# Relation between variance of gaussian noise and intensity variance in Bilateral filter

So I implemented the code for bilateral filter from here and ran it for various values of spatial sigma and intensity sigma. I noticed that when I add gaussian noise to an image with variance say 0.02, and then try to filter it with bilateral filter, and if I enter value of spatial sigma say 18 and of intensity sigma as 0.02, the filtered image looks apparently same as the noisy one.

I am guessing that 'intensity sigma' (or sigma r as mentioned in this paper) tells us the difference in intensity levels between neighbouring pixels that we are allowing (though I am not sure if this is correct). So when we are smoothing with sigma r value same as variance of gaussian noise, essentially it makes no change since the intensity difference in the noisy image is within the same bounds as allowed by our bilateral filter.

It smooths the picture nicely with sigma r = 0.25.