Abstract
Abstract cell complexes (ACC’ s)were introduced by Ko- valevsky as a means of solving certain connectivity paradoxes in graph- theoretic digital topology,and to this extent provide an improved the- oretical basis for image analysis. We argue that ACC’s are a very nat- ural setting for digital convexity,to the extent that their use permits simple,almost trivial formulations of major convexity results such as Caratheodory’s, Helly’s and Radon’s theorems. ACC’s also permit the use in digital geometry of axiomaticcombinatorial geometries such as oriented matroids. We give a brief indication of how standard convex- ity algorithms from computational eometry applied to the points of an ACC can form a substantial part of digital convexity algorithms.
This work has been supported by the EPSRC project “Digital Topology and Geometry: an AxiomaticApproach with Applications to GIS and Spatial Reasoning.”
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Webster, J. (2001). Cell Complexes and Digital Convexity. In: Bertrand, G., Imiya, A., Klette, R. (eds) Digital and Image Geometry. Lecture Notes in Computer Science, vol 2243. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45576-0_16
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DOI: https://doi.org/10.1007/3-540-45576-0_16
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