Digital straight line segments in finite topological spaces

Abstract

By introducing topological structures in a discrete space, the authors are constructing a discrete geometry and are researching its applications in image processing. In this paper, by using only the topological structure of a discrete space, the authors introduce the concept of digital straight line segments. The nature and characteristics of this concept are examined and its relevance demonstrated. It is found that line segments can be defined universally on various spaces and topological structures. It is also possible to characterize and study their individual natures. By using these results, algorithms for generating line segments in many kinds of spaces can be considered and their correctness verified. © 1998 Scripta Technica. Electron Comm Jpn Pt. 3, 81(2): 34–45, 1998