Otsu’s thresholding without using MATLAB function graythresh

  To perform the thresholding I followed these steps:

a.       Reshape the 2 dimensional grayscale image to 1 dimensional.

b.      Find the histogram of the image using  ‘hist’ function.

c.       Initialize a matrix with values from 0 to 255

d.      Find the weight , mean and the variance for the foreground and background

e.      calculate weight of foreground* variance of foreground + weight of background* variance of background.

f.       Find the minimum value.

MATLAB CODE:
%To threshold image without using graythresh function

function mygraythresh

global H Index;

B=imread('tire.tif');

Here I converted the 2d matrix to 1d matrix.

 V=reshape(B,[],1);

The histogram of the values from 0 to 255 is stored.

For instance, G(1) contains the number of occurrence of the value zero in the image.

 G=hist(V,0:255);

 H=reshape(G,[],1);

 'index' is a 1 dimensional matrix ranging between 0 and 255

 Ind=0:255;

 Index=reshape(Ind,[],1);

 result=zeros(size([1 256]));

To avoid more for loops I used only 1 for loop and a function to calculate the weight, mean and variance.

Let me explain the foreground and the background for a value of ‘i’.

if ‘i’ value is 5 then the foreground values will be 0,1,2,3,4,5

and the background values will be 6 to 255.

 for i=0:255

     [wbk,varbk]=calculate(1,i);

     [wfg,varfg]=calculate(i+1,255);

    

After calculating the weights and the variance, the final computation is stored in the array ‘result’.

     result(i+1)=(wbk*varbk)+(wfg*varfg);

    

    

 end

 Find the minimum value in the array.                   [threshold_value,val]=min(result);

    

     tval=(val-1)/256;

Now convert the image to binary with the calculated threshold value.

     bin_im=im2bw(B,tval);

     figure,imshow(bin_im);

 function [weight,var]=calculate(m,n)

%Weight Calculation

     weight=sum(H(m:n))/sum(H);

    

%Mean Calculation

     value=H(m:n).*Index(m:n);

     total=sum(value);

     mean=total/sum(H(m:n));

     if(isnan(mean)==1)

         mean=0;

     end

%Variance calculation.

    value2=(Index(m:n)-mean).^2;

     numer=sum(value2.*H(m:n));

     var=numer/sum(H(m:n));

     if(isnan(var)==1)

         var=0;

     end

    

 end

 end

Threshold value:0.3242

Reference:

Digital Image Processing (3rd Edition)Chapter: Image Segmentation-Basic Global thresholding