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Proceedings Paper

Point spaces and raster spaces in digital geometry and topology
Author(s): Li Chen
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Paper Abstract

In digital geometry and topology, there are two popular kinds of digital spaces: point spaces and raster spaces. In point-spaces, a digital object is presented by a set of elements. In raster spaces as defined in this note, a digital object is a subset of a 'relation' on the space. In an Euclidean space, given a set S of points which are called sites, we can get the Voronoi diagram of S and its Delaunay triangulation. The Voronoi diagram is just a raster space as well as Delaunay simple decomposition is a point space. Thus, a point space is a dual space of a raster space. This note reviews some research results in point spaces and raster spaces and present the author's opinions on the following problems: how to define digital curves, surfaces, and manifolds in point spaces or raster spaces. What are the difference and relationship between them. What are the advantages and/or disadvantages to use point spaces or raster spaces in practical computation. The purpose of the note is to show a global consideration and to unify some basic concepts in digital geometry and topology.

Paper Details

Date Published: 2 October 1998
PDF: 11 pages
Proc. SPIE 3454, Vision Geometry VII, (2 October 1998); doi: 10.1117/12.323251
Show Author Affiliations
Li Chen, Scientific and Practical Computing and Wuhan Univ. (United States)

Published in SPIE Proceedings Vol. 3454:
Vision Geometry VII
Robert A. Melter; Angela Y. Wu; Longin Jan Latecki, Editor(s)

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