Topology-preserving general operators in arbitrary binary pictures

Abstract

A general operator may transform a binary picture by changing both black and white points. Sequential operators traverse the points of a picture, and consider a single point for possible alteration, while parallel operators can alter a set of points simultaneously. An orderindependent transition function yields the same sequential operator for arbitrary visiting orders. Two operators are called equivalent if they produce the same result for each input picture. A transition function is said to be equivalent if it specifies a pair of equivalent parallel and sequential operators. This paper establishes a necessary and sufficient condition for order-independent transition functions, a sufficient criterion for equivalent transition functions, and a sufficient condition for topologypreserving parallel general operators in arbitrary binary pictures.