Similiarity of Columns in Images

I have two images, and I am interested in determining the Gaussian similarly (not equal) of columns in each image. Can someone assist me on how to accomplish it?

Answer 1

[Walter Roberson]

Assuming a grayscale image YourImage,

[r, c] = size(YourImage);
gsim = zeros(c, c);
for c1 = 1 : c - 1;
  for c2 = c1 + 1 : c
    [h, p] = kstest2(YourImage(:,c1), YourImage(:,c2));
    gsim(c1, c2) = p;
    gsim(c2, c1) = p;
  end
end

imagesc(gsim)

[J Parker]

Thank you so much! Could you help explain the code? Also, what does the output image show?

[Walter Roberson]

The pixel at location (J,K) of the output image shows you the similarity of column J compared to column K of the original image.

The dark blue areas have little gaussian similarities; the yellow areas have higher similarity. The image is symmetric because the similarity of two columns does not depend on the order of the columns.

"Gaussian similarly" is not well defined, so I guessed that you what you wanted was a measure of the probability that two given columns were drawn from the same Gaussian distribution (same mean, same standard deviation.) This test is completely insensitive to reordering the rows -- it would give exactly the same answer if you had done sort(YourImage,'rows'). Anyhow, the way to estimate the probability that two vectors are from the same gaussian distribution is to call kstest2()

[J Parker]

Thanks so much for your help! I appreciate it so much! Is it possible to overlay the similar columns with respect to the images. I am interested in knowing where in the two image they are similar.

[Walter Roberson]

preferred_num_to_select = 6;

tgsim = triu(gsim);
[~, sort_idx] = sort( tgsim(:), 'descending');
num_to_select = min(preferred_num_to_select, length(best_gsim));    %usually 6, but really small images might not have 6
best_idx = sort_idx(1:num_to_select);
[bc1, bc2] = ind2sub( size(gsim), best_idx );

cmap = prism(num_to_select);   %a colormap

figure(2)
image(YourImage);
hold on
pointsize = 20;
for K = 1 : num_to_select
  scatter([bc1(K); bc2(K)], [K;K], pointsize, cmap(K,:), '*');
end
hold off

What this does is put up the image, and then near the top, puts up pairs of '*' markers in various colors. Each pair marks a pair of similar columns. The similarity is keyed by colors: red for the most similar, then orange, yellow, green, blue, purple. Also, the higher up in the image the marker is placed, the greater the degree of similarity

This is a crude representation, but you are asking for pairwise columns to somehow be distinguishably noted on a full image.

[J Parker]

Thanks so much for your assistance. When I try to compare the same image with itself, for example img1 to img1, I suspected to determine the similarity image to be entirely yellow. But, it's not. Is there a reason for it? Also, I noticed in the similarity image some green. Is that a progression from blue (not as similar) to yellow (very similar)

[Walter Roberson]

Sorry this code was designed to compare the columns within one image, not to work with two images. I would need to think more about how to handle two images.

[Image Analyst]

J, why don't you simply subtract the images? Or use built-in functions like immse() or psnr()? Or compute the mean (or median) absolute deviation?

[Walter Roberson]

[r1, c1, p1] = size(FirstImage);
[r2, c2, p2] = size(SecondImage);

if c1 ~= c2
  error('Images must have the same number of columns');
end
if p1 ~= 1 || p2 ~= 1
  error('This code is for grayscale images only');
end

gsim = zeros(1, c1);
for c = 1 : c1
    [h, p] = kstest2(FirstImage(:,c), SecondImage(:,c));
    gsim(1, c) = p;
  end
end

figure(2)
image(gsim);            %I do not recommend imshow for this purpose
colormap(parula(256))