On the topology preservation property of local parallel operations

Abstract

Quasi-preservation of topological structures of binary pictures by a group of parallel local operations is considered. The topology is defined in terms of adjacency among binary components. Parallel local operations treated here are allowed to alter the topology only by deleting simply connected components. They also are required to annihilate all components except for the background. The window for these operations is 2 × 2, and is asymmetric with respect to the point whose value is to be calculated at the next step of operation. The group of operations are obtained by determining the necessary and sufficient conditions for a parallel operation to satisfy the quasi-preservation property thus defined. Some other considerations are also given.