Correlation among 2 images

Question

I am trying to find the following correlation among two images f1 and f2 where the size of the image is PXP.

I have written a for loop program for the same but I think an inbuilt function would be faster for the same.

Which function in matlab can help me compute this ?

Also if the size of both the images are M X N can someone tell me how this formula will change or if the function will be able to handle it.

EDIT:

Is there any faster function than xcorr2 that can help me seeing that it takes too much time when I only need to have the value for correlation the unshifted images....

Solution 1

This is the function used to do correlation (coefficient) between two images (matrices):

r = corr2(A,B) computes the correlation coefficient between A and B, where A and B are matrices or vectors of the same size.

while xcorr2 (A, B) solves for CROSS correlation.

Solution 2

MATLAB has xcorr2 just for this purpose. I suppose your code would look something like:

r = xcorr2(f1, f2) / (P .^ 2)

Where f1 and f2 are the two images. The resulting matrix r is a (2P-1)×(2P-1) matrix, and each of its elements reflect the measure of similarity between f1 and f2, when the two images are shifted by an offset corresponding to that element's offset from the center.

Note that if you're interested only in the correlation between two unshifted images, then you should save execution time and use corr2, like @TheByzantine has suggested in his answer.

Solution 3

use the xcorr2 function. For example:

 C=xcorr2(A,B)

Comments

[Serg]

if you need correlation, it's just dot product between two arrays f(:) after centering (mean and variance). This is very fast and is done by corr2: type edit corr2 to see how. if you need cross-correlation, then there are xcorr2 or imfilter, but they can't be fast because of the number of computations.

[user671805]

For both M X N images is it supposed to give me a matrix rather than a single number ?

[Eitan T]

@user671805 Yes, the resulting correlation matrix would be (2P-1)x(2P-1).

[user671805]

But it is supposed to be a single number since this measure has been used as a similarity measure between 2 images.... Or would it be sum(sum(r)) ?

[Eitan T]

@user671805 No, r is supposed to be a matrix, where each element reflects the measure of similarity between f1 and f2, with the corresponding offset (phase) of that element from the center. For example, element (0, 0) shows the correlation between the images if one is shifted by P pixels in each axis relative to the other. This means that if you want a number that tells how similar the pictures without any shift, that would be the element in the (P, P) position.

[user671805]

@Eitan The link you have mentioned talks about sliding one matrix on top of another....Just to check , when the 2 matrices are exactly on top of each other, to get the co-relation would be equivalent to finding ( M , N ) position in xcorr2 ?

[user671805]

Hey, Is there a faster method seeing that I only want the unshifted value ? Its taking a huge time to compute...

[Eitan T]

@user671805 You should use corr2 then, like @TheByzantine suggested.

[Eitan T]

Apparently that's what the OP wants, so +1 for you.