Classification of simple surface points and a global theorem for simple closed surfaces in three-dimensional digital spaces

摘要

Abstract: In this paper, we present two theorems: classification theorem and corner point theorem for closed digital surfaces. The classification theorem deals with the categorization of simple surface points and states that there are exactly six different types of simple surface points. On the basis of the classification theorem and Euler formula on planar graph, we have proved the corner point theorem: Any simple closed surface has at least eight corner points, where a corner point of a closed surface is a point in the surface which has exactly three adjacent points in the closed surface. Another result reported in this paper is that any simple closed surface has at least fourteen points. !12