CS482 Selected Topics in Digital Image Processing بسم الله الرحمن الرحيم Instructor: Dr. Abdullah Basuhail,CSD, FCIT, KAU, 1432H Chapter 2: Digital Image.

CS482 CS482

Selected Topics in Digital Image Selected Topics in Digital Image ProcessingProcessing

الرحيم الرحمن الله الرحيم بسم الرحمن الله بسم

Instructor: Dr. Abdullah Basuhail ,CSD, FCIT, KAU, 1432H

Chapter 2: Chapter 2: Digital Image Digital Image FundamentalsFundamentals

CS382, CSD, FCIT, KAU, KSA Based on textbook: Digital Image Processing, 3rd Edition, by Gonzalez and Woods Compiled by: Dr. Abdullah Basuhail , 1432H 2

Visual PerceptionVisual Perception Mach bands: visual system tends to

undershoot or overshoot around the boundary of regions of different intensities

Simultaneous contrast: region’s perceived brightness does not depend on its intensity

Optical illusions: eye fills in nonexisting information or wrongly perceives geometrical properties of objects

Digital Image Processing, 3rd ed.Digital Image Processing, 3rd ed.

www.ImageProcessingPlace.com

© 1992–2008 R. C. Gonzalez & R. E. Woods

Gonzalez & Woods

Chapter 2 Digital Image Fundamentals





Gonzalez & Woods






Gonzalez & Woods




Representing Digital ImagesRepresenting Digital Images Digital image

M N array L discrete intensities – power of 2

L = 2k

Integers in the interval [0, L - 1] Dynamic range: ratio of maximum / minimum intensity

Low: image has a dull, washed-out gray look Contrast: difference between highest and lowest

intensity High: image have high contrast




Gonzalez & Woods




Representing Digital ImagesRepresenting Digital Images Digital image

# bits to store : b = M N k When M = N: b = N2k k-bit image: e.g. an image with 256 possible

discrete intensity values is called an 8-bit image




Gonzalez & Woods




Spatial and Intensity Spatial and Intensity ResolutionResolution Resolution: dots (pixels) per unit distance dpi: dots per inch




Gonzalez & Woods




Variation of Number of Intensity Variation of Number of Intensity LevelsLevels Reducing the number of bits from k=7 to

k=1 while keeping the image size constant Insufficient number of intensity levels in smooth

areas of digital image leads to false contouring




Gonzalez & Woods






Gonzalez & Woods




Image InterpolationImage Interpolation Using known data to estimate values at unknown

locations Used for zooming, shrinking, rotating, and geometric

corrections Nearest Neighbor interpolation

Use closest pixel to estimate the intensity simple but has tendency to produce artifact

Bilinear interpolation use 4 nearest neighbor to estimate the intensity Much better result

Bicubic interpolation Use 16 nearest neighbors of a point




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16

Interpolation works by using known data to estimate values at unknown points .For example: if you wanted to know the temperature at noon, but only measured it

at 11AM and 1PM, you could estimate its value by performing a linear interpolation:

If you had an additional measurement at 11:30AM, you could see that the bulk of the temperature rise occurred before noon, and could use this additional data point

to perform a quadratic interpolation:




Gonzalez & Woods



The more temperature measurements you have which are close to noon, the more sophisticated (and hopefully more accurate) your interpolation algorithm can be.




Gonzalez & Woods



Nearest neighbor is the most basic and requires the least processing time of all the interpolation algorithms because it only considers one pixel — the closest one

to the interpolated point. This has the effect of simply making each pixel bigger.

NEAREST NEIGHBOR INTERPOLATION




Gonzalez & Woods



BILINEAR INTERPOLATION

Bilinear interpolation considers the closest 2x2 neighborhood of known pixel values surrounding the unknown pixel. It then takes a weighted average of

these 4 pixels to arrive at its final interpolated value .

This results in much smoother looking images than nearest neighbor.

The diagram to the left is for a case when all known pixel distances are equal, so the interpolated value is simply their sum divided by four.

dcxybyaxyxv ),(




Gonzalez & Woods



BICUBIC INTERPOLATION

Bicubic goes one step beyond bilinear by considering the closest 4x4 neighborhood of known pixels — for a total of 16 pixels.

Since these are at various distances from the unknown pixel, closer pixels are given a higher weighting in the calculation .

Bicubic produces noticeably sharper images than the previous two methods, and is perhaps the ideal combination of processing time and output quality.

For this reason it is a standard in many image editing programs (including Adobe Photoshop), printer drivers and in-camera interpolation.

ji

i jij yxayxv

3

0

3

0

),(




Gonzalez & Woods



The intensity value assigned to point (x,y) is obtained by equation where the sixteen coefficients are determined from the sixteen equations in sixteen unknowns that can be written using the sixteen nearest neighbours of point (x,y)




Gonzalez & Woods




Arithmetic OperationsArithmetic Operations Array operations between images Carried out between corresponding pixel

pairs Four arithmetic

s(x, y) = f(x, y) + g(x, y)

d(x, y) = f(x, y) – g(x, y)

p(x, y) = f(x, y) g(x, y)

v(x, y) = f(x, y) ÷ g(x, y)

e.g. Averaging K different noisy images can decrease noise Used in the field of astronomy




Gonzalez & Woods



Averaging K different noisy images can decrease noise. Used in astronomy




Gonzalez & Woods



Enhancement of difference between images using image subtraction




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Mask mode radiography




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Shading correction by image multiplication (and division)




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Masking (ROI) using image multiplication


Arithmetic OperationsArithmetic Operations To guarantee that the full range of an

arithmetic operation between images is captured into a fixed number of bits, the following approach is performed on image f

fm = f – min(f)

which creates an image whose minimum value is 0. Then the scaled image is

fs = K [ fm / max(fm)]

whose value is in the range [0, K]


Set and Logical OperationsSet and Logical Operations Sets can be used to let the elements of sets

be the coordinates of pixels (ordered pairs of integers) representing regions (objects) in an image Union Intersection Complement Difference

Logical operations OR AND NOT XOR




Gonzalez & Woods






Gonzalez & Woods






Gonzalez & Woods




Spatial OperationsSpatial Operations Single-pixel operations

For example, transformation to obtain the negative of an 8-bit image

S = T (z)




Gonzalez & Woods




Spatial OperationsSpatial Operations Neighborhood operations

For example, compute the average value of the pixels in a rectangular neighborhood of size m n centered on (x, y)

xyScr

crfmn

yxg),(

),(1

),(




Gonzalez & Woods




Spatial OperationsSpatial Operations Geometric spatial transformations

Called rubber-sheet transformations Consists of two operations

Spatial transformation of coordinatese.g. (x, y) = T { ( v, w) } = ( v/2, w/2) Affine transform: scale, rotate, transform, or sheer a

set of points Intensity interpolation

1

0t

0tt

1] w[v T 1] w[]1 [

3231

2221

1211

tt

tvyx




Gonzalez & Woods






Gonzalez & Woods






Gonzalez & Woods




Vector and Matrix OperationsVector and Matrix Operations RGB images Multispectral images




Gonzalez & Woods




Image TransformsImage Transforms Image processing tasks are best

formulated by Transforming the images Carrying the specified task un a transform

domain Applying the inverse transform




Gonzalez & Woods






Gonzalez & Woods



CS482 Selected Topics in Digital Image Processing بسم الله الرحمن الرحيم Instructor: Dr. Abdullah Basuhail,CSD, FCIT, KAU, 1432H Chapter 2: Digital Image.

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