Blurring/Smoothing

From Computer Vision: a Modern Approach

Images typically have the property that the value of a pixel usually is similar to that of its neighbor. Assume that the image is affected by noise of a form where we can reasonably expect that this property is preserved. For example there might be occasional
dead pixels, or small random numbers with zero mean might have been added to the pixel values. It is natural to attempt to reduce the effects of this noise by replacing each pixel with a weighted average of its neighbors, a process often referred to as smoothing
or blurring.

Although a unifrom local average may seem to give a good blurring model, it generates effects not usually seen in defocusing a lens.

The uniform average produces a set of narrow vertical and horizontal bars--an effect often known as ringing.

Replacing each pixel with an unweighted average computed over some fixed region centred at the pixel is the same as convolution with a kernel that is a block of ones multiplied by a constant.