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International Workshop on Combinatorial Image Analysis

IWCIA 2011: Combinatorial Image Analysis pp 120–131Cite as

A Jordan Curve Theorem in the Digital Plane

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Part of the book series: Lecture Notes in Computer Science ((LNIP,volume 6636))

Abstract

We study a certain Alexandroff topology on ℤ2 and some of its quotient topologies including the Khalimsky one. By proving an analogue of the Jordan curve theorem for this topology we show that it provides a large variety of digital Jordan curves. Some consequences of this result are discussed, too.

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Author information

Authors and Affiliations

  1. Department of Mathematics, Brno University of Technology, 616 69, Brno, Czech Republic

    Josef Slapal

Authors
  1. Josef Slapal
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Editor information

Editors and Affiliations

  1. Department of Electrical and Computer Engineering, The University of Texas, 1 University Station C0803, 78712-0240, Austin, TX, USA

    Jake K. Aggarwal

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

    Reneta P. Barneva

  3. Mathematics Department, SUNY Buffalo State College, 1300 Elmwood Ave., 14222, Buffalo, NY, USA

    Valentin E. Brimkov

  4. Esuela Politécnica Superior, Departamento de Ingenería Informática, Universidad Autónoma de Madrid, c/Tomas y Valiente, 11, 28049, Cantoblanco, Madrid, Spain

    Kostadin N. Koroutchev

  5. Departamento de Física Fundamental, Universidad Nacional de Educación a Distancia, c/ Senda del Rey 9, 28080, Madrid, Spain

    Elka R. Korutcheva

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© 2011 Springer-Verlag Berlin Heidelberg

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Slapal, J. (2011). A Jordan Curve Theorem in the Digital Plane. In: Aggarwal, J.K., Barneva, R.P., Brimkov, V.E., Koroutchev, K.N., Korutcheva, E.R. (eds) Combinatorial Image Analysis. IWCIA 2011. Lecture Notes in Computer Science, vol 6636. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-21073-0_13

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  • DOI: https://doi.org/10.1007/978-3-642-21073-0_13

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-21072-3

  • Online ISBN: 978-3-642-21073-0

  • eBook Packages: Computer ScienceComputer Science (R0)

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