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Maintaining significant information of the image

Matlab Code
 clear;  
 % Threshold level parameter alfa:  
 alfa=0.1;% less than 1/3  
 [x,map]=gifread('lena.gif');  
 ix=ind2gray(x,map);  
 I_max=max(max(ix));  
 I_min=min(min(ix));  
 level1=alfa*(I_max-I_min)+I_min;  
 level2=2*level1;  
 level3=3*level1;  
 thix1=max(ix,level1.*ones(size(ix)));  
 thix2=max(ix,level2.*ones(size(ix)));  
 thix3=max(ix,level3.*ones(size(ix)));  
 figure(1);  
 colormap(gray);  
 subplot(2,2,1);  
 imagesc(ix);  
 title('lena');  
 subplot(2,2,2);  
 imagesc(thix1);  
 title('1');  
 subplot(2,2,3);  
 imagesc(thix2);  
 title('2');  
 subplot(2,2,4);  
 imagesc(thix3);  
 title('3');  

Input
lena.gif

Output / Results

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