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Elastic Shape Analysis of Boundaries of Planar Objects with Multiple Components and Arbitrary Topologies

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Computer Vision -- ACCV 2014 (ACCV 2014)

Part of the book series: Lecture Notes in Computer Science ((LNIP,volume 9004))

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Abstract

We consider boundaries of planar objects as level set distance functions and present a Riemannian metric for their comparison and analysis. The metric is based on a parameterization-invariant framework for shape analysis of quadrilateral surfaces. Most previous Riemannian formulations of 2D shape analysis are restricted to curves that can be parameterized with a single parameter domain. However, 2D shapes may contain multiple connected components and many internal details that cannot be captured with such parameterizations. In this paper we propose to register planar curves of arbitrary topologies by utilizing the re-parameterization group of quadrilateral surfaces. The criterion used for computing this registration is a proper distance, which can be used to quantify differences between the level set functions and is especially useful in classification. We demonstrate this framework with multiple examples using toy curves, medical imaging data, subsets of the TOSCA data set, 2D hand-drawn sketches, and a 2D version of the SHREC07 data set. We demonstrate that our method outperforms the state-of-the-art in the classification of 2D sketches and performs well compared to other state-of-the-art methods on complex planar shapes.

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Acknowledgement

This work is partially funded by the Australian Research Council (ARC) and the South Australian Government, Department of Further Education, Employment, Science and Technology.

Author information

Authors and Affiliations

  1. Department of Statistics, The Ohio State University, Columbus, USA

    Sebastian Kurtek

  2. Phenomics and Bioinformatics Research Centre, University of South Australia, Adelaide, Australia

    Hamid Laga

  3. Australian Centre for Plant Functional Genomics, PtyLtd, Adelaide, Australia

    Hamid Laga

  4. Department of Statistics, Florida State University, Tallahassee, Florida

    Qian Xie

Authors
  1. Sebastian Kurtek
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  2. Hamid Laga
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  3. Qian Xie
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Corresponding author

Correspondence to Hamid Laga .

Editor information

Editors and Affiliations

  1. Technische Universität München, Garching, Bayern, Germany

    Daniel Cremers

  2. University of Adelaide, Adelaide, South Australia, Australia

    Ian Reid

  3. Keio University, Yokohama, Kanagawa, Japan

    Hideo Saito

  4. University of California at Merced, Merced, California, USA

    Ming-Hsuan Yang

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Kurtek, S., Laga, H., Xie, Q. (2015). Elastic Shape Analysis of Boundaries of Planar Objects with Multiple Components and Arbitrary Topologies. In: Cremers, D., Reid, I., Saito, H., Yang, MH. (eds) Computer Vision -- ACCV 2014. ACCV 2014. Lecture Notes in Computer Science(), vol 9004. Springer, Cham. https://doi.org/10.1007/978-3-319-16808-1_29

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  • DOI: https://doi.org/10.1007/978-3-319-16808-1_29

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-16807-4

  • Online ISBN: 978-3-319-16808-1

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