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Provably Scale-Covariant Networks from Oriented Quasi Quadrature Measures in Cascade

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Scale Space and Variational Methods in Computer Vision (SSVM 2019)

Part of the book series: Lecture Notes in Computer Science ((LNIP,volume 11603))

Abstract

This article presents a continuous model for hierarchical networks based on a combination of mathematically derived models of receptive fields and biologically inspired computations. Based on a functional model of complex cells in terms of an oriented quasi quadrature combination of first- and second-order directional Gaussian derivatives, we couple such primitive computations in cascade over combinatorial expansions over image orientations. Scale-space properties of the computational primitives are analysed and it is shown that the resulting representation allows for provable scale and rotation covariance. A prototype application to texture analysis is developed and it is demonstrated that a simplified mean-reduced representation of the resulting QuasiQuadNet leads to promising experimental results on three texture datasets.

The support from the Swedish Research Council (contract 2018-03586) is gratefully acknowledged.

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Authors and Affiliations

  1. Computational Brain Science Lab, Division of Computational Science and Technology, KTH Royal Institute of Technology, Stockholm, Sweden

    Tony Lindeberg

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  1. Tony Lindeberg
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Correspondence to Tony Lindeberg .

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Editors and Affiliations

  1. University of Lübeck, Lübeck, Germany

    Jan Lellmann

  2. University of Erlangen-Nuremberg (FAU), Erlangen, Germany

    Martin Burger

  3. University of Lübeck, Lübeck, Germany

    Jan Modersitzki

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Lindeberg, T. (2019). Provably Scale-Covariant Networks from Oriented Quasi Quadrature Measures in Cascade. In: Lellmann, J., Burger, M., Modersitzki, J. (eds) Scale Space and Variational Methods in Computer Vision. SSVM 2019. Lecture Notes in Computer Science(), vol 11603. Springer, Cham. https://doi.org/10.1007/978-3-030-22368-7_26

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  • DOI: https://doi.org/10.1007/978-3-030-22368-7_26

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-22367-0

  • Online ISBN: 978-3-030-22368-7

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