Grey Level Segmentation

8/10/2019 Grey Level Segmentation

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stanbul Teknik niversitesiElektrik Elektronik Fakltesi

Telekomnikasyon MhendisliiBlm

TEL 432 E

DIGITAL IMAGE

PROCESSING

-Homework 4-

Batuhan Osmanoglu040010250


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Segmentation Algorithms

Introduction

Five segmentation methods are employed on 3 images such as: face, hand-written

text and sky. Original gray level images are given below.

Face: Text: Sky:

Histograms of these images are;


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The first segmentation method is Mean Gray Level. Then, we will continue with,

Two Peaks, Edge Pixels, Iterative Selection and Percentage of Black Pixels.

Mean Gray Level

Mean Gray Level Algorithm is simply applied by summing up all the pixel valuesin the image and then taking the mean of it to obtain the threshold. MatLab code andoutput images are given below.

Image Face Image Text Image Sky ImageThreshold Value 71 189 126

Outputs


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MatLab Code

%TEL 432E HW 4%MEAN GRAY LEVEL%Segmentation

imface = imread('face.jpg');imtext = imread('text.jpg');imsky = imread('sky.jpg');

%FACE%calculate mean grey level[rmax cmax]=size(imface);T=0;T=sum(sum(imface));T=T/(rmax*cmax)imface(find(imface=T))=1;

%Text%calculate mean grey level[rmax cmax]=size(imtext);T=0;T=sum(sum(imtext));T=T/(rmax*cmax)imtext(find(imtext=T))=1;

%Sky%calculate mean grey level[rmax cmax]=size(imsky);T=0;T=sum(sum(imsky));T=T/(rmax*cmax)imsky(find(imsky=T))=1;

figure(1);colormap('gray'); imagesc(imface);figure(2);colormap('gray'); imagesc(imtext);

figure(3);colormap('gray'); imagesc(imsky);


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Two PeaksMethod of Two Peaks is employed by finding two local maximum points in the

histogram and defining a threshold separating them.


Outputs


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MatLab Code

%TEL 432E HW 4%Two Peaks%Segmentation


%FACEhistog=hist(double(imface),256);histogram=sum(histog');figure(2);plot(histogram,'r');title('face-histogram');locmax=find(histogram==max(histogram));T=zeros(1,256);for hi=1:256

T(hi)=histogram(hi)*(hi-locmax)^2;endlocmaxx=find(T==max(T));tresh=(locmax+locmaxx)/2imface(find(imface=tresh))=1;

%Texthistog=hist(double(imtext),256);histogram=sum(histog');figure(4);plot(histogram,'r');title('text-histogram');

locmax=find(histogram==max(histogram));T=zeros(1,256);for hi=1:256

T(hi)=histogram(hi)*(hi-locmax)^2;endlocmaxx=find(T==max(T));tresh=(locmax+locmaxx)/2imtext(find(imtext=tresh))=1;

%Skyhistog=hist(double(imsky),256);histogram=sum(histog');figure(6);plot(histogram,'r');title('sky-histogram');locmax=find(histogram==max(histogram));T=zeros(1,256);for hi=1:256

T(hi)=histogram(hi)*(hi-locmax)^2;


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endlocmaxx=find(T==max(T));tresh=(locmax+locmaxx)/2imsky(find(imsky=tresh))=1;

figure(1);colormap('gray'); imagesc(imface);title('faceimage');

figure(3);colormap('gray'); imagesc(imtext);title('textimage');

figure(5);colormap('gray'); imagesc(imsky);title('skyimage');

Edge Pixels

Laplacian is calculated for each pixel and then histogram of pixels with largelaplacians is created. Using this new histogram a threshold can be detected using any ofthe previous methods.


Outputs


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MatLab Code

%TEL 432E HW 4%EDGE PIXELS

%Segmentation


%FACE%calculate laplacian[rmax cmax]=size(imface);L=zeros(size(imface));for r=2:rmax-1

for c=2:cmax-1L(r,c)=double(imface(r-

1,c))+double(imface(r+1,c))+double(imface(r,c-1))+double(imface(r,c+1))-4*double(imface(r,c));

endendef=rmax*cmax*0.85;%number of eightyfive percent of pixelsLL=zeros(size(L));%new image with only eighty five percent and aboveki=0;while ki


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L(r,c)=double(imtext(r-1,c))+double(imtext(r+1,c))+double(imtext(r,c-1))+double(imtext(r,c+1))-4*double(imtext(r,c));

endendef=rmax*cmax*0.85;%number of eightyfive percent of pixelsLL=zeros(size(L));%new image with only eighty five percent and aboveki=0;while ki


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T=T/(ef)imsky(find(imsky=T))=1;

figure(1);colormap('gray'); imagesc(imface);figure(2);colormap('gray'); imagesc(imtext);figure(3);colormap('gray'); imagesc(imsky);

Iterative Threshold Method

In this method a threshold is iteratively calculated and refined by consecutive passes through the image.


Outputs


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MatLab Code

%TEL 432E HW 4%Iterative Selection%Segmentation

clear all; clc;


tresholds=zeros(1,3);%FACE%calculate mean grey level[rmax cmax]=size(imface);T=0;T=sum(sum(imface));T=T/(rmax*cmax)Tnew =-1;while round(T)~=round(Tnew) %not equal

if Tnew~=-1T=Tnew;

endTlow=

sum(sum(imface(find(imface=T)))

Tnew=(Tlow+Thigh)/2end

imface(find(imface=T))=1;figure(1);colormap('gray'); imagesc(imface);tresholds(1,1)=T;%Text%calculate mean grey level[rmax cmax]=size(imtext);

T=0;T=sum(sum(imtext));T=T/(rmax*cmax)Tnew =-1;while round(T)~=round(Tnew) %not equal

if Tnew~=-1T=Tnew;

end


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Tlow=sum(sum(imtext(find(imtext=T)))

Tnew=(Tlow+Thigh)/2end

imtext(find(imtext=T))=1;

figure(2);colormap('gray'); imagesc(imtext);tresholds(1,2)=T;%Sky%calculate mean grey level[rmax cmax]=size(imsky);T=0;T=sum(sum(imsky));T=T/(rmax*cmax)Tnew =-1;while round(T)~=round(Tnew) %not equal

if Tnew~=-1T=Tnew;

endTlow=

sum(sum(imsky(find(imsky=T)))Tnew=(Tlow+Thigh)/2

end

imsky(find(imsky=T))=1;

figure(3);colormap('gray'); imagesc(imsky);tresholds(1,3)=T;thresholds

Percentage of Black Pixels

Assuming that percentage of black pixels is a constant for some types of images,lower pixel values up to the number of assumed pixels are segmented as background or

black.

Image Face Image Text Image Sky ImageThreshold 94 178 111

Percentage ofBlack Pixels

60 20 50


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Outputs


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MatLab Code

%TEL 432E HW 4%Percentage of Black Pixels%Segmentation

clear all; clc;

imface = imread('face.jpg');imtext = imread('text.jpg');imsky = imread('sky.jpg');tresholds=zeros(2,3);%FACE%Assumption of black pixel percentagep=60;%percentage of Black pixels[rmax cmax]=size(imface);pxn=rmax*cmax; %number of pixelsT=0;while max(size(find(imface==0))) < p*pxn/100

T=T+1;imface(find(imface==T))=0;

endimface(find(imface>T))=1;tresholds(1,1)=T;tresholds(2,1)=p;


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figure(1);colormap('gray'); imagesc(imface);

%Text%Assumption of black pixel percentagep=20;%percentage of Black pixels[rmax cmax]=size(imtext);pxn=rmax*cmax; %number of pixelsT=0;while max(size(find(imtext==0))) < p*pxn/100

T=T+1;imtext(find(imtext==T))=0;

endimtext(find(imtext>T))=1;tresholds(1,2)=T;tresholds(2,2)=p;

figure(2);colormap('gray'); imagesc(imtext);

%Sky%Assumption of black pixel percentagep=50;%percentage of Black pixels[rmax cmax]=size(imsky);pxn=rmax*cmax; %number of pixelsT=0;while max(size(find(imsky==0))) < p*pxn/100

T=T+1;imsky(find(imsky==T))=0;

endimsky(find(imsky>T))=1;tresholds(1,3)=T;tresholds(2,3)=p;

figure(3);colormap('gray'); imagesc(imsky);thresholds


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Gray Level Histogram

Gray Level Histogram method is based on minimizing the ratio of between classesvariance to total variance of gray level pixels.

Total gray level variance is the variance of two separate Gaussian functions,representing the background and object pixels. In case there are two pixel groups withGaussian distribution, it is not a great deal to calculate the overall variance of the wholeimage, denoted by t

2.

Moreover, it is possible to calculate the variance of the object and the background pixels separately, for any predefined threshold. This is denoted by w

2 and called withinclass variance. This term, within class variance is a measure of standard deviation of

background and object pixels. As a matter of fact, if it is possible to perfectly separateobject and background pixels than we will have two separate Gaussian functions with twoexact within class variance. Even though it is an important measure in ANOVA (Analysis

of Variance), we are not going to deal with this term in Gray Level Histogram Method.Variations of the mean values for each class from the mean of whole image are

named as between classes variance. This is a value that we want to minimize. The nameimplies that it is the between classes variance. We would like to have no relation

between two classes to be able to make a perfect distinction. Therefore, we are going to pick up the best threshold value, which minimizes the ratio of b2/ t2 where b2 represents between classes variance.

Overall variance t2 is going to be calculated from the image, using histogramvalues. On the other hand, it is not that easy to calculate between classes variance. Anexpression to calculate

b

2 is;

200

2 )( iib =

In this formula 0 and i represents the mean values of overall and pixels up togray level i. Other terms, w 0 and w i are calculated using the expression below:

00

0 1 == =

ii

t

i

p

And;

i

t

it

t T i

i pi =

==

= 0000 1

Where p i is the probability of gray level i and t is the mean of the whole image.

Given these expressions one can calculate each b2/ t

2 ratio for any t. Value t thatgives the minimum result for that ratio is to be selected as the optimal threshold.


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Sources:

1. Advanced Methods in Grey Level Segmentation.2. Gray Levels and Histogram , December 2004, Ruye Wang

http://fourier.eng.hmc.edu/e161/lectures/digital_image/node9.html

3.

Analysis of Variance between groups, December 2004,http://www.physics.csbsju.edu/stats/anova.html

Grey Level Segmentation

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