Combinatorial boundary of a 3D lattice point set

Boundary extraction and surface generation are important topological topics for three-dimensional digital image analysis. However, there is no adequate theory to establish relations between these different topological procedures in a completely discrete way. In this paper, we present a new boundary extraction algorithm which gives not only a set of border points but also a polyhedral surface whose vertices are border points by using the concepts of combinatorial/algebraic topologies. We show that our boundary can be considered to be a triangulation or polyhedrization of border points in the sense of general topology, that is, we clarify relations between border points and the triangulated surface.