Thinning on cell complexes from polygonal tilings

This paper provides a theoretical foundation of a thinning method due to Kovalevsky for 2D digital binary images modelled by cell complexes or, equivalently, by Alexandroff T0T0 topological spaces, whenever these are constructed from polygonal tilings. We analyze the relation between local and global simplicity of cells, and prove their equivalence under certain conditions. For the proof we apply a digital Jordan theorem due to Neumann–Lara/Wilson which is valid in any connected planar locally Hamiltonian graph. Therefore we first prove that the incidence graph of the cell complex constructed from any polygonal tiling has these properties, showing that it is a triangulation of the plane. Moreover, we prove that the parallel performance of Kovalevsky’s thinning method preserves topology in the sense that the numbers of connected components, for both the object and of the background, remain the same.