Deletion Rules for Equivalent Sequential and Parallel Reductions

Abstract

A reduction operator transforms a binary picture only by changing some black points to white ones, which is referred to as deletion. Sequential reductions may delete just one point at a time, while parallel reductions can alter a set of points simultaneously. Two reductions are called equivalent if they produce the same result for each input picture. This work lays a bridge between the parallel and the sequential strategies. A class of deletion rules are proposed that provide 2D parallel reductions being equivalent to sequential reductions. Some new sufficient conditions for topology-preserving parallel reductions are also reported.