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I have performed 2D convolution on image matrix using: A. Matrix multiplication B. Fast Fourier Transformation.

My question is can I apply any of the above techniques (let's say FFT) for performing convolutions using spatially varying kernel?

My understanding is spatially varying kernel is applying different kernel on different parts of an image. But doesn't it violate the basic rule of convolution?

Tsyvarev
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d_n2001
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  • You can apply something that looks like a convolution, changing the kernel at every pixel (see for example the bilateral filter), but that no longer is a convolution, and you cannot analyze it using the Fourier transform, nor implement it through the FFT. – Cris Luengo Mar 09 '22 at 16:42
  • @CrisLuengo So only way to implement it, is by using nested for loops? – d_n2001 Mar 09 '22 at 16:50
  • Yes, that is the only way. – Cris Luengo Mar 09 '22 at 17:09

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