03 intensity transformations

Khawar Khurshid, 20121

Advanced Digital Image Processing

Spring ’14

Intensity TransformationsIntensity TransformationsIntensity TransformationsIntensity Transformations

LookLookLookLook----up Tablesup Tablesup Tablesup Tables

Linear Contrast StretchLinear Contrast StretchLinear Contrast StretchLinear Contrast Stretch

PiecePiecePiecePiece----wise Contrast Stretchwise Contrast Stretchwise Contrast Stretchwise Contrast Stretch

Histogram EqualizationHistogram EqualizationHistogram EqualizationHistogram Equalization

Power LawPower LawPower LawPower Law

Log Transform Log Transform Log Transform Log Transform –––– Gamma correctionGamma correctionGamma correctionGamma correction


Dynamic Range Dynamic Range Dynamic Range Dynamic Range vsvsvsvs ContrastContrastContrastContrast


Dynamic Range Minimum Possible Intensity to Maximum Possible Intensity

Contrast Minimum Image Intensity to Maximum Image Intensity

What do you think is the dynamic range of this image?

What is the approximate contrast range?

3

� Point/Pixel operationsOutput value at specific coordinates(x,y) is dependent only on the inputvalue at (x,y)

� Local operationsThe output value at (x,y) isdependent on the input values in theneighborhood of (x,y)

�Global operationsThe output value at (x,y) isdependent on all the values in theinput image



Basic Concept

Most spatial domain enhancement operations can be generalized as:

f (x, y) = Input image

g (x, y) = Processed/output image

T = Operator defined over some neighbourhood of (x, y)

[ ]( , ) ( , )g x y T f x y=



Point Processing using Look-up Tables

ce

ll in

de

x

co

nte

nts

0 0

64 32

128 128

192 224

255 255

...

...

...

...

...

...

...

...

input output

a pixel with this value

a pixel with this value

is mapped to this value

is mapped to this value

Look up Table MappingLook up Table MappingLook up Table MappingLook up Table Mapping


Linear Contrast StretchLinear Contrast StretchLinear Contrast StretchLinear Contrast Stretch


� Objective� Increase the dynamic

range of the gray levelsfor low contrast images

� Rather than using a well

defined mathematical

function we can use

arbitrary user-defined

transforms

� If r1 = s1 & r2 = s2, no change in gray levels

� If r1 = r2, s1 = 0 & s2 = L-1, then it is a threshold function. The resulting image is binary

PiecePiecePiecePiece----wise Contrast Stretchingwise Contrast Stretchingwise Contrast Stretchingwise Contrast Stretching


PiecePiecePiecePiece----wise Contrast Stretchingwise Contrast Stretchingwise Contrast Stretchingwise Contrast Stretching


Window LevelWindow LevelWindow LevelWindow Level


Selecting a Window of the intensity values to be enhanced.

10



Window of dark intensity values are enhanced.

11



Intensity values corresponding to the Lungs is enhanced.

12

HistogramHistogramHistogramHistogramOfOfOfOf

ImagesImagesImagesImages


• The histogram of a digital image with gray values is the discrete function

• Nk : Number of pixels with gray value rk

• N : Total number of pixels in the image

• The function p(rk) represents the fraction of the total number of pixels with gray value rk.

n

nrp k

k =)( 1,...,1,0 −= Lk

Image Histogram Image Histogram Image Histogram Image Histogram


0 1 1 2 4

2 1 0 0 2

5 2 0 0 4

1 1 2 4 1

The (intensity or brightness) histogram shows how many times a particular grey level (intensity) appears in an image.

For example, 0 - black, 255 – white

0

1

2

3

4

5

6

7

0 1 2 3 4 5 6

Image Histogram

Image Histogram Image Histogram Image Histogram Image Histogram


I = imread('rain.jpg');

G = rgb2gray(I);

[x,y] = size(G);

H = zeros(1,256);

for i=1:x

for j=1:y

H(G(i,j)+1) = H(G(i,j)+1) + 1;

end

end

stem(H);

Histogram CalculationHistogram CalculationHistogram CalculationHistogram Calculation


( ) the number

of pixels in

with graylevel .

Ih g

I

g

=( ) the number

of pixels in

with graylevel .

Ih g

I

g

=

Histogram Histogram Histogram Histogram –––– Gray Scale ImageGray Scale ImageGray Scale ImageGray Scale Image


There is one histo-gram per color bandR, G, & B. Luminosity histogram is from 1 band = (R+G+B)/3

There is one histo-gram per color bandR, G, & B. Luminosity histogram is from 1 band = (R+G+B)/3

Histogram Histogram Histogram Histogram –––– Color ImageColor ImageColor ImageColor Image


Histogram Histogram Histogram Histogram –––– Color ImageColor ImageColor ImageColor Image




pdf

The CDF (cumulative distribution) is the LUT for remapping.


CDF



pdf



LUT



Histogram Equalization Histogram Equalization Histogram Equalization Histogram Equalization ---- LocalLocalLocalLocal


Original Image Local EqualizationGlobal Equalization

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Histogram Equalization istogram Equalization istogram Equalization istogram Equalization ---- ProblemProblemProblemProblem

Khawar Khurshid, 2012Problem with Histogram Equalization

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� Power law transformations have the following form

� Map a narrow range of dark input values into a wider range of output values or vice versa

� Varying γ gives a whole family of curves

s c rγ= ×

Power Law Power Law Power Law Power Law TransformationsTransformationsTransformationsTransformations


� For g < 1: Expands values of dark pixels, compress values of brighter pixels

� For g > 1: Compresses values of dark pixels, expand values of brighter pixels

� If g=1 & c=1: Identity transformation (s = r)

� A variety of devices (image capture, printing, display)respond according to a power law and need to be corrected.

� Gamma (g) correctionThe process used to correct the power-law responsephenomena.



MR image of

human spine

Result after

Power law

transformation

γγγγ = 0.6

Result after

Power law

transformation

γγγγ = 0.4

Result after

Power law

transformation

γγγγ = 0.3

Power Law TransformationsPower Law TransformationsPower Law TransformationsPower Law Transformations


Image has a washed-outappearance – needs γ > 1



Aerial

Image

Result of

Power law

transformation

γγγγ = 3.0

(suitable)

Result of

Power law

transformation

γγγγ = 4.0

(suitable)

Result of

Power law

transformation

γγγγ = 5.0

(high contrast,

some regions are

too dark)



� The general form of the log transformation is

� The log transformation maps a narrow range of low input grey level values into a wider range of output values

� The inverse log transformation performs the opposite transformation

log(1 )s c r= × +

Logarithmic TransformationsLogarithmic TransformationsLogarithmic TransformationsLogarithmic Transformations


� Properties

� For lower amplitudes ofinput image the range ofgray levels is expanded.

� For higher amplitudes ofinput image the range ofgray levels is compressed.

Logarithmic TransformationsLogarithmic TransformationsLogarithmic TransformationsLogarithmic Transformations


Negative of an image?

Intensity Slicing?



Orientation EffectOrientation EffectOrientation EffectOrientation Effect


Orientation EffectOrientation EffectOrientation EffectOrientation Effect



EndIntensity Transformations

Technology

03 intensity transformations