Why image is shifted when using ifft2

Hi, I'm implementing 2-D convolution by using FFT. Here is my code:

img = im2single(imread('dog.bmp'));
filter = fspecial('gaussian', 53, 3);

F = fft2(img);
mask = fft2(filter, size(img, 1), size(img, 2));

filtered_img = ifft2(F .* mask);
imshow(real(filtered_img));

Here is the original image:

And the result:

Why this happens? How can I fix it? Please help me.

Many thanks.

[Yulin WANG]

Well, you are applying a Gaussian Filter on an image in frequency domain and convert it back to the spatial domain, and that's why the image becomes a bit blurry than the orginal one.

I did not see anything wrong with this.

Answer 1

[Cris LaPierre]

The shift is related to your hsize value in fspecial (shifted ~0.5*hsize in both X and Y).

I'm not sure I can do any better explaining than what you can find googling, but you need to center your frequency domain in the center of the image. You can do this using fftshift and ifftshift. See here, and here.

Also note that, in the comment of the second link, there is a recommendation to use psf2otf to take the FFT of a point spread function.

After some playing around with a built in image, I came up with this code:

img = im2single(imread('autumn.tif'));
imshow(img)
filter = fspecial('gaussian', 53, 2);

F = fftshift(fft2(img));
mask = fftshift(psf2otf(filter,[size(img, 1), size(img, 2)]));

filtered_img = ifft2(ifftshift(F .* mask));
imshow(abs(filtered_img));

[Cris LaPierre]

A little more playing suggests that you really only need to replace

mask = fft2(filter, size(img, 1), size(img, 2));

with

mask = psf2otf(filter, [size(img, 1), size(img, 2)]);

in your code.