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A Novel Line Integral Transform for 2D Affine-Invariant Shape Retrieval

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Computer Vision – ECCV 2020 (ECCV 2020)

Part of the book series: Lecture Notes in Computer Science ((LNIP,volume 12373))

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Abstract

Radon transform is a popular mathematical tool for shape analysis. However, it cannot handle affine deformation. Although its extended version, trace transform, allow us to construct affine invariants, they are less informative and computational expensive due to the loss of spatial relationship between trace lines and the extensive repeated calculation of transform. To address this issue, a novel line integral transform is proposed. We first use binding line pairs that have the desirable property of affine preserving as a reference frame to rewrite the diametrical dimension parameters of the lines in a relative manner which make them independent on affine transform. Along polar angle dimension of the line parameters, a moment-based normalization is then conducted to degrade the affine transform to similarity transform which can be easily normalized by Fourier transform. The proposed transform is not only invariant to affine transform, but also preserves the spatial relationship between line integrals which make it very informative. Another advantage of the proposed transform is that it is more efficient than the trace transform. Conducting it one time can allow us to achieve a 2D matrix of affine invariants. While conducting the trace transform once only generates a single feature and multiple trace transforms of different functionals are needed to derive more to make the descriptors informative. The effectiveness of the proposed transform has been validated on two types of standard shape test cases, affinely distorted contour shape dataset and region shape dataset, respectively.

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Acknowledgement

This work was supported in part by the Australian Research Council (ARC) under Discovery Grant DP140101075 and the Natural Science Foundation of China under Grant 61372158.

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Authors and Affiliations

  1. Griffith University, Nathan, QLD, 4111, Australia

    Bin Wang & Yongsheng Gao

  2. Nanjing University of Finance & Economics, Nanjing, 210023, China

    Bin Wang

Authors
  1. Bin Wang
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  2. Yongsheng Gao
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Correspondence to Bin Wang .

Editor information

Editors and Affiliations

  1. University of Oxford, Oxford, UK

    Andrea Vedaldi

  2. Graz University of Technology, Graz, Austria

    Horst Bischof

  3. University of Freiburg, Freiburg im Breisgau, Germany

    Thomas Brox

  4. University of North Carolina at Chapel Hill, Chapel Hill, NC, USA

    Jan-Michael Frahm

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Wang, B., Gao, Y. (2020). A Novel Line Integral Transform for 2D Affine-Invariant Shape Retrieval. In: Vedaldi, A., Bischof, H., Brox, T., Frahm, JM. (eds) Computer Vision – ECCV 2020. ECCV 2020. Lecture Notes in Computer Science(), vol 12373. Springer, Cham. https://doi.org/10.1007/978-3-030-58604-1_36

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  • DOI: https://doi.org/10.1007/978-3-030-58604-1_36

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-58603-4

  • Online ISBN: 978-3-030-58604-1

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