I want to perform the following operation on an image: consider a square window around every pixel, find the maximum value in this window, and replace the central pixel value with this maximum value. If I consider a $n \times n$ square window around every pixel, this becomes the morphological dilation operation (with a square $n \times n$ structuring element).
In my work I need to have windows of different sizes around every pixel, i.e. I might need a $n \times n$ window around pixel $A$ and a $m \times m$ window around pixel $B$.
(1) Does this operation have a name? Is it widely used?
(2) Do you know of any fast algorithm to perform this operation?
Relevant info: For fixed window sizes, there does exist a fast algorithm, for example Algorithm 1 in the following paper (which in fact requires just a constant number of operations per pixel, regardless of window size):
Chaudhury, K. N. "Acceleration of the Shiftable O(1) Algorithm for Bilateral Filtering and Nonlocal Means." IEEE Transactions on image processing, 22.4 (2013): 1291-1300.