I have a rectangular planar grid, with each cell assigned some integer weight. I am looking for an algorithm to identify clusters of 3 to 6 adjacent cells with higher-than-average weight. These blobs should have approximately circular shape.

For my case the average weight of the cells not containing a cluster is around 6, and that for cells containing a cluster is around 6+4, i.e. there is a "background weight" somewhere around 6. The weights fluctuate with a Poisson statistic.

For small background greedy or seeded algorithms perform pretty well, but this breaks down if my cluster cells have weights close to fluctuations in the background. Also, I cannot do a brute-force search looping through all possible setups because my grid is large (something like 1000x1000). I have the impression there might exist ways to tackle this in graph theory. I heard of vertex-covers and cliques, but am not sure how to best translate my problem into their language.