Kernel based operations are common in a variety of applications, such as image processing (e.g., blurring), generating smoothed estimation maps, and so on. A common approach is to select four surrounding cells (see the following figure: A the green colored cells) then calculate the average value of them including the value of the central cell to be assigned as the estimate.
Some questions appear to me to have a discussion:
1- I propose two other cell selections i.e., B and C. The question is what kind of statistical justification could help to recommend one of them?
2- Which part of statistical analysis would fit to discuss such conceptual/practical questions?
my understanding is:
Because those cells (green ones in A) are the closest to the central cell (the cell of interest for estimation etc). For case B compared to A it is obvious so B is not a better choice. In comparison between A and C however the case A has a disadvantage, lacking diagonal supports while for case C it covers full orientations. I think the case A is good because of less computation required however with the expense of biases diagonally.
Here is an example implementation of those ideas:
Hope this helps a bit more in understanding the difference brought by applying different kernel averaging configurations.
Applications: A sample application can be found in "After Kernel Averaging" in which type C has been applied.
