Characterization of Simple Closed Surfaces in Z3: A New Proposition with a Graph-Theoretical Approach

In the present paper, we propose a topological characterization of digital surfaces. We introduce simple local conditions on the neighborhood of a voxel. If each voxel of a 26-connected digital set satisfies them, we prove a Jordan theorem and ensure that this set is strong 6-separating in Z3. Thus, we consider it as a digital surface.