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The Reed-Muller-Fourier Transform Applied to Pattern Analysis

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Computer Aided Systems Theory – EUROCAST 2017 (EUROCAST 2017)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 10672))

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Abstract

This paper introduces the analysis of pattern properties by means of the two-sided Reed-Muller-Fourier transform. Patterns are modelled as matrices of pixels and an integer coding for the colors is chosen. Work is done in the ring \((Z_{p},\oplus , \cdot )\), where \(p >2\) is not necessarily a prime. It is shown that the transform preserves the (diagonal) symmetry of patterns, is compatible with different operations on patterns, and allows detecting and localizing noise pixels in a pattern. Finally, it is shown that there are patterns which are fixed points of the transform.

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References

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Authors and Affiliations

  1. Faculty of Computer Science, TU Dortmund University, 44221, Dortmund, Germany

    Claudio Moraga

  2. Department of Computer Science, Faculty of Electronic Engineering, University of Niš, 18000, Niš, Serbia

    Radomir S. Stanković

Authors
  1. Claudio Moraga
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  2. Radomir S. Stanković
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Correspondence to Claudio Moraga .

Editor information

Editors and Affiliations

  1. University of Las Palmas de Gran Canaria, Las Palmas de Gran Canaria, Spain

    Roberto Moreno-Díaz

  2. Johannes Kepler University Linz, Linz, Austria

    Franz Pichler

  3. University of Las Palmas de Gran Canaria, Las Palmas de Gran Canaria, Spain

    Alexis Quesada-Arencibia

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Moraga, C., Stanković, R.S. (2018). The Reed-Muller-Fourier Transform Applied to Pattern Analysis. In: Moreno-Díaz, R., Pichler, F., Quesada-Arencibia, A. (eds) Computer Aided Systems Theory – EUROCAST 2017. EUROCAST 2017. Lecture Notes in Computer Science(), vol 10672. Springer, Cham. https://doi.org/10.1007/978-3-319-74727-9_30

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  • DOI: https://doi.org/10.1007/978-3-319-74727-9_30

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-74726-2

  • Online ISBN: 978-3-319-74727-9

  • eBook Packages: Computer ScienceComputer Science (R0)

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