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Brouwer–Lebesgue Tiling Theorem and Nerve Complexes That Cover Surface Shapes

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Book cover Computational Geometry, Topology and Physics of Digital Images with Applications

Part of the book series: Intelligent Systems Reference Library ((ISRL,volume 162))

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Abstract

This chapter takes a look at the Alexandroff version of the Brouwer–Lebesgue tiling theorem and introduces systems of nerve complexes that have proximity to each other and which are known shapes that cover all or part of the interior of unknown surface shapes in visual scenes.

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Notes

  1. 1.

    This sample shape is produced using the Mathematica script from https://www.mathematica.stackexchange.com/questions/23546/.

  2. 2.

    Many thanks for Arjuna P. H. Don for this photo.

  3. 3.

    Many thanks to Sheela Ramanna for contributing this picture.

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Authors and Affiliations

  1. Department of Electrical and Computer Engineering, Engineering and Information Technology Complex, University of Manitoba, Winnipeg, MB, Canada

    James F. Peters

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  1. James F. Peters
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Correspondence to James F. Peters .

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Peters, J.F. (2020). Brouwer–Lebesgue Tiling Theorem and Nerve Complexes That Cover Surface Shapes. In: Computational Geometry, Topology and Physics of Digital Images with Applications. Intelligent Systems Reference Library, vol 162. Springer, Cham. https://doi.org/10.1007/978-3-030-22192-8_8

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