A Convenient Graph Connectedness for Digital Imagery

摘要

In a simple undirected graph, we introduce a special connectedness induced by a set of paths of length 2. We focus on the 8-adjacency graph (with the vertex set Z~2) and study the connectedness induced by a certain set of paths of length 2 in the graph. For this connectedness, we prove a digital Jordan curve theorem by determining the Jordan curves, i.e., the circles in the graph that separate Z~2 into exactly two connected components. These Jordan curves are shown to have an advantage over those given by the Khalimsky topology on Z~2.