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I converted a Gauss filter, as well as an image I want to filter, into the fourier space. Are the rules of applying filters in the fourier space the same like in the image space? (e.g. just applying a convolution with np.convolve)?

Cris Luengo
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Severin Spörri
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1 Answers1

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According to the Convolution theorem, convolution in image space corresponds to multiplication in Fourier space.

So in order to apply the filter, you do element-wise multiplication of the Fourier-transformed image with the Fourier-transformed filter.

The product is the Fourier-transformed filtered image. To get the filtered image in image space, you apply the inverse Fourier transform.

mkrieger1
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  • thank you! according to the article, and what you've written, I used np.multiply, and it worked! (still have to transform it back of course) – Severin Spörri May 26 '22 at 21:35