How would you apply a 7 x 7 Laplacian of Gaussian filter on an image using the Fourier transform in MATLAB?

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1. I = imread(‘moon.tif’);
2. % Fourier filter must have equal size
3. laplacian = zeros(size(I));
4. % Placing our ‘Mexican hat’ in the left upper corner:
5. laplacian(1:7,1:7) = […
6. 0, 0,-1,-1,-1, 0, 0;…
7. 0,-1,-3,-3,-3,-1, 0;…
8. -1,-3, 0, 7, 0,-3,-1;…
9. -1,-3, 7,24, 7,-3,-1;…
10. -1,-3, 0, 7, 0,-3,-1;…
11. 0,-1,-3,-3,-3,-1, 0;…
12. 0, 0,-1,-1,-1, 0, 0]/48;
13. % Shifting the filter’s center to the [1,1] index:
14. laplacian = circshift(laplacian,-3*[1,1]);
15. % Apply convolution theorem (multiply in Fourier domain)
16. LapFilteredImage = real(ifftn(fftn(I).*fftn(laplacian)));
17. % Show results:
18. figure;
19. subplot(1,2,1); imagesc(I); colormap gray;
20. subplot(1,2,2); imagesc(LapFilteredImage); colormap gray;