When doing quadrat counting, how do you construct the quadrats?

Question

I want to perform quadrat count analysis on several point processes (or one marked point process), to then apply some dimensionality reduction techniques.

The marks are not identically distributed, i.e. some marks are appearing quite often, and some are pretty rare. Thus, I cannot simply divide my 2D space in a regular grid, because the more frequent marks will "overwhelm" the lesser frequent ones, masking their appearance.

Thus, I tried to build my grid such that each cell has at most N points in it (to do so, I simply divide each cell in four smaller (and equally sized) cells, recursively, until no cell has more than N points in it).

What do you think of this "normalization" technique ? Is there a standard way to do such things ?

Answer 1

I have used quadrat analysis only on regular grids. It was helpful in regards to the purpose which was to compare the dispersion of sampling data with a known process e.g., random. Therefore regular grid worked well.
The method you developed and described not sure to be quadrat counting. For example in moving average method one option is to count number of neighbors for the process i.e., averaging which is simply done by searching within a circle (in 2D) or sphere (in 3D). Your method looks similar so with a slightly different use of those selected samples.