Partial polygon matching

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 ?

There is quite a bit of work on this important problem. Some of the most
insightful work is by Helmut Alt and collaborators. He wrote a survey in 2009:


Helmut Alt. "The computational geometry of comparing shapes." Efficient Algorithms. Springer Berlin Heidelberg, 2009. 235-248.
(Springer link.)

         

Image from Helmut Alt & Leonidas J. Guibas.
"Discrete geometric shapes: Matching, interpolation, and approximation." Handbook of computational geometry 1 (1999): 121-153.).

StackExchange Computer Science Q#51376, answer score: 6