Fast FFT convolution in 2D
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Alex Kurek
on 28 Feb 2016
Answered: Image Analyst
on 28 Feb 2016
Hello,
Is there a way to do fast 2D convolution according to: FFT Convolution performance ? In 2D it is not any faster, than standard MAtlab`s convolution. The same is reported of MathWorkd central files repository
pd = fspecial('Gaussian', 61, 10);
noise = poissrnd(0.2, [260 260]);
tic
zz1 = imfilter(noise, pd);
toc
tic
zz2 = conv2fft(noise, pd);
toc
% Compare the relative accuracy (the results are nearly identical)
zz2 = zz2(31:end-30, 31:end-30);
aa = max(abs(zz1-zz2)./abs(zz1));
disp(max(aa))
figure( 'units', 'normalized', 'outerposition', [0 0 1 1], 'name', 'Conv FFT 2D', 'numbertitle', 'off' );
subplot 141, imshow(zz1, []); title('Convolution');
subplot 142, imshow(zz2, []); title('FFT');
subplot 143, imshow(zz1-zz2, []); title('Convolution - FFT'); impixelinfo
subplot 144, surf(zz1-zz2); title('Convolution - FFT'); rotate3d on; colormap parula
Results:
Elapsed time is 0.048178 seconds
Elapsed time is 0.021171 seconds
1.0758e-15.
In 1D FFT version is ~300x faster.
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Accepted Answer
Image Analyst
on 28 Feb 2016
2D convolution is already very highly optimized in the functions conv2() and imfilter(), even more so for separable kernels. I know for a fact that they put special effort into making these as fast and efficient as possible.
Convolution via fft2 may not be faster, especially for smaller matrices like you have. In fact it might even be slower. Generally the fft method becomes faster only for very large matrices. You can test that by increasing the size of your matrices.
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