Topology-preserving equivalent parallel and sequential 4-subiteration 2D thinning algorithms

Thinning is a frequently applied technique for extracting centerlines from 2D binary objects. Parallel thinning algorithms can remove a set of object points simultaneously, while sequential algorithms traverse the boundary of objects, and consider the actually visited single point for possible removal. Two thinning algorithms are called equivalent if they produce the same result for each input picture. This paper presents the very first pair of equivalent 2D sequential and parallel subiteration-based thinning algorithms. These algorithms can be implemented directly on a conventional sequential computer or on a parallel computing device. Both of them preserve topology for (8, 4) pictures sampled on the square grid.