matlab - Why should the size of the kernel be odd?

Question

When using the mean filter in image processing, why should the size of the kernel be odd? It Always takes a odd size as 3x3 or 5x5. Could anyone explain it with reasons?

Answer 1

The kernel doesn't need to be odd. It's perfectly possible to define an even-sized kernel. When the kernel size is even, it is less obvious which of the pixels should be at the origin, but this is not a problem. You have seen mostly odd-sized filter kernels because they are symmetric around the origin, which is a good property.

Here is an example in MATLAB where we filter the image with a 4x4 averaging kernel (mean filter):

img = imread('cameraman.tif');
img = imfilter(img,fspecial('average',4));
imshow(img)