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Concepts of Binary Morphological Operations Dilation and Erosion on the Triangular Grid

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Computational Modeling of Objects Presented in Images. Fundamentals, Methods, and Applications (CompIMAGE 2016)

Part of the book series: Lecture Notes in Computer Science ((LNIP,volume 10149))

Abstract

In this paper, basic concepts of digital binary morphological operations, i.e., dilation and erosion are investigated on a triangular grid. Every triangle pixel is addressed by a unique coordinate triplet with sum zero (even pixels) or one (odd pixels). Even and odd pixels have different orientations. The triangular grid is not a lattice, that is, not every translation with a grid vector maps the grid to itself. Therefore, to extend the morphological operations to the triangular grid is not straightforward. We introduce three types of definition for both of dilation and erosion. Various examples and properties of the considered dilation and erosion are analyzed on the triangular grid.

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Authors and Affiliations

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

    Mohsen Abdalla & Benedek Nagy

Authors
  1. Mohsen Abdalla
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  2. Benedek Nagy
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Corresponding author

Correspondence to Benedek Nagy .

Editor information

Editors and Affiliations

  1. State University of New York at Fredonia , Fredonia, New York, USA

    Reneta P. Barneva

  2. State University of New York , Buffalo, New York, USA

    Valentin E. Brimkov

  3. Universidade do Porto , Porto, Portugal

    João Manuel R.S. Tavares

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Abdalla, M., Nagy, B. (2017). Concepts of Binary Morphological Operations Dilation and Erosion on the Triangular Grid. In: Barneva, R., Brimkov, V., Tavares, J. (eds) Computational Modeling of Objects Presented in Images. Fundamentals, Methods, and Applications. CompIMAGE 2016. Lecture Notes in Computer Science(), vol 10149. Springer, Cham. https://doi.org/10.1007/978-3-319-54609-4_7

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  • DOI: https://doi.org/10.1007/978-3-319-54609-4_7

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-54608-7

  • Online ISBN: 978-3-319-54609-4

  • eBook Packages: Computer ScienceComputer Science (R0)

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