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A Convenient Graph Connectedness for Digital Imagery

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High Performance Computing in Science and Engineering (HPCSE 2019)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 12456))

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Abstract

In a simple undirected graph, we introduce a special connectedness induced by a set of paths of length 2. We focus on the 8-adjacency graph (with the vertex set \(\mathbb {Z}^2\)) and study the connectedness induced by a certain set of paths of length 2 in the graph. For this connectedness, we prove a digital Jordan curve theorem by determining the Jordan curves, i.e., the circles in the graph that separate \(\mathbb {Z}^2\) into exactly two connected components. These Jordan curves are shown to have an advantage over those given by the Khalimsky topology on \(\mathbb {Z}^2\).

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Acknowledgement

This work was supported by the Ministry of Education, Youth and Sports of the Czech Republic from the National Programme of Sustainability (NPU II) project IT4Innovations excellence in science - LQ1602.

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Authors and Affiliations

  1. IT4Innovations Centre of Excellence, Brno University of Technology, Brno, Czech Republic

    Josef Šlapal

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  1. Josef Šlapal
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Correspondence to Josef Šlapal .

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Editors and Affiliations

  1. VSB - Technical University of Ostrava, Ostrava-Poruba, Czech Republic

    Tomáš Kozubek

  2. ETH Zurich, Zurich, Switzerland

    Peter Arbenz

  3. Brno University of Technology, Brno, Czech Republic

    Jiří Jaroš

  4. Technical University of Ostrava, Ostrava-Poruba, Czech Republic

    Lubomír Říha

  5. Institute of Mathematics of the CAS, Prague, Czech Republic

    Jakub Šístek

  6. Charles University in Prague, Prague, Czech Republic

    Petr Tichý

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Šlapal, J. (2021). A Convenient Graph Connectedness for Digital Imagery. In: Kozubek, T., Arbenz, P., Jaroš, J., Říha, L., Šístek, J., Tichý, P. (eds) High Performance Computing in Science and Engineering. HPCSE 2019. Lecture Notes in Computer Science(), vol 12456. Springer, Cham. https://doi.org/10.1007/978-3-030-67077-1_9

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  • DOI: https://doi.org/10.1007/978-3-030-67077-1_9

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-67076-4

  • Online ISBN: 978-3-030-67077-1

  • eBook Packages: Computer ScienceComputer Science (R0)

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