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engrhassan2k13 on 07/07/15

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Automatic Thresholding with Expectation Maximization Algorithm in Matlab

/ Published in: MatLab

This code uses the Expectation Maximization algorithm for automatically thresholding an image.

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%read image
img1 = rgb2gray(imread('dino.jpg'));%use your image here
imshow(img1);

%parameter initialization for EM-Algo
temp =[];
phi1 = 0.5;
phi2 = 0.5;
u1  = 0;
u2 = 50;
sig1 = 2;
sig2 = 3;
tempimg1 = reshape(img1,1,numel(img1));
tempimg1 = double(tempimg1);
img = double (img1);

for k = 1 : 3

for i = 1 : numel(img1)
       %Expectation Step 
       prob1 =  -0.9181-reallog(sig1)-(  (( img(i)- u1 )^2)/(2*(sig1^2))  );
       prob2 =  -0.9181-reallog(sig2)-(  (( img(i)- u2 )^2)/(2*(sig2^2))  );
       
       probc1 = ( prob1*phi1 ) / ( (prob1*phi1)+ (prob2*phi2) );
       probc2 = ( prob2*phi2 )/( (prob1*phi1) + (prob2*phi2) );
       
       temp = [temp ; probc1 probc2];
    
end
       %Maximization Step

phi1 = ( sum(temp(:,1)) )*(1/numel(img));
       phi2 = (sum(temp(:,2)))*(1/numel(img));
      
       
       u1 = ( sum((temp(:,1)').*tempimg1) )/( sum(temp(:,1)) );
       u2 = ( sum((temp(:,2)').*tempimg1) )/( sum(temp(:,2)) );
       
       var1 =   ( sum( ( (tempimg1 - u1).^2  ).*( temp(:,1)' ) ) ) / ( sum(temp(:,1)) ); 
       sig1 = sqrt(var1);
       var2 =   ( sum( ( (tempimg1 - u2).^2  ).*( temp(:,2)' ) ) ) / ( sum(temp(:,2)) );
       sig2 = sqrt(var2);
       
       temp = [];
       
end
       
%Thresholding
thresh = ((u2 + u1)/2);

for m = 1 : numel(img1)
    if img1(m) > thresh
        img1(m) = 255;
    else
        img1(m) = 0;
    end
end

figure;
imshow(img1);

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