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Fourfold Symmetry Detection in Digital Images Based on Finite Gaussian Fields

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Proceedings of the First International Scientific Conference “Intelligent Information Technologies for Industry” (IITI’16)

Part of the book series: Advances in Intelligent Systems and Computing ((AISC,volume 451))

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Abstract

This paper considers an algebraic method for symmetry analysis of digital images, based on the interpretation of such images as functions on “Gaussian fields”. These are finite fields \( {{\mathbb{G}}{\mathbb{F}}}(p^{2} ) \) of special characteristics \( p = 4k + 3 \), where \( k > 0 \) is an integer. It is shown that such fields may be considered as “finite complex planes” and some properties of such fields are studied. The concept of logarithm in Gaussian fields is introduced and used to define a “log-polar”-representation of digital images. Next, an algorithm for fourfold rotational symmetry detection in gray-level images is proposed.

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Acknowledgements

This research has been partially supported by the Russian Foundation for Basic Research grant no. 16-07-00648.

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Authors and Affiliations

  1. Southern Federal University, 105/42, Bolshaya Sadovaya, 344006, Rostov-na-Donu, Russia

    Alexander Karkishchenko & Valeriy Mnukhin

Authors
  1. Alexander Karkishchenko
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  2. Valeriy Mnukhin
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Corresponding author

Correspondence to Valeriy Mnukhin .

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Editors and Affiliations

  1. Sci N/w for Innova and Research Exc, Machine Intelligence Research Labs, Auburn, Washington, USA

    Ajith Abraham

  2. Rostov State Transport University, Rostov-on-Don, Russia

    Sergey Kovalev

  3. Bauman Moscow State Technical University, Moscow, Russia

    Valery Tarassov

  4. Institute of Mathematics, VŠB-Technical University of Ostrava, Ostrava, Czech Republic

    Václav Snášel

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Karkishchenko, A., Mnukhin, V. (2016). Fourfold Symmetry Detection in Digital Images Based on Finite Gaussian Fields. In: Abraham, A., Kovalev, S., Tarassov, V., Snášel, V. (eds) Proceedings of the First International Scientific Conference “Intelligent Information Technologies for Industry” (IITI’16). Advances in Intelligent Systems and Computing, vol 451. Springer, Cham. https://doi.org/10.1007/978-3-319-33816-3_16

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  • DOI: https://doi.org/10.1007/978-3-319-33816-3_16

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-33815-6

  • Online ISBN: 978-3-319-33816-3

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