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On the Computation of the Euler Characteristic of Binary Images in the Triangular Grid

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Computer Analysis of Images and Patterns (CAIP 2019)

Part of the book series: Lecture Notes in Computer Science ((LNIP,volume 11679))

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Abstract

Apart from the widely used square grid, other regular grids (hexagonal and triangular) are gaining prominence in topological data analysis and image analysis/processing communities. One basic but important integer-valued topological descriptor of binary images in these grids is the Euler characteristic.

We extend two algorithms for the computation of the Euler characteristic from the square to the triangular grid, taking into account specific properties of the triangular grid. The first algorithm is based on simple cell counting, and the second is based on critical point approach. Both algorithms iterate over the grid vertices. We extend also their improvement based on reusing information common to the previous and the next vertex in the scan order. Our experiments show that the critical point based algorithms outperform the naive cell-counting ones, with the improved versions reducing the average runtime further.

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Acknowledgement

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 & Andrija Blesić

Authors
  1. Lidija Čomić
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  2. Andrija Blesić
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Correspondence to Andrija Blesić .

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Editors and Affiliations

  1. Department of Computer and Electrical Engineering and Applied Mathematics, University of Salerno, Fisciano (SA), Italy

    Mario Vento

  2. Department of Computer and Electrical Engineering and Applied Mathematics, University of Salerno, Fisciano (SA), Italy

    Gennaro Percannella

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Čomić, L., Blesić, A. (2019). On the Computation of the Euler Characteristic of Binary Images in the Triangular Grid. In: Vento, M., Percannella, G. (eds) Computer Analysis of Images and Patterns. CAIP 2019. Lecture Notes in Computer Science(), vol 11679. Springer, Cham. https://doi.org/10.1007/978-3-030-29891-3_49

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  • DOI: https://doi.org/10.1007/978-3-030-29891-3_49

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-29890-6

  • Online ISBN: 978-3-030-29891-3

  • eBook Packages: Computer ScienceComputer Science (R0)

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