Many computer vision algorithms allow the programmer to choose an arbitrary neighborhood. Such algorithms typically create a new image by calculating each new pixel value as a function of not only the corresponding old pixel value, but also its neighboring old pixel values. The neighborhood around a pixel is also often called a "window" or "peephole" around that pixel. The non-zero entries in a "convolution kernel" form one kind of neighborhood. A morphological structuring element is another kind of neighborhood.
"Square Neighbourhoods" (3 by 3, 5 by 5) are often used, but circular neighbourhoods are used too.
Pixels in neighbourhoods are often numbered in a anticlockwise spiral, with 0 at the center.