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. !16
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