Recognition of Surfaces in Three-Dimensional Digital Images

This is a continuation of a series of papers on the digital geometry of three-dimensional images. In an earlier paper by Morgenthaler and Rosenfeld, a three-dimensional analog of the two-dimensional Jordan curve theorem was established. This was accomplished by defining simple surface points under the symmetric consideration of 6-connectedness and 26-connectedness and by characterizing a simple closed surface as a connected collection of “orientable” simple surface points. The necessity of the assumption of orientability, a condition of often prohibitive computational cost to establish, was the major unresolved issue of that paper. In this paper, the assumption is shown not to be necessary in the case of 6-connectedness and, unexpectedly, it is shown that the property of orientability is not symmetric with respect to the two types of connectedness.