How Sufficient Conditions are Related for Topology-Preserving Reductions

Abstract

A crucial issue in digital topology is to ensure topology preservation for reductions acting on binary pictures (i.e., operators that never change a white point to black one). Some sufficient conditions for topology-preserving reductions have been proposed for pictures on the three possible regular partitionings of the plane (i.e., the triangular, the square, and the hexagonal grids). In this paper, the relationships among these conditions are stated.