Geometry of neighbourhood sequences

摘要

In this paper we generalize some former results of Das and Chatterji [Inform. Sci. 50 (1990) 123] about geometric properties of two-dimensional periodic neighbourhood sequences. We use a more general definition of neighbourhood sequences, which does not require periodicity. As an extension of the former 2D results, we study the geometric behavior of general neighbourhood sequences in arbitrary finite dimension. Since 2D and 3D digital spaces are the most important in digital geometry and in digital image processing, we study these spaces in detail.