The equivalence between two definitions of digital surfaces

Digital surfaces deal with properties of surfaces in digital spaces. In the early 80's, researchers began to establish definitions for digital surfaces. Unlike surfaces in continuous spaces, digital surfaces have different characteristics. A general and intuitive definition for digital surfaces is still an open problem. This paper presents a proof of the equivalence of two digital surface definitions. One of the definitions was developed based on simple surface points given by Morgenthaler and Rosenfeld [1], and the second uses a parallel-move concept as given by direct adjacency [2,3]. A by-product of this proof of equivalence is that any simple surface point in a simple surface belongs to one of six types of simple surface points. (C) 1999 Elsevier Science Inc. All rights reserved.