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Geometrical and Statistical Properties of the Rational Order Pyramid Transform and Dilation Filtering

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Computer Analysis of Images and Patterns (CAIP 2019)

Part of the book series: Lecture Notes in Computer Science ((LNIP,volume 11679))

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Abstract

The pyramid transform of rational orders is described using matrix transform. This matrix expression of the rational order pyramid transform clarifies the eigenspace properties of the transform. The matrix-based expression, however, derives orthogonal base in each resolution. This orthogonal property of base of signals derive a unified computation of linear transformation to images any rational resolutions. Furthermore, the eigenspace property allows us to define the rational pyramid transform families using the discrete cosine transform. Numerical evaluation of the transform clarifies that rational order pyramid transform preserves the normalised distribution of grey-scale in images.

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Author information

Authors and Affiliations

  1. School of Science and Engineering, Chiba University, Yayoi-cho 1-33, Inage-ku, Chiba, 263-8522, Japan

    Kento Hosoya & Kouki Nozawa

  2. Institute of Management and Information Technologies, Chiba University, Yayoi-cho 1-33, Inage-ku, Chiba, 263-8522, Japan

    Atsushi Imiya

Authors
  1. Kento Hosoya
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  2. Kouki Nozawa
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  3. Atsushi Imiya
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Corresponding author

Correspondence to Atsushi Imiya .

Editor information

Editors and Affiliations

  1. Department of Computer and Electrical Engineering and Applied Mathematics, University of Salerno, Fisciano (SA), Italy

    Mario Vento

  2. Department of Computer and Electrical Engineering and Applied Mathematics, University of Salerno, Fisciano (SA), Italy

    Gennaro Percannella

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Hosoya, K., Nozawa, K., Imiya, A. (2019). Geometrical and Statistical Properties of the Rational Order Pyramid Transform and Dilation Filtering. In: Vento, M., Percannella, G. (eds) Computer Analysis of Images and Patterns. CAIP 2019. Lecture Notes in Computer Science(), vol 11679. Springer, Cham. https://doi.org/10.1007/978-3-030-29891-3_14

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  • DOI: https://doi.org/10.1007/978-3-030-29891-3_14

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-29890-6

  • Online ISBN: 978-3-030-29891-3

  • eBook Packages: Computer ScienceComputer Science (R0)

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