Partial polygon matching

Question

I am looking for fast procedures for polygon matching, i.e. checking polygon similarity under different transforms

• translation only,
• translation + rotation,
• translation + scaling,
• translation + rotation + scaling (= similarity).

The matching can be partial, meaning that there can be a good match on a significant fraction of the outline (say > 70%), and complete mismatch elsewhere.

The number of vertices is reasonable (say N<50).

In a variant of the problem, you need to compare two polygons. In another variant, you compare one polygon to a series of polygons, with preprocessing of the single polygon allowed. In a third variant, preprocessing is allowed on all polygons.

Are you aware of solutions to this problem ?