I am trying to display an image of covariance(covariance map) using this code but I receive a false result , please would you help me with this (I need this for my master degree)

clc
close all
clear all

img = imread('C:\test\image\image1.jpg'); %lire l'image de reference
I = rgb2gray(img); %convertir en niveau de gris
I1 = medfilt2(I, [5 5]);

C=imcrop(I1, [18.5 29.5 31 29]); %imcrop an ROI(left ventricular)

[m,n]=size(C);

for i=1:m
  for j=1:n
    for num=1:16
       file=['image', num2str(num),'.','jpg'];
       im = im2double(imread(fullfile('C:\test\image', file)));

            im = rgb2gray(im); %convertir en niveau de gris
          I2 = medfilt2(im, [5 5]);
          C=imcrop(I2,[18.5 29.5 31 29]); 

      a(i,j)= C(i,j); 
  C1 = imcrop(C, [20.5 16.5 5 4]); %ROI2 inside the first ROI
  [m1,n1]= size(C1);
      end
  mua(i,j)=((1/16)*(sum(C(i,j))));  
    end
  end

for num=1:16
    for i=1:m1
      for j=1:n1
        a1(i,j)=C1(i,j);
      end
    end

AR(num)=((1/(m1*n1))*(a1(i,j))); %%%%%%%%%%%%
end

% % 
for i=1:m1
        for j=1:n1
            muar =((1/16)*sum(AR)); 
        end
end

for i=1:m1
        for j=1:n1
            for num=1:16
            cov(i,j) = sum((a1(i,j) - mua(i,j))*(AR - muar));
            end

   covtot(i,j) = ((1/16)*sum(cov(i,j)));

          end
  end

figure(1);
imagesc(covtot),title('image de covariance'),
colorbar, colormap(jet);

[Walter Roberson]

You did not explain how you know the output is false. You did not attach the original input image so we cannot test your code.

You have

for num=1:16
    for i=1:m1
      for j=1:n1
        a1(i,j)=C1(i,j);
      end
    end

AR(num)=((1/(m1*n1))*(a1(i,j))); %%%%%%%%%%%%
end

The assignment to AR is after the end of the i and j loops. At the end of a for loop, the loop control variable is left at its last value, so after the two for loops, i will be left at m1 and j will be left at n1. That final line is therefore equivalent to coding

for num=1:16
   AR(num) = ((1/(m1*n1))*(C1(m1,n1)));
end

which is constant in num and so will give the same result for all AR entries.

[chaima kadess]

thanx for response , i want to display a covariance map like this one. i was following a pseudo code from an article

[chaima kadess]

and this what i get

[chaima kadess]

this is the fist image of the sequence

[Walter Roberson]

"i was following a pseudo code from an article"

Which article?

[chaima kadess]

Hamrouni, K., & Khalifa, N. (2006). Two Methods for Analysis of Dynamic Scintigraphic Images of the Heart. (section 5)

the difference that i work with 2d images.

[Walter Roberson]

The article appears to be available from http://www.ccis2k.org/iajit/PDF/vol.3,no.2/4-Kamel.pdf

[Walter Roberson]

If you are working with a single image instead of a sequence of images, then t is only ever 1, and AR(t) = mean2(C1);

[chaima kadess]

yes it is

[chaima kadess]

no ,I am working with a sequence of 16 images and I want to display finally one image of covariance from this 16 images.

Answer 1

[Walter Roberson]

You should replace a bunch of your code.

    numimg = 16;
    mut = zeros(m, n);
    for num = 1:numimg
       file = ['image', num2str(num),'.','jpg'];
       im = im2double(imread(fullfile('C:\test\image', file)));
       im = rgb2gray(im); %convertir en niveau de gris
       I2 = medfilt2(im, [5 5]);
       C = imcrop(I2,[18.5 29.5 31 29]); 
       mut = mut + C;
       C1 = imcrop(C, [20.5 16.5 5 4]); %ROI2 inside the first ROI
       AR(num) = mean2(C1);
    end

   mua = mut ./ numimg;

I had to make an assumption here about what you were calculating with mua.

[chaima kadess]

mua represents the average value of a (i, j)

[Walter Roberson]

If it is the average of a(i,j) over all of the images, then that is what I have the code calculate.

[chaima kadess]

thank you for responding me , but unfortunately it doesn't works , I have a sequence of 16 cardiac images ,the first image will be taken as a reference(c1(i,j)) following this equation : cov(i,j)=(1/T)*((C1(i,j)-mua(i,j))*(AR-muar)) where T is the frame number and mua(i,j) is the mean of the (i j) pixel value in the image series and AR is the mean value of all pixels located in the region of reference and muar is the mean value of the references series.so i am looking to display an image of the calculated covariance . hopefully you can help me mrs.