Optimiziation of overlapping 2D-point-patterns

A brief overview of what already exists:

I have a set of hundreds or thousands of 2D-points (x and y) where i should find all occurences of a given pattern. The pattern is also a set of 2D-points (x and y), but significant smaller. The first set is called "point-cloud" and the second just "pattern".

Again, to clarify: I really need to find all occurences/matchings, even if it is just rotated or covers the same points that are already included in another matching. In a big set of points there are thousands or even millions of matchings that can be found.

I have already a working solution / algorithm for this - it work fine.

Where is the problem / challenge now?

I now have to find/filter out a set of matchings that perfectly fits the point-cloud - ideally without overlapping. The result should be a (nearly complete) covered point-cloud.

Does someone know interesting research-area, that focus on this problem? Is it even solvable at the moment (without an unrealistic amount of calculation power)? Are there papers covering this problem? Or maybe a heuristic that delivers "good" results?