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)?

CodePudding user response：

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.