers
                                                                                                                                                                                                                  • What can you do after today
                                                                                                                                                                                                                  • Oslashvelsesrapport over oslashvelse 4 - 02511
                                                                                                                                                                                                                  • Exercises
                                                                                                                                                                                                                    A0
                                                                                                                                                                                                                    B0
                                                                                                                                                                                                                    C5
                                                                                                                                                                                                                    D0
                                                                                                                                                                                                                    E6
                                                                                                                                                                                                                    A
                                                                                                                                                                                                                    B
                                                                                                                                                                                                                    C
                                                                                                                                                                                                                    D
                                                                                                                                                                                                                    E

                                                                                                                                                                                                                    Chart1

                                                                                                                                                                                                                    0
                                                                                                                                                                                                                    0
                                                                                                                                                                                                                    5
                                                                                                                                                                                                                    0
                                                                                                                                                                                                                    6

                                                                                                                                                                                                                    Sheet1

                                                                                                                                                                                                                    DTU Compute

                                                                                                                                                                                                                    2122018Introduction to Medical Image Analysis83 DTU Compute Technical University of Denmark

                                                                                                                                                                                                                    What can you do after today Describe the difference between point processing and neighbourhood

                                                                                                                                                                                                                    processing Compute a rank filtered image using the min max median and

                                                                                                                                                                                                                    difference rank filters Compute a mean filtered image Decide if median or average filtering should be used for noise removal Choose the appropriate image border handling based on a given input

                                                                                                                                                                                                                    image Implement and apply template matching Compute the normalised cross correlation and explain why it should be

                                                                                                                                                                                                                    used Apply given image filter kernels to images Use edge filters on images Describe finite difference approximation of image gradients Describe the concept of edge detection

                                                                                                                                                                                                                    DTU Compute

                                                                                                                                                                                                                    2122018Introduction to Medical Image Analysis84 DTU Compute Technical University of Denmark

                                                                                                                                                                                                                    Oslashvelsesrapport over oslashvelse 4 - 02511 Oslashvelser taeligller cirka 30 af karakteren Skal afleveres senest den 7 marts kl 2359 Kan afleveres af 1 eller 2 personer

                                                                                                                                                                                                                    ndash I skal skrive jeres egen oslashvelsesrapportndash Brug mindst et af jeres egne billeder

                                                                                                                                                                                                                    Afleveres som PDF Lad vaeligre med at kopiere opgaveteksten ind i jeres

                                                                                                                                                                                                                    opgave Put Matlab kode i et Appendix og henvis fra teksten Eksempel rapport over oslashvelse findes paring

                                                                                                                                                                                                                    hjemmesiden under eksamen

                                                                                                                                                                                                                    DTU Compute

                                                                                                                                                                                                                    2122018Introduction to Medical Image Analysis85 DTU Compute Technical University of Denmark

                                                                                                                                                                                                                    Exercises

                                                                                                                                                                                                                    • Introduction to Medical Image Analysis
                                                                                                                                                                                                                    • Lecture 4 ndash Neighbourhood Processing
                                                                                                                                                                                                                    • What can you do after today
                                                                                                                                                                                                                    • Point processing
                                                                                                                                                                                                                    • Point processing
                                                                                                                                                                                                                    • Neighbourhood processing
                                                                                                                                                                                                                    • Use of filtering
                                                                                                                                                                                                                    • Salt and pepper noise
                                                                                                                                                                                                                    • Salt and pepper noise
                                                                                                                                                                                                                    • What is so special about noise
                                                                                                                                                                                                                    • Noise ndash go away
                                                                                                                                                                                                                    • What is the median Value
                                                                                                                                                                                                                    • The median value
                                                                                                                                                                                                                    • Noise away ndash the median filter
                                                                                                                                                                                                                    • Noise removal ndash average filter
                                                                                                                                                                                                                    • Noise removal ndash median filter
                                                                                                                                                                                                                    • Image Filtering
                                                                                                                                                                                                                    • Median filter
                                                                                                                                                                                                                    • Rank filters
                                                                                                                                                                                                                    • Median filter
                                                                                                                                                                                                                    • Correlation
                                                                                                                                                                                                                    • Why do we need similarity
                                                                                                                                                                                                                    • Correlation (1D)
                                                                                                                                                                                                                    • Correlation (1D)
                                                                                                                                                                                                                    • Normalisation
                                                                                                                                                                                                                    • Normalisation
                                                                                                                                                                                                                    • Correlation on images
                                                                                                                                                                                                                    • Correlation on images
                                                                                                                                                                                                                    • Correlation on images
                                                                                                                                                                                                                    • Draw your filter
                                                                                                                                                                                                                    • Correlation on images ndash no normalisation
                                                                                                                                                                                                                    • Correlation on images ndash no normalisation 2
                                                                                                                                                                                                                    • Mathematics of 2D Correlation
                                                                                                                                                                                                                    • Mathematics of 2D Correlation
                                                                                                                                                                                                                    • Mathematics of 2D Correlation
                                                                                                                                                                                                                    • Slide Number 40
                                                                                                                                                                                                                    • 2D Kernel Normalisation
                                                                                                                                                                                                                    • Correlation
                                                                                                                                                                                                                    • Smoothing filters
                                                                                                                                                                                                                    • Use of smoothing
                                                                                                                                                                                                                    • Use of smoothing
                                                                                                                                                                                                                    • Mean filter
                                                                                                                                                                                                                    • Border handling
                                                                                                                                                                                                                    • Border handling ndash extend the input
                                                                                                                                                                                                                    • Correlation with zero padding
                                                                                                                                                                                                                    • Border handling ndash extend the input
                                                                                                                                                                                                                    • Template Matching
                                                                                                                                                                                                                    • Template Matching
                                                                                                                                                                                                                    • Template Matching
                                                                                                                                                                                                                    • Template Matching
                                                                                                                                                                                                                    • Problematic Correlation
                                                                                                                                                                                                                    • Normalised Cross Correlation
                                                                                                                                                                                                                    • Length of template
                                                                                                                                                                                                                    • Length of image patch
                                                                                                                                                                                                                    • Normalised Cross Correlation
                                                                                                                                                                                                                    • Normalised Cross Correlation
                                                                                                                                                                                                                    • Normalised Cross Correlation
                                                                                                                                                                                                                    • Edges
                                                                                                                                                                                                                    • Edges
                                                                                                                                                                                                                    • Finite Difference
                                                                                                                                                                                                                    • Edges
                                                                                                                                                                                                                    • Edges in 2D
                                                                                                                                                                                                                    • Edge filter kernel
                                                                                                                                                                                                                    • Prewitt filter
                                                                                                                                                                                                                    • Edge detection
                                                                                                                                                                                                                    • Edge filtering
                                                                                                                                                                                                                    • 02511 - Niveau af dagens emne forelaeligsing
                                                                                                                                                                                                                    • 02512 - Niveau af dagens emne forelaeligsing
                                                                                                                                                                                                                    • 02511 - Mit eget udbytte af dagen
                                                                                                                                                                                                                    • 02512 - Mit eget udbytte af dagen
                                                                                                                                                                                                                    • 02511 - Sidste uges oslashvelser (pixelwise operations)
                                                                                                                                                                                                                    • 02512 - Sidste uges oslashvelser (pixelwise operations)
                                                                                                                                                                                                                    • Denne uges brug af clickers
                                                                                                                                                                                                                    • What can you do after today
                                                                                                                                                                                                                    • Oslashvelsesrapport over oslashvelse 4 - 02511
                                                                                                                                                                                                                    • Exercises
                                                                                                                                                                                                                      A0
                                                                                                                                                                                                                      B0
                                                                                                                                                                                                                      C5
                                                                                                                                                                                                                      D0
                                                                                                                                                                                                                      E6
                                                                                                                                                                                                                      A
                                                                                                                                                                                                                      B
                                                                                                                                                                                                                      C
                                                                                                                                                                                                                      D
                                                                                                                                                                                                                      E

                                                                                                                                                                                                                      Sheet1

                                                                                                                                                                                                                      DTU Compute

                                                                                                                                                                                                                      2122018Introduction to Medical Image Analysis83 DTU Compute Technical University of Denmark

                                                                                                                                                                                                                      What can you do after today Describe the difference between point processing and neighbourhood

                                                                                                                                                                                                                      processing Compute a rank filtered image using the min max median and

                                                                                                                                                                                                                      difference rank filters Compute a mean filtered image Decide if median or average filtering should be used for noise removal Choose the appropriate image border handling based on a given input

                                                                                                                                                                                                                      image Implement and apply template matching Compute the normalised cross correlation and explain why it should be

                                                                                                                                                                                                                      used Apply given image filter kernels to images Use edge filters on images Describe finite difference approximation of image gradients Describe the concept of edge detection

                                                                                                                                                                                                                      DTU Compute

                                                                                                                                                                                                                      2122018Introduction to Medical Image Analysis84 DTU Compute Technical University of Denmark

                                                                                                                                                                                                                      Oslashvelsesrapport over oslashvelse 4 - 02511 Oslashvelser taeligller cirka 30 af karakteren Skal afleveres senest den 7 marts kl 2359 Kan afleveres af 1 eller 2 personer

                                                                                                                                                                                                                      ndash I skal skrive jeres egen oslashvelsesrapportndash Brug mindst et af jeres egne billeder

                                                                                                                                                                                                                      Afleveres som PDF Lad vaeligre med at kopiere opgaveteksten ind i jeres

                                                                                                                                                                                                                      opgave Put Matlab kode i et Appendix og henvis fra teksten Eksempel rapport over oslashvelse findes paring

                                                                                                                                                                                                                      hjemmesiden under eksamen

                                                                                                                                                                                                                      DTU Compute

                                                                                                                                                                                                                      2122018Introduction to Medical Image Analysis85 DTU Compute Technical University of Denmark

                                                                                                                                                                                                                      Exercises

                                                                                                                                                                                                                      • Introduction to Medical Image Analysis
                                                                                                                                                                                                                      • Lecture 4 ndash Neighbourhood Processing
                                                                                                                                                                                                                      • What can you do after today
                                                                                                                                                                                                                      • Point processing
                                                                                                                                                                                                                      • Point processing
                                                                                                                                                                                                                      • Neighbourhood processing
                                                                                                                                                                                                                      • Use of filtering
                                                                                                                                                                                                                      • Salt and pepper noise
                                                                                                                                                                                                                      • Salt and pepper noise
                                                                                                                                                                                                                      • What is so special about noise
                                                                                                                                                                                                                      • Noise ndash go away
                                                                                                                                                                                                                      • What is the median Value
                                                                                                                                                                                                                      • The median value
                                                                                                                                                                                                                      • Noise away ndash the median filter
                                                                                                                                                                                                                      • Noise removal ndash average filter
                                                                                                                                                                                                                      • Noise removal ndash median filter
                                                                                                                                                                                                                      • Image Filtering
                                                                                                                                                                                                                      • Median filter
                                                                                                                                                                                                                      • Rank filters
                                                                                                                                                                                                                      • Median filter
                                                                                                                                                                                                                      • Correlation
                                                                                                                                                                                                                      • Why do we need similarity
                                                                                                                                                                                                                      • Correlation (1D)
                                                                                                                                                                                                                      • Correlation (1D)
                                                                                                                                                                                                                      • Normalisation
                                                                                                                                                                                                                      • Normalisation
                                                                                                                                                                                                                      • Correlation on images
                                                                                                                                                                                                                      • Correlation on images
                                                                                                                                                                                                                      • Correlation on images
                                                                                                                                                                                                                      • Draw your filter
                                                                                                                                                                                                                      • Correlation on images ndash no normalisation
                                                                                                                                                                                                                      • Correlation on images ndash no normalisation 2
                                                                                                                                                                                                                      • Mathematics of 2D Correlation
                                                                                                                                                                                                                      • Mathematics of 2D Correlation
                                                                                                                                                                                                                      • Mathematics of 2D Correlation
                                                                                                                                                                                                                      • Slide Number 40
                                                                                                                                                                                                                      • 2D Kernel Normalisation
                                                                                                                                                                                                                      • Correlation
                                                                                                                                                                                                                      • Smoothing filters
                                                                                                                                                                                                                      • Use of smoothing
                                                                                                                                                                                                                      • Use of smoothing
                                                                                                                                                                                                                      • Mean filter
                                                                                                                                                                                                                      • Border handling
                                                                                                                                                                                                                      • Border handling ndash extend the input
                                                                                                                                                                                                                      • Correlation with zero padding
                                                                                                                                                                                                                      • Border handling ndash extend the input
                                                                                                                                                                                                                      • Template Matching
                                                                                                                                                                                                                      • Template Matching
                                                                                                                                                                                                                      • Template Matching
                                                                                                                                                                                                                      • Template Matching
                                                                                                                                                                                                                      • Problematic Correlation
                                                                                                                                                                                                                      • Normalised Cross Correlation
                                                                                                                                                                                                                      • Length of template
                                                                                                                                                                                                                      • Length of image patch
                                                                                                                                                                                                                      • Normalised Cross Correlation
                                                                                                                                                                                                                      • Normalised Cross Correlation
                                                                                                                                                                                                                      • Normalised Cross Correlation
                                                                                                                                                                                                                      • Edges
                                                                                                                                                                                                                      • Edges
                                                                                                                                                                                                                      • Finite Difference
                                                                                                                                                                                                                      • Edges
                                                                                                                                                                                                                      • Edges in 2D
                                                                                                                                                                                                                      • Edge filter kernel
                                                                                                                                                                                                                      • Prewitt filter
                                                                                                                                                                                                                      • Edge detection
                                                                                                                                                                                                                      • Edge filtering
                                                                                                                                                                                                                      • 02511 - Niveau af dagens emne forelaeligsing
                                                                                                                                                                                                                      • 02512 - Niveau af dagens emne forelaeligsing
                                                                                                                                                                                                                      • 02511 - Mit eget udbytte af dagen
                                                                                                                                                                                                                      • 02512 - Mit eget udbytte af dagen
                                                                                                                                                                                                                      • 02511 - Sidste uges oslashvelser (pixelwise operations)
                                                                                                                                                                                                                      • 02512 - Sidste uges oslashvelser (pixelwise operations)
                                                                                                                                                                                                                      • Denne uges brug af clickers
                                                                                                                                                                                                                      • What can you do after today
                                                                                                                                                                                                                      • Oslashvelsesrapport over oslashvelse 4 - 02511
                                                                                                                                                                                                                      • Exercises
                                                                                                                                                                                                                        A0
                                                                                                                                                                                                                        B0
                                                                                                                                                                                                                        C5
                                                                                                                                                                                                                        D0
                                                                                                                                                                                                                        E6

                                                                                                                                                                                                                        DTU Compute

                                                                                                                                                                                                                        2122018Introduction to Medical Image Analysis83 DTU Compute Technical University of Denmark

                                                                                                                                                                                                                        What can you do after today Describe the difference between point processing and neighbourhood

                                                                                                                                                                                                                        processing Compute a rank filtered image using the min max median and

                                                                                                                                                                                                                        difference rank filters Compute a mean filtered image Decide if median or average filtering should be used for noise removal Choose the appropriate image border handling based on a given input

                                                                                                                                                                                                                        image Implement and apply template matching Compute the normalised cross correlation and explain why it should be

                                                                                                                                                                                                                        used Apply given image filter kernels to images Use edge filters on images Describe finite difference approximation of image gradients Describe the concept of edge detection

                                                                                                                                                                                                                        DTU Compute

                                                                                                                                                                                                                        2122018Introduction to Medical Image Analysis84 DTU Compute Technical University of Denmark

                                                                                                                                                                                                                        Oslashvelsesrapport over oslashvelse 4 - 02511 Oslashvelser taeligller cirka 30 af karakteren Skal afleveres senest den 7 marts kl 2359 Kan afleveres af 1 eller 2 personer

                                                                                                                                                                                                                        ndash I skal skrive jeres egen oslashvelsesrapportndash Brug mindst et af jeres egne billeder

                                                                                                                                                                                                                        Afleveres som PDF Lad vaeligre med at kopiere opgaveteksten ind i jeres

                                                                                                                                                                                                                        opgave Put Matlab kode i et Appendix og henvis fra teksten Eksempel rapport over oslashvelse findes paring

                                                                                                                                                                                                                        hjemmesiden under eksamen

                                                                                                                                                                                                                        DTU Compute

                                                                                                                                                                                                                        2122018Introduction to Medical Image Analysis85 DTU Compute Technical University of Denmark

                                                                                                                                                                                                                        Exercises

                                                                                                                                                                                                                        • Introduction to Medical Image Analysis
                                                                                                                                                                                                                        • Lecture 4 ndash Neighbourhood Processing
                                                                                                                                                                                                                        • What can you do after today
                                                                                                                                                                                                                        • Point processing
                                                                                                                                                                                                                        • Point processing
                                                                                                                                                                                                                        • Neighbourhood processing
                                                                                                                                                                                                                        • Use of filtering
                                                                                                                                                                                                                        • Salt and pepper noise
                                                                                                                                                                                                                        • Salt and pepper noise
                                                                                                                                                                                                                        • What is so special about noise
                                                                                                                                                                                                                        • Noise ndash go away
                                                                                                                                                                                                                        • What is the median Value
                                                                                                                                                                                                                        • The median value
                                                                                                                                                                                                                        • Noise away ndash the median filter
                                                                                                                                                                                                                        • Noise removal ndash average filter
                                                                                                                                                                                                                        • Noise removal ndash median filter
                                                                                                                                                                                                                        • Image Filtering
                                                                                                                                                                                                                        • Median filter
                                                                                                                                                                                                                        • Rank filters
                                                                                                                                                                                                                        • Median filter
                                                                                                                                                                                                                        • Correlation
                                                                                                                                                                                                                        • Why do we need similarity
                                                                                                                                                                                                                        • Correlation (1D)
                                                                                                                                                                                                                        • Correlation (1D)
                                                                                                                                                                                                                        • Normalisation
                                                                                                                                                                                                                        • Normalisation
                                                                                                                                                                                                                        • Correlation on images
                                                                                                                                                                                                                        • Correlation on images
                                                                                                                                                                                                                        • Correlation on images
                                                                                                                                                                                                                        • Draw your filter
                                                                                                                                                                                                                        • Correlation on images ndash no normalisation
                                                                                                                                                                                                                        • Correlation on images ndash no normalisation 2
                                                                                                                                                                                                                        • Mathematics of 2D Correlation
                                                                                                                                                                                                                        • Mathematics of 2D Correlation
                                                                                                                                                                                                                        • Mathematics of 2D Correlation
                                                                                                                                                                                                                        • Slide Number 40
                                                                                                                                                                                                                        • 2D Kernel Normalisation
                                                                                                                                                                                                                        • Correlation
                                                                                                                                                                                                                        • Smoothing filters
                                                                                                                                                                                                                        • Use of smoothing
                                                                                                                                                                                                                        • Use of smoothing
                                                                                                                                                                                                                        • Mean filter
                                                                                                                                                                                                                        • Border handling
                                                                                                                                                                                                                        • Border handling ndash extend the input
                                                                                                                                                                                                                        • Correlation with zero padding
                                                                                                                                                                                                                        • Border handling ndash extend the input
                                                                                                                                                                                                                        • Template Matching
                                                                                                                                                                                                                        • Template Matching
                                                                                                                                                                                                                        • Template Matching
                                                                                                                                                                                                                        • Template Matching
                                                                                                                                                                                                                        • Problematic Correlation
                                                                                                                                                                                                                        • Normalised Cross Correlation
                                                                                                                                                                                                                        • Length of template
                                                                                                                                                                                                                        • Length of image patch
                                                                                                                                                                                                                        • Normalised Cross Correlation
                                                                                                                                                                                                                        • Normalised Cross Correlation
                                                                                                                                                                                                                        • Normalised Cross Correlation
                                                                                                                                                                                                                        • Edges
                                                                                                                                                                                                                        • Edges
                                                                                                                                                                                                                        • Finite Difference
                                                                                                                                                                                                                        • Edges
                                                                                                                                                                                                                        • Edges in 2D
                                                                                                                                                                                                                        • Edge filter kernel
                                                                                                                                                                                                                        • Prewitt filter
                                                                                                                                                                                                                        • Edge detection
                                                                                                                                                                                                                        • Edge filtering
                                                                                                                                                                                                                        • 02511 - Niveau af dagens emne forelaeligsing
                                                                                                                                                                                                                        • 02512 - Niveau af dagens emne forelaeligsing
                                                                                                                                                                                                                        • 02511 - Mit eget udbytte af dagen
                                                                                                                                                                                                                        • 02512 - Mit eget udbytte af dagen
                                                                                                                                                                                                                        • 02511 - Sidste uges oslashvelser (pixelwise operations)
                                                                                                                                                                                                                        • 02512 - Sidste uges oslashvelser (pixelwise operations)
                                                                                                                                                                                                                        • Denne uges brug af clickers
                                                                                                                                                                                                                        • What can you do after today
                                                                                                                                                                                                                        • Oslashvelsesrapport over oslashvelse 4 - 02511
                                                                                                                                                                                                                        • Exercises

                                                                                                                                                                                                                          DTU Compute

                                                                                                                                                                                                                          2122018Introduction to Medical Image Analysis84 DTU Compute Technical University of Denmark

                                                                                                                                                                                                                          Oslashvelsesrapport over oslashvelse 4 - 02511 Oslashvelser taeligller cirka 30 af karakteren Skal afleveres senest den 7 marts kl 2359 Kan afleveres af 1 eller 2 personer

                                                                                                                                                                                                                          ndash I skal skrive jeres egen oslashvelsesrapportndash Brug mindst et af jeres egne billeder

                                                                                                                                                                                                                          Afleveres som PDF Lad vaeligre med at kopiere opgaveteksten ind i jeres

                                                                                                                                                                                                                          opgave Put Matlab kode i et Appendix og henvis fra teksten Eksempel rapport over oslashvelse findes paring

                                                                                                                                                                                                                          hjemmesiden under eksamen

                                                                                                                                                                                                                          DTU Compute

                                                                                                                                                                                                                          2122018Introduction to Medical Image Analysis85 DTU Compute Technical University of Denmark

                                                                                                                                                                                                                          Exercises

                                                                                                                                                                                                                          • Introduction to Medical Image Analysis
                                                                                                                                                                                                                          • Lecture 4 ndash Neighbourhood Processing
                                                                                                                                                                                                                          • What can you do after today
                                                                                                                                                                                                                          • Point processing
                                                                                                                                                                                                                          • Point processing
                                                                                                                                                                                                                          • Neighbourhood processing
                                                                                                                                                                                                                          • Use of filtering
                                                                                                                                                                                                                          • Salt and pepper noise
                                                                                                                                                                                                                          • Salt and pepper noise
                                                                                                                                                                                                                          • What is so special about noise
                                                                                                                                                                                                                          • Noise ndash go away
                                                                                                                                                                                                                          • What is the median Value
                                                                                                                                                                                                                          • The median value
                                                                                                                                                                                                                          • Noise away ndash the median filter
                                                                                                                                                                                                                          • Noise removal ndash average filter
                                                                                                                                                                                                                          • Noise removal ndash median filter
                                                                                                                                                                                                                          • Image Filtering
                                                                                                                                                                                                                          • Median filter
                                                                                                                                                                                                                          • Rank filters
                                                                                                                                                                                                                          • Median filter
                                                                                                                                                                                                                          • Correlation
                                                                                                                                                                                                                          • Why do we need similarity
                                                                                                                                                                                                                          • Correlation (1D)
                                                                                                                                                                                                                          • Correlation (1D)
                                                                                                                                                                                                                          • Normalisation
                                                                                                                                                                                                                          • Normalisation
                                                                                                                                                                                                                          • Correlation on images
                                                                                                                                                                                                                          • Correlation on images
                                                                                                                                                                                                                          • Correlation on images
                                                                                                                                                                                                                          • Draw your filter
                                                                                                                                                                                                                          • Correlation on images ndash no normalisation
                                                                                                                                                                                                                          • Correlation on images ndash no normalisation 2
                                                                                                                                                                                                                          • Mathematics of 2D Correlation
                                                                                                                                                                                                                          • Mathematics of 2D Correlation
                                                                                                                                                                                                                          • Mathematics of 2D Correlation
                                                                                                                                                                                                                          • Slide Number 40
                                                                                                                                                                                                                          • 2D Kernel Normalisation
                                                                                                                                                                                                                          • Correlation
                                                                                                                                                                                                                          • Smoothing filters
                                                                                                                                                                                                                          • Use of smoothing
                                                                                                                                                                                                                          • Use of smoothing
                                                                                                                                                                                                                          • Mean filter
                                                                                                                                                                                                                          • Border handling
                                                                                                                                                                                                                          • Border handling ndash extend the input
                                                                                                                                                                                                                          • Correlation with zero padding
                                                                                                                                                                                                                          • Border handling ndash extend the input
                                                                                                                                                                                                                          • Template Matching
                                                                                                                                                                                                                          • Template Matching
                                                                                                                                                                                                                          • Template Matching
                                                                                                                                                                                                                          • Template Matching
                                                                                                                                                                                                                          • Problematic Correlation
                                                                                                                                                                                                                          • Normalised Cross Correlation
                                                                                                                                                                                                                          • Length of template
                                                                                                                                                                                                                          • Length of image patch
                                                                                                                                                                                                                          • Normalised Cross Correlation
                                                                                                                                                                                                                          • Normalised Cross Correlation
                                                                                                                                                                                                                          • Normalised Cross Correlation
                                                                                                                                                                                                                          • Edges
                                                                                                                                                                                                                          • Edges
                                                                                                                                                                                                                          • Finite Difference
                                                                                                                                                                                                                          • Edges
                                                                                                                                                                                                                          • Edges in 2D
                                                                                                                                                                                                                          • Edge filter kernel
                                                                                                                                                                                                                          • Prewitt filter
                                                                                                                                                                                                                          • Edge detection
                                                                                                                                                                                                                          • Edge filtering
                                                                                                                                                                                                                          • 02511 - Niveau af dagens emne forelaeligsing
                                                                                                                                                                                                                          • 02512 - Niveau af dagens emne forelaeligsing
                                                                                                                                                                                                                          • 02511 - Mit eget udbytte af dagen
                                                                                                                                                                                                                          • 02512 - Mit eget udbytte af dagen
                                                                                                                                                                                                                          • 02511 - Sidste uges oslashvelser (pixelwise operations)
                                                                                                                                                                                                                          • 02512 - Sidste uges oslashvelser (pixelwise operations)
                                                                                                                                                                                                                          • Denne uges brug af clickers
                                                                                                                                                                                                                          • What can you do after today
                                                                                                                                                                                                                          • Oslashvelsesrapport over oslashvelse 4 - 02511
                                                                                                                                                                                                                          • Exercises

                                                                                                                                                                                                                            DTU Compute

                                                                                                                                                                                                                            2122018Introduction to Medical Image Analysis85 DTU Compute Technical University of Denmark

                                                                                                                                                                                                                            Exercises

                                                                                                                                                                                                                            • Introduction to Medical Image Analysis
                                                                                                                                                                                                                            • Lecture 4 ndash Neighbourhood Processing
                                                                                                                                                                                                                            • What can you do after today
                                                                                                                                                                                                                            • Point processing
                                                                                                                                                                                                                            • Point processing
                                                                                                                                                                                                                            • Neighbourhood processing
                                                                                                                                                                                                                            • Use of filtering
                                                                                                                                                                                                                            • Salt and pepper noise
                                                                                                                                                                                                                            • Salt and pepper noise
                                                                                                                                                                                                                            • What is so special about noise
                                                                                                                                                                                                                            • Noise ndash go away
                                                                                                                                                                                                                            • What is the median Value
                                                                                                                                                                                                                            • The median value
                                                                                                                                                                                                                            • Noise away ndash the median filter
                                                                                                                                                                                                                            • Noise removal ndash average filter
                                                                                                                                                                                                                            • Noise removal ndash median filter
                                                                                                                                                                                                                            • Image Filtering
                                                                                                                                                                                                                            • Median filter
                                                                                                                                                                                                                            • Rank filters
                                                                                                                                                                                                                            • Median filter
                                                                                                                                                                                                                            • Correlation
                                                                                                                                                                                                                            • Why do we need similarity
                                                                                                                                                                                                                            • Correlation (1D)
                                                                                                                                                                                                                            • Correlation (1D)
                                                                                                                                                                                                                            • Normalisation
                                                                                                                                                                                                                            • Normalisation
                                                                                                                                                                                                                            • Correlation on images
                                                                                                                                                                                                                            • Correlation on images
                                                                                                                                                                                                                            • Correlation on images
                                                                                                                                                                                                                            • Draw your filter
                                                                                                                                                                                                                            • Correlation on images ndash no normalisation
                                                                                                                                                                                                                            • Correlation on images ndash no normalisation 2
                                                                                                                                                                                                                            • Mathematics of 2D Correlation
                                                                                                                                                                                                                            • Mathematics of 2D Correlation
                                                                                                                                                                                                                            • Mathematics of 2D Correlation
                                                                                                                                                                                                                            • Slide Number 40
                                                                                                                                                                                                                            • 2D Kernel Normalisation
                                                                                                                                                                                                                            • Correlation
                                                                                                                                                                                                                            • Smoothing filters
                                                                                                                                                                                                                            • Use of smoothing
                                                                                                                                                                                                                            • Use of smoothing
                                                                                                                                                                                                                            • Mean filter
                                                                                                                                                                                                                            • Border handling
                                                                                                                                                                                                                            • Border handling ndash extend the input
                                                                                                                                                                                                                            • Correlation with zero padding
                                                                                                                                                                                                                            • Border handling ndash extend the input
                                                                                                                                                                                                                            • Template Matching
                                                                                                                                                                                                                            • Template Matching
                                                                                                                                                                                                                            • Template Matching
                                                                                                                                                                                                                            • Template Matching
                                                                                                                                                                                                                            • Problematic Correlation
                                                                                                                                                                                                                            • Normalised Cross Correlation
                                                                                                                                                                                                                            • Length of template
                                                                                                                                                                                                                            • Length of image patch
                                                                                                                                                                                                                            • Normalised Cross Correlation
                                                                                                                                                                                                                            • Normalised Cross Correlation
                                                                                                                                                                                                                            • Normalised Cross Correlation
                                                                                                                                                                                                                            • Edges
                                                                                                                                                                                                                            • Edges
                                                                                                                                                                                                                            • Finite Difference
                                                                                                                                                                                                                            • Edges
                                                                                                                                                                                                                            • Edges in 2D
                                                                                                                                                                                                                            • Edge filter kernel
                                                                                                                                                                                                                            • Prewitt filter
                                                                                                                                                                                                                            • Edge detection
                                                                                                                                                                                                                            • Edge filtering
                                                                                                                                                                                                                            • 02511 - Niveau af dagens emne forelaeligsing
                                                                                                                                                                                                                            • 02512 - Niveau af dagens emne forelaeligsing
                                                                                                                                                                                                                            • 02511 - Mit eget udbytte af dagen
                                                                                                                                                                                                                            • 02512 - Mit eget udbytte af dagen
                                                                                                                                                                                                                            • 02511 - Sidste uges oslashvelser (pixelwise operations)
                                                                                                                                                                                                                            • 02512 - Sidste uges oslashvelser (pixelwise operations)
                                                                                                                                                                                                                            • Denne uges brug af clickers
                                                                                                                                                                                                                            • What can you do after today
                                                                                                                                                                                                                            • Oslashvelsesrapport over oslashvelse 4 - 02511
                                                                                                                                                                                                                            • Exercises

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