# Cross-correlation in frequency domain and xcorr2 in MATLAB

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Shy on 11 May 2024
Commented: Shy on 12 May 2024
What are the reasons for the differences between my frequency domain cross-correlation results and those obtained using the xcorr2() function in MATLAB? Is it possible that xcorr2() performs spatial domain cross-correlation, and how might this affect the results?
img1_gray = rgb2gray(img1);
img2_gray = rgb2gray(img2);
[m, n] = size(img1_gray);
[p, q] = size(img2_gray);
fft_img1 = fft2(img1_gray, m + p - 1, n + q - 1);
fft_img2 = fft2(img2_gray, m + p - 1, n + q - 1);
cross_correlation = (fft_img1 .* conj(fft_img2));
cross_correlation = ifft2(cross_correlation);
cross_correlation = fftshift(cross_correlation);
cross_correlation_xcorr2 = xcorr2(img2_gray, img1_gray);
figure;
subplot(2, 1, 1);
imshow(cross_correlation, []);
title('Custom Cross-Correlation');
subplot(2, 1, 2);
imshow(cross_correlation_xcorr2, []);
title('xcorr2');
Results:
Paul on 11 May 2024
Can you add 1.jpg and 2.jpg to your post using the Paperclip icon on the Insert menu?
Shy on 11 May 2024
Sure.

Paul on 11 May 2024
Hi Shy,
Assuming that the output of the xcorr2 is the expected result, it can be obtained with the changes below
img1_gray = rgb2gray(img1);
img2_gray = rgb2gray(img2);
[m, n] = size(img1_gray);
[p, q] = size(img2_gray);
%fft_img1 = fft2(img1_gray, m + p - 1, n + q - 1);
fft_img1 = fft2(flipud(fliplr(img1_gray)), m + p - 1, n + q - 1);
fft_img2 = fft2(img2_gray, m + p - 1, n + q - 1);
%cross_correlation = (fft_img1 .* conj(fft_img2));
cross_correlation = (fft_img1 .* fft_img2);
cross_correlation = ifft2(cross_correlation);
%cross_correlation = fftshift(cross_correlation);
cross_correlation_xcorr2 = xcorr2(img2_gray, img1_gray);
figure;
subplot(2, 1, 1);
imshow(cross_correlation, []);
title('Custom Cross-Correlation');
subplot(2, 1, 2);
imshow(cross_correlation_xcorr2, []);
title('xcorr2');
##### 3 CommentsShow 1 older commentHide 1 older comment
Paul on 11 May 2024
As I undersand it, xcorr2(x,y) is the the same as conv2 of x and the 2D-reversed conjugate of y. But in this case, img1_gray is real, so its conjugate is itself. With that understanding, I just made the fft stuff implement the convolution of img2 and the 2D-reverse of img1 (because img1 is the second argument to xcorr2).
Shy on 12 May 2024
Okay, I get it. Thanks

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