Topology preservation in 3D digital space

摘要

In a 3D two-tone digital space, the conditions under which sequential transformation of an object point to a non-object point, or its inverse, does not affect the image topology are investigated. The concept of border-connectivity is introduced and an efficient algorithm for checking a simple point is proposed. In this connection, some other interesting properties of 3D digital geometry are also discussed. This investigation may be used in thinning and topology preserving morphological transformations in 3D digital space.