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Gaps and Well-Composed Objects in the Triangular Grid

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Computational Topology in Image Context (CTIC 2019)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 11382))

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Abstract

We extend the notion of a gap from the square to the triangular grid, and we propose a possible classification of gaps in this grid. We give four definitions of well-composed objects in the triangular grid by translating the existing definitions of such objects in the square grid. We show that these definitions in the triangular grid are equivalent, as they are in the square grid.

We give a formula relating the number of gaps of different types in an object in this grid with the number of boundary cells in the object, as well as three short intuitive proofs of this formula.

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Acknowledgement

We are grateful to the anonymous reviewers for careful reading of the paper and constructive comments. This work has been partially supported by the Ministry of Education and Science of the Republic of Serbia within the Project No. 34014.

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Authors and Affiliations

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

    Lidija Čomić

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  1. Lidija Čomić
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Correspondence to Lidija Čomić .

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Editors and Affiliations

  1. Universidad de Málaga, Málaga, Spain

    Rebeca Marfil

  2. Universidad de Málaga, Málaga, Spain

    Mariletty Calderón

  3. University of Seville, Sevilla, Spain

    Fernando Díaz del Río

  4. University of Seville, Sevilla, Spain

    Pedro Real

  5. Universidad de Málaga, Málaga, Spain

    Antonio Bandera

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Čomić, L. (2019). Gaps and Well-Composed Objects in the Triangular Grid. In: Marfil, R., Calderón, M., Díaz del Río, F., Real, P., Bandera, A. (eds) Computational Topology in Image Context. CTIC 2019. Lecture Notes in Computer Science(), vol 11382. Springer, Cham. https://doi.org/10.1007/978-3-030-10828-1_5

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  • DOI: https://doi.org/10.1007/978-3-030-10828-1_5

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