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Why image is shifted when using ifft2

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Khang Truong
Khang Truong on 2 Oct 2019
Commented: Cris LaPierre on 3 Oct 2019
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: dog.bmp
And the result:
untitled.jpg
Why this happens? How can I fix it? Please help me.
Many thanks.

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Answers (1)

Cris LaPierre
Cris LaPierre on 3 Oct 2019
Edited: Cris LaPierre on 3 Oct 2019
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));

  1 Comment

Cris LaPierre
Cris LaPierre on 3 Oct 2019
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.

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