DIGITAL IMAGE PROCESSING - Osmanoglu€¦ · · 2013-03-17DIGITAL IMAGE PROCESSING ... 040010250 . Segmentation Algorithms Introduction Five segmentation methods are employed on

Đstanbul Teknik Üniversitesi Elektrik Elektronik Fakültesi

Telekomünikasyon Mühendisliği

Bölümü

TEL 432 E

DIGITAL IMAGE

PROCESSING

-Homework 4-

Batuhan Osmanoglu 040010250

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;

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 values

in the image and then taking the mean of it to obtain the threshold. MatLab code and

output images are given below.

Image Face Image Text Image Sky Image Threshold Value 71 189 126

Outputs

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))=0;

imface(find(imface>=T))=1;

%Text


[rmax cmax]=size(imtext);

T=0;

T=sum(sum(imtext));

T=T/(rmax*cmax)

imtext(find(imtext<T))=0;

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

%Sky


[rmax cmax]=size(imsky);

T=0;

T=sum(sum(imsky));

T=T/(rmax*cmax)

imsky(find(imsky<T))=0;

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

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

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

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

Two Peaks “Method of Two Peaks” is employed by finding two local maximum points in the

histogram and defining a threshold separating them.


Outputs


%Two Peaks

%Segmentation




%FACE

histog=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;

end

locmaxx=find(T==max(T));

tresh=(locmax+locmaxx)/2

imface(find(imface<tresh))=0;

imface(find(imface>=tresh))=1;

%Text

histog=hist(double(imtext),256);


figure(4);plot(histogram,'r');title('text-histogram');


T=zeros(1,256);

for hi=1:256


end



imtext(find(imtext<tresh))=0;

imtext(find(imtext>=tresh))=1;

%Sky

histog=hist(double(imsky),256);


figure(6);plot(histogram,'r');title('sky-histogram');


T=zeros(1,256);

for hi=1:256


end



imsky(find(imsky<tresh))=0;

imsky(find(imsky>=tresh))=1;

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

image');

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

image');

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

image');

Edge Pixels

Laplacian is calculated for each pixel and then histogram of pixels with large

laplacians is created. Using this new histogram a threshold can be detected using any of

the previous methods.


Outputs


%EDGE PIXELS

%Segmentation




%FACE

%calculate laplacian


L=zeros(size(imface));

for r=2:rmax-1

for c=2:cmax-1

L(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));

end

end

ef=rmax*cmax*0.85;%number of eightyfive percent of pixels

LL=zeros(size(L));

%new image with only eighty five percent and above

ki=0;

while ki<ef

loc=find(L==max(max(L)));

LL(loc)=imface(loc);

L(loc)=0; %do not take this pixel into account again

ki=ki+max(size(loc));

end

%use LL to find Treshold

T=sum(sum(LL));

T=T/(ef)



%Text



L=zeros(size(imtext));

for r=2:rmax-1

for c=2:cmax-1

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));

end

end


LL=zeros(size(L));


ki=0;

while ki<ef


LL(loc)=imtext(loc);



end


T=sum(sum(LL));

T=T/(ef)



%SKY



L=zeros(size(imsky));

for r=2:rmax-1

for c=2:cmax-1

L(r,c)=double(imsky(r-

1,c))+double(imsky(r+1,c))+double(imsky(r,c-

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

end

end


LL=zeros(size(L));


ki=0;

while ki<ef


LL(loc)=imsky(loc);



end


T=sum(sum(LL));

T=T/(ef)






Iterative Threshold Method In this method a threshold is iteratively calculated and refined by consecutive

passes through the image.


Outputs


%Iterative Selection

%Segmentation

clear all; clc;




tresholds=zeros(1,3);

%FACE



T=0;

T=sum(sum(imface));

T=T/(rmax*cmax)

Tnew =-1;

while round(T)~=round(Tnew) %not equal

if Tnew~=-1

T=Tnew;

end

Tlow=

sum(sum(imface(find(imface<T))))/max(size(find(imface<T)))

Thigh=

sum(sum(imface(find(imface>=T))))/max(size(find(imface>=T)))

Tnew=(Tlow+Thigh)/2

end




tresholds(1,1)=T;

%Text



T=0;

T=sum(sum(imtext));

T=T/(rmax*cmax)

Tnew =-1;


if Tnew~=-1

T=Tnew;

end

Tlow=

sum(sum(imtext(find(imtext<T))))/max(size(find(imtext<T)))

Thigh=

sum(sum(imtext(find(imtext>=T))))/max(size(find(imtext>=T)))

Tnew=(Tlow+Thigh)/2

end




tresholds(1,2)=T;

%Sky



T=0;

T=sum(sum(imsky));

T=T/(rmax*cmax)

Tnew =-1;


if Tnew~=-1

T=Tnew;

end

Tlow=

sum(sum(imsky(find(imsky<T))))/max(size(find(imsky<T)))

Thigh=

sum(sum(imsky(find(imsky>=T))))/max(size(find(imsky>=T)))

Tnew=(Tlow+Thigh)/2

end




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 Image Threshold 94 178 111

Percentage of Black Pixels

60 20 50

Outputs


%Percentage of Black Pixels

%Segmentation

clear all; clc;




tresholds=zeros(2,3);

%FACE

%Assumption of black pixel percentage

p=60;%percentage of Black pixels


pxn=rmax*cmax; %number of pixels

T=0;

while max(size(find(imface==0))) < p*pxn/100

T=T+1;

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

end

imface(find(imface>T))=1;

tresholds(1,1)=T;

tresholds(2,1)=p;


%Text





T=0;

while max(size(find(imtext==0))) < p*pxn/100

T=T+1;

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

end

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

tresholds(1,2)=T;

tresholds(2,2)=p;


%Sky





T=0;

while max(size(find(imsky==0))) < p*pxn/100

T=T+1;

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

end

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

tresholds(1,3)=T;

tresholds(2,3)=p;


thresholds

Gray Level Histogram

Gray Level Histogram method is based on minimizing the ratio of between classes

variance 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 with

Gaussian distribution, it is not a great deal to calculate the overall variance of the whole

image, denoted by σt2.

Moreover, it is possible to calculate the variance of the object and the background

pixels separately, for any predefined threshold. This is denoted by σw2

and called within

class 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 separate

object and background pixels than we will have two separate Gaussian functions with two

exact 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 name

implies 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 σb2/σt

2 where σb

2 represents

between classes’ variance.

Overall variance σt2 is going to be calculated from the image, using histogram

values. On the other hand, it is not that easy to calculate between classes’ variance. An

expression to calculate σb2 is;

2

00

2 )( iib µµωωσ =

In this formula µ0 and µi represents the mean values of overall and pixels up to

gray level i. Other terms, w0 and wi are calculated using the expression below:

0

0

0 1 ωωω −=⇔=∑=

ii

t

i

p

And;

i

t

i

t

tT

i

i pi×=⇔−

−=⇔= ∑

=000

01

µω

µµµ

ω

µµ

Where pi is the probability of gray level i and tµ is the mean of the whole image.

Given these expressions one can calculate each σb2/ σt

2 ratio for any t. Value t that

gives the minimum result for that ratio is to be selected as the optimal threshold.

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

DIGITAL IMAGE PROCESSING - Osmanoglu€¦ · · 2013-03-17DIGITAL IMAGE PROCESSING ... 040010250 . Segmentation Algorithms Introduction Five segmentation methods are employed on

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