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Digital Geometry Algorithms pp 215–243Cite as

Separability and Tight Enclosure of Point Sets

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Part of the book series: Lecture Notes in Computational Vision and Biomechanics ((LNCVB,volume 2))

Abstract

In this chapter we focus on the separation and enclosure of finite sets of points. When a surface separates or encloses a point set as tightly as possible, it will touch the set in a small number of points. The results in this chapter center on how the surfaces touch the set, and on the side of a surface at which a point lies. The subject is closely related to theory of oriented matroids, where oriented matroids are used to describe hyperplane arrangements, but there are some differences in focus, as well. Oriented matroids are very useful to prove that an abstract configuration of lines and points can or cannot be realized in real space. In digital geometry, however, the realization is given, for example, as a set of edge points in a digital image. The emphasis is on finding models that explain how the digitized points and lines could arise. We give a general overview of the use of preimages (or domains) and elemental subsets in digital geometry and we also present some new results on the relation between elemental subsets and separability.

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Authors and Affiliations

  1. Ghent University, Schoonmeersstraat 52, 9000, Ghent, Belgium

    Peter Veelaert

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  1. Peter Veelaert
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Correspondence to Peter Veelaert .

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Editors and Affiliations

  1. Buffalo State College, Department of Mathematics, State University of New York, Elmwood Avenue 1300, Buffalo, 14222, New York, USA

    Valentin E. Brimkov

  2. Department of Computer Science, State University of New York at Fredonia, Central Ave. 280, Fredonia, 14063, New York, USA

    Reneta P. Barneva

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Veelaert, P. (2012). Separability and Tight Enclosure of Point Sets. In: Brimkov, V., Barneva, R. (eds) Digital Geometry Algorithms. Lecture Notes in Computational Vision and Biomechanics, vol 2. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-4174-4_8

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  • DOI: https://doi.org/10.1007/978-94-007-4174-4_8

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-94-007-4173-7

  • Online ISBN: 978-94-007-4174-4

  • eBook Packages: EngineeringEngineering (R0)

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