Point spaces and raster spaces in digital geometry and topology

Li Chen

doi:10.1117/12.323251

2 October 1998 Point spaces and raster spaces in digital geometry and topology

Li Chen

Proceedings Volume 3454, Vision Geometry VII; (1998) https://doi.org/10.1117/12.323251
Event: SPIE's International Symposium on Optical Science, Engineering, and Instrumentation, 1998, San Diego, CA, United States

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.

Citation Download Citation

Li Chen "Point spaces and raster spaces in digital geometry and topology", Proc. SPIE 3454, Vision Geometry VII, (2 October 1998); https://doi.org/10.1117/12.323251

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