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A Combinatorial 4-Coordinate System for the Diamond Grid

  • Conference paper
Mathematical Morphology and Its Applications to Signal and Image Processing (ISMM 2015)

Part of the book series: Lecture Notes in Computer Science ((LNIP,volume 9082))

Abstract

A new combinatorial coordinate system for cells in the diamond grid is presented, and some of its properties are detailed. Four dependent coordinates are used to address the voxels (triakis truncated tetrahedra), their faces (hexagons and triangles), their edges and the points at their corners. The incidence (boundary and co-boundary) and adjacency relations of the cells can easily be captured by these coordinate values. Therefore, the new coordinate system can effectively by applied in morphological and topological operations.

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Author information

Authors and Affiliations

  1. Department of Fundamental Sciences, Faculty of Technical Sciences, University of Novi Sad, Serbia, Novi Sad

    Lidija Čomić

  2. Department of Mathematics, Faculty of Arts and Sciences, Eastern Mediterranean University, Mersin-10, Famagusta, North Cyprus, Turkey

    Benedek Nagy

  3. Department of Computer Science, Faculty of Informatics, University of Debrecen, Debrecen, Hungary

    Benedek Nagy

Authors
  1. Lidija Čomić
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  2. Benedek Nagy
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Corresponding author

Correspondence to Lidija Čomić .

Editor information

Editors and Affiliations

  1. University of Iceland, Reykjavik, Iceland

    Jón Atli Benediktsson

  2. Université de Grenoble Alpes, Grenoble, France

    Jocelyn Chanussot

  3. ESIEE Paris, Noisy-le-Grand Cedex, France

    Laurent Najman

  4. ESIEE Paris, Noisy-le-Grand Cedex, France

    Hugues Talbot

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© 2015 Springer International Publishing Switzerland

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Čomić, L., Nagy, B. (2015). A Combinatorial 4-Coordinate System for the Diamond Grid. In: Benediktsson, J., Chanussot, J., Najman, L., Talbot, H. (eds) Mathematical Morphology and Its Applications to Signal and Image Processing. ISMM 2015. Lecture Notes in Computer Science(), vol 9082. Springer, Cham. https://doi.org/10.1007/978-3-319-18720-4_49

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  • DOI: https://doi.org/10.1007/978-3-319-18720-4_49

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-18719-8

  • Online ISBN: 978-3-319-18720-4

  • eBook Packages: Computer ScienceComputer Science (R0)

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