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On the Number of hv-Convex Discrete Sets

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Combinatorial Image Analysis (IWCIA 2008)

Part of the book series: Lecture Notes in Computer Science ((LNIP,volume 4958))

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Abstract

One of the basic problems in discrete tomography is the reconstruction of discrete sets from few projections. Assuming that the set to be reconstructed fulfills some geometrical properties is a commonly used technique to reduce the number of possibly many different solutions of the same reconstruction problem. The class of hv-convex discrete sets and its subclasses have a well-developed theory. Several reconstruction algorithms as well as some complexity results are known for those classes. The key to achieve polynomial-time reconstruction of an hv-convex discrete set is to have the additional assumption that the set is connected as well. This paper collects several statistics on hv-convex discrete sets, which are of great importance in the analysis of algorithms for reconstructing such kind of discrete sets.

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Authors and Affiliations

  1. Department of Image Processing and Computer Graphics, University of Szeged, Árpád tér 2, H-6720, Szeged, Hungary

    Péter Balázs

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  1. Péter Balázs
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Valentin E. Brimkov Reneta P. Barneva Herbert A. Hauptman

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Balázs, P. (2008). On the Number of hv-Convex Discrete Sets. In: Brimkov, V.E., Barneva, R.P., Hauptman, H.A. (eds) Combinatorial Image Analysis. IWCIA 2008. Lecture Notes in Computer Science, vol 4958. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-78275-9_10

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  • DOI: https://doi.org/10.1007/978-3-540-78275-9_10

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-78274-2

  • Online ISBN: 978-3-540-78275-9

  • eBook Packages: Computer ScienceComputer Science (R0)

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