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Computational Symmetry

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Synonyms

Symmetry detection; Symmetry-based X

Footnote 1

Related Concepts

Definition

Symmetry is a mathematical concept as well as a widely used word for describing observed patterns. Formally:

Definition 1

Let S be a proper subset of Rn. Then an isometry (a distance preserving mapping) g is a symmetry of S if and only if g(S) = S.

Computational symmetry is a branch of research using computers to model, analyze, synthesize, and manipulate symmetries in digital form [41].

Background

Symmetry is a pervasive phenomenon presenting itself in all forms and scales, from galaxies to microscopic biological structures, in nature and man-made environments. Much of one’s understanding of the world is based on the perception and recognition of recurring patterns that are generalized by the mathematical concept of symmetries [85, 14, 12]. Humans and animals have an innate ability to perceive and take advantage of symmetry in everyday life [80, 22, 73, 84], while harnessing this...

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Notes

  1. 1.

    Electronic Supplementary Material: The online version of this article (https://doi.org/10.1007/978-3-030-03243-2_640-2) contains supplementary material, which is available to authorized users.

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  1. The Penn State University, University Park, PA, USA

    Yanxi Liu

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Liu, Y. (2021). Computational Symmetry. In: Computer Vision. Springer, Cham. https://doi.org/10.1007/978-3-030-03243-2_640-2

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  • DOI: https://doi.org/10.1007/978-3-030-03243-2_640-2

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Chapter history

  1. Latest

    Computational Symmetry
    Published:
    19 June 2021

    DOI: https://doi.org/10.1007/978-3-030-03243-2_640-2

  2. Original

    Computational Symmetry
    Published:
    24 February 2021

    DOI: https://doi.org/10.1007/978-3-030-03243-2_640-1

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