Computer Vision: Simple Noise Reduction

Question

In computer vision, we often want to remove noise from an image. We can do this by getting an image and replacing distorted pixels with an average of its neighbours. I have no trouble understanding this but what are all the variables in the following equation meant to be? I've just found it in some slides but it doesn't come with any explanation:

The (i,j) is probably a given pixel and its neighbour, but what is the function f, the Omega, and the w? Any guesses?!

Cheers guys.

Answer 1

This is way too vague. Notation changes between papers and different approaches. Generally speaking that formula is doing some averaging within a neighbouring set of the i,j point (defined by the points in \Omega_{ij}) w is some normalization constant and f(m,n) is some function which typically assigns a value to m,n proportional to its distance from i,j

As I said your question is a bit too vague to say anything else...

Answer 2

This looks similar to motion prediction in video encoding.

g(i,j) is likely the ith, jth pixel in a block / screen. whose value is the weighted sum of another heuristic function taking the neighbor positions (m,n)

Since I see Omega I suspect you are working in signal space. This might filter out high frequencies not found in our neighbors m,n