Topological skeleton matching techniques
I think you should look/google in the direction of graph matching. 

This is because you can represent your skeleton as a graph by creating nodes at endpoints and crossings, and creating edges for the connected endpoints and crossings. There is much more research done in the direction of graph matching than just topological skeleton matching. However for the latter I found this paper, which you might find interesting.

You can also look through the references of the Wikipedia page of Topological skeletonization, there are also some references about matching skeletons.