ho2_PixelOps_2013

7/27/2019 ho2_PixelOps_2013

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Pixel Operations

4c8

Dr. David Corrigan

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Pixel Operations

• This handout looks at the most basic type of image processingapplications.

• These are simple point-wise operations of the form:

, = ((,))

– I(h,k) is the input image

– g(h,k) if the output

– (.) is some image processing function

• In a point-wise operation the output at (h,k) is dependent only onthe value of the input (h,k) and not on the value of the input oroutput at any other location.

• These types of operations are used mainly for image enhancement.

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Matlab

• Images are represented as a matrix

• So G = 2.0 * I multiplies each pixel intensity by 2

and G = I + 10 increases the brightness by 2.

• Point wise operations are fast and easy to implement inhardware.

),(),(),(

),(),(),(

),(),(),(

M N I N I N I

M I I I

M I I I

I

21

22212

12111

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Image Histograms

• Records the number of pixels that have a particularintensity value

• Typically displayed as a plot of frequency v intensity

• Sometimes normalised so all the frequencies sum to 1

(ie. an approximation of the pdf of image intensities)• Colour images have 3D histograms but it is more

common to use separate histograms for each colourchannel.

•

Summaries where most of the pixels are so is useful fordesigning image enhancement operations

• Matlab function hist() or imhist()

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Image Histograms

Y

U

V

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Image Histograms

Bin Width = 1 Bin Width = 4 Bin Width = 20

It is also common to increase the bin width.

Each frequency represents the number of

pels in a particular range of intensities.

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Contrast Enhancement & Clipping

• used when you want to alter contrast or brightness of an image.

, =

0 , < min

, + min < , < max255 , > max

– m defines the alteration to the contrast.

– c defines a global brightness change.

–

min and

max

define the range for clipping.

• Clipping is necessary to ensure that all intensities in the output stayinside the valid range (ie. when min = 0 and max = 255) but canalso be used to eliminate contrast in very bright and dark regions.(ie. when min > 0 and max < 255)

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Contrast Enhancement & Clipping

min intensity = 12 max intensity = 191

intensities fit full range

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Gamma Correction

• Gamma Correction is a non-linear modification of image contrast.

, = ,

• If < 1 the contrast in the dark regions is increasedand the contrast in the bright areas is increased

• The opposite occurs if

> 1

• Gamma Correction avoids the need for clipping sosome contrast can be maintained in the dark/brightregions.

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Histogram Equalisation

• An automatic technique for imageenhancement (no parameter choice required).

• However, results are unpredictable and may

look worse.• The idea is to alter the intensities so that the

histogram is as flat as possible.

•If the histogram contains a lot of pixels in anarrow range, it should be stretched out alongthe intensity range.

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Histogram Equalisation1 2 3 4 5 6 7 8

1 7 21 35 35 21 7 1

16 16 16 16 16 16 16 16

Levels i

H(i)

Target H(i)m

To have 16 pels at intensity 1,take all from I=1,2 and 8 from I = 3 and map onto intensity 1

because H(1) + H(2)+ 8 = 16

To have 16 pels at intensity 2Take remainder (21-8)=13 at level 3, add to 3 from level 4

So intensity mapping is 1,2,3 -> 1; 3,4 ->2 etc etc

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Histogram

Cumulative Histogram(scaled to fit axes)

0

1

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• A problem arises because most bins will mappedonto more than one output bins. It is difficult todo this consistently.

• Instead the cumulative histogram is used todesign the mapping. Again the idea is to matchthe cumulative histogram to a target cumulativehistogram.

• The target cumulative histogram is a straight line,

having a slope of 1/255, a max of 1 and a min of 0. This corresponds to a flat histogram.

• Matlab function histeq()

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Hist. Equalisation with CuF1 2 3 4 5 6 7 8

1 7 21 35 35 21 7 1

1 8 29 64 99 120 127 128

16 16 16 16 16 16 16 16

16 32 48 64 80 96 112 128

Levels i

H(i)

Target H(i)m

CuF(i)

Target CuF(i)m

Match Bins of Cumulative Histogram to theclosest bin in the target.

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1 7 21 35 35 21 7 1

1 8 29 64 99 120 127 128

16 16 16 16 16 16 16 16

16 32 48 64 80 96 112 128

Levels i

H(i)

Target H(i)m

CuF(i)

Target CuF(i)m

Resultingtransformation

1 2 3 4 5 6 7 8

1 1 2 4 6 7 8 8

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1 7 21 35 35 21 7 1

1 8 29 64 99 120 127 128

16 16 16 16 16 16 16 16

16 32 48 64 80 96 112 128

8 21 0 35 0 35 21 8

8 29 29 64 64 99 120 128

Levels i

H(i)

Output H(i)

CuF(i)

Output CuF(i)

Target H(i)

Target CuF(i)

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Matlabimadjdemo

Try it

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Histogram EqualisationNotice how the transformationbetween input and output relatesto the cumulative histogram of the

input.

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Basic Segmentation (Thresholding)

• Sometimes it is required to extract a part of an image which

contains all the relevant in formation.

Eg. We might want to isolate the

table to do some further analysis.

If the information is contained in a

limited band we can define a simplethresholding operation to segment

the image in two.

, = 0 , < 2 5 5 < , < 0 , >

We choose

and

so that the part of

the image he want fits inside this range.

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Intensity Based Segmentation

Histogram of Hue

Peak Corresponding toTable

Segmented Table = 100, = 110 Extracted Table

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• The previous result can beimproved by alsoincorporating a threshold onsaturation

• The condition for the table is

now > 100 & < 110& > 128 Histogram of Saturation

Grayscale Representation

of Saturation Segmented Table

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Segmentation with Hue aloneSegmentation using Hue andSaturation

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Matlab Implementation

• Read the picture from file (eg. pic =imread(‘pool.jpg’);) – pic is a × × 3 array storing the image in rgb format

– pic(:,:,1) stores the red channel, pic(:,:,2) storesthe green channel and pic(:,:,3) stores the blue channel.

• Convert the image to the hsv and extract the hue andsaturation channels colour space

hsv = rgb2hsv(pic);hue = hsv(:,:,1);

sat = hsv(:,:,2);

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• Now we can define the segmentation operation

mask = ((hue>100)&(hue<110)&(sat>128));

• To see the part of the image that has been segmented we create anew images as follows

new_pic(:,:,1) = pic(:,:,1).*mask;

new_pic(:,:,2) = pic(:,:,2).*mask;

new_pic(:,:,3) = pic(:,:,3).*mask;

– These lines create an image that is the same as the originalimage in the area of the table and is black in the background.

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• People unfamiliar with Matlab get confused by the last part. In C++ itwould be an if/else statement inside a for loop …

for(int x = 0; x<width; x++){

for(int y = 0; y<height; y++){

for(int chan = 0; chan < 3; chan++){if(mask[x][y]!=0)

new_pic[x][y][chan]=pic[x][y][chan];

else

new_pic[x][y][chan]= 0;

}}

}

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Lab 1

• The first lab will get you to perform some of these pixel opsinside matlab. The segmentation code will help, however itis not complete!

•

In particular pay particular attention to the scaling of eachcolour channel – above we assumed that the hue channel was scaled between 0

and 360 and the saturation channel was scaled between 0 and255. This will not be the case by default.

• You will also have to learn what the best data type to use isint, float etc. You will also have to display your results asimages and perhaps write them as files.

ho2_PixelOps_2013

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