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 imagewithoutusinggraythreshfunctionfunction mygraythreshglobal 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 many 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 Calculationweight=sum(H(m:n))/sum(H);%Mean Calculationvalue=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;endendend

Threshold value:0.3242 |

## 7 comments:

hi pleasssssssssssssssssse i need you help i need the answer of this Q.

use a thresholding program (or write your own

)

and see an image at many thresholding levels .find a suitable thresholding to get the best representation of an object in the image .now select another object and find the best thresholding for it.repeat this experiment with several images

pleasssssssssssse help me before next sunday

my regard

very nice code

the threshold value is not being displayed. can you please tell what is the mistake

@abcxyz

The threshold value is stored in tval.

Use 'display tval' to check the threshold value.

Hi, I'm having trouble with this part:

for i=0:255

[wbk,varbk]=calculate(1,i);

[wfg,varfg]=calculate(i+1,255);

this function does not work! How should I use it? grateful

threshold value is not displayed even after I gave display tval. Can u suggest me what to do

Hi help me please i can't do it i have trouble

for i=0:255

[wbk,varbk]=calculate(1,i);

[wfg,varfg]=calculate(i+1,255);

this function does not work! How should I use it? grateful

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