Topology-preserving hexagonal thinning

Thinning is a well-known technique for producing skeleton-like shape features from digital binary objects in a topology-preserving way. Most of the existing thinning algorithms work on input images that are sampled on orthogonal grids; however, it is also possible to perform thinning on hexagonal grids (or triangular lattices). In this paper, we point out to the main similarities and differences between the topological properties of these two types of sampling schemes. We give various characterizations of simple points and present some new sufficient conditions for topology-preserving reductions working on hexagonal grids.