In this section, we will see more applications of convolution on images using Python modules such as scipy signal
and ndimage
. Let's start with convolution theorem and see how the convolution operation becomes easier in the frequency domain.
The convolution theorem says that convolution in an image domain is equivalent to asimple multiplication in the frequency domain:
Following diagram shows the application of fourier transforms:
The next diagram shows the basic steps in frequency domain filtering. We have the original image, F
, and a kernel
(a mask or a degradation/enhancement function) as input. First, both input items need to be converted into the frequency domain with DFT
, and then the convolution needs to be applied, which by convolution theorem is just an (element-wise) multiplication. This outputs the convolved image in the frequency domain, on which we need to apply IDFT
to obtain the reconstructed...