3D DIGITAL-TOPOLOGY UNDER BINARY TRANSFORMATION WITH APPLICATIONS

In this paper we study 3D digital topology under the transformation of an object point to a nonobject point and vice versa. As a result of s uch a transformation, an object component in the 3 x 3 x 3 neighborhoo d of the affected point may vanish or split into two or more component s or more than one object components may merge into one. Also, cavitie s or tunnels in the 3 x 3 x 3 neighborhood may be destroyed or created . One of the goals of this paper is to develop an efficient algorithm (topo_para) to compute the change in the numbers of object components, tunnels and cavities in the 3 x 3 x 3 neighborhood of the transformed point. Another important contribution is the classification of differ ent types of points (e.g., are inner point, are edge point, surface in ner point, surface edge point) and detection of different types of jun ction points (e.g., junction between arcs, junction between surfaces a nd arcs, junction between surfaces) on the surface skeleton representa tion of a 3D digital image. Using these junction points it is possible to segment a 3D digital surface topologically into meaningful parts. Also, we describe an efficient algorithm for computing the Euler numbe r of a 3D digital image using the topological parameters computed by t ogo_para. (C) 1996 Academic Press, Inc.