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International Symposium on Geometry and Vision

ISGV 2021: Geometry and Vision pp 203–218Cite as

Algorithms for Computing Topological Invariants in Digital Spaces

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Part of the book series: Communications in Computer and Information Science ((CCIS,volume 1386))

Abstract

Based on previous results in digital topology, this paper focuses on algorithms related to topological invariants of objects in 2D and 3D Digital Spaces. Specifically, we are interested in hole counting objects in 2D and closed surface genus calculation in 3D. We also present a proof of the hole counting formula in 2D. This paper includes fast algorithms and implementations for topological invariants such as connected components, hole counting in 2D, and boundary surface genus for 3D. For 2D images, we designed a linear time algorithm to solve the hole counting problem. In 3D, we also designed a O(n) time algorithm to obtain the genus of a closed surface. These two algorithms are both in \(O(\log n)\) space complexity.

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Author information

Authors and Affiliations

  1. University of the District of Columbia, Washington, D.C., USA

    Li Chen

Authors
  1. Li Chen
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Correspondence to Li Chen .

Editor information

Editors and Affiliations

  1. Auckland University of Technology, Auckland, New Zealand

    Minh Nguyen

  2. Auckland University of Technology, Auckland, New Zealand

    Wei Qi Yan

  3. Auckland Bioengineering House, Auckland, New Zealand

    Harvey Ho

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Chen, L. (2021). Algorithms for Computing Topological Invariants in Digital Spaces. In: Nguyen, M., Yan, W.Q., Ho, H. (eds) Geometry and Vision. ISGV 2021. Communications in Computer and Information Science, vol 1386. Springer, Cham. https://doi.org/10.1007/978-3-030-72073-5_16

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  • DOI: https://doi.org/10.1007/978-3-030-72073-5_16

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-72072-8

  • Online ISBN: 978-3-030-72073-5

  • eBook Packages: Computer ScienceComputer Science (R0)

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