Uniform Smoothing Filter Operation Using Square Odd Window Size (Digital Image Processing)

Question

I have something that I need to do using uniform smoothing filter operation on an image. I was wondering if someone could just answer a few questions for me. What is "Square Odd Window Size"? What is the difference 2D smoothing and separable 1D smoothing?

Thank you

Answer 1

Square Odd Window Size just means that the filter window is square (N by N) and N is odd. N being odd ensures a well defined center to the window. 1D separable smoothing is a method used to implement 2D smoothing. It allows for you to smooth and image in O(M²N) time rather than O(M²N²) where M is the height and width of the image being smoothed.

If you do smoothing in the frequency domain using an FFT you can do this in O(M²log²(M) + N²log²(N)) which is an order of magnitude speed up if the smoothing filter is large.