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Landmark-Constrained Statistical Shape Analysis of Elastic Curves and Surfaces

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New Advances in Statistics and Data Science

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Abstract

We present a framework for landmark-constrained elastic shape analysis of curves and surfaces. While most of statistical shape analysis focuses on either landmark-based or curve-based representations, we describe a new approach that is able to unify them. The described method has its roots in elastic shape analysis, where elastic metrics are used for comparisons and statistical analysis of shapes. The landmark information is incorporated into the shape representation via hard constraints in the re-parameterization group. We use the square-root velocity function representation for curves and square-root normal field representation for surfaces to greatly simplify the implementation of these methods. We give multiple complex examples from graphics and computer vision, wherein the landmark-constrained shape analysis framework is able to provide natural deformations between shapes as well as representative summaries, including the average and principal directions of variability, of samples of shapes.

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Notes

  1. 1.

    http://www.dabi.temple.edu/~shape/MPEG7/dataset.html.

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Acknowledgements

We would like to thank Dr. Hamid Laga (Murdoch University) for providing the spherically parameterized meshes for the TOSCA and SHREC 2007 datasets. This research was partially supported by NSF DMS 1613054 (SK).

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Authors and Affiliations

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

    Justin Strait & Sebastian Kurtek

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  1. Justin Strait
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  2. Sebastian Kurtek
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Correspondence to Justin Strait .

Editor information

Editors and Affiliations

  1. University of North Carolina, Chapel Hill, North Carolina, USA

    Ding-Geng Chen

  2. Columbia University, New York, New York, USA

    Zhezhen Jin

  3. University of California, Los Angeles, California, USA

    Gang Li

  4. University of Michigan-Ann Arbor, Ann Arbor, Michigan, USA

    Yi Li

  5. National Institutes of Health, Bethesda, Maryland, USA

    Aiyi Liu

  6. Georgia State University, Atlanta, Georgia, USA

    Yichuan Zhao

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Strait, J., Kurtek, S. (2017). Landmark-Constrained Statistical Shape Analysis of Elastic Curves and Surfaces. In: Chen, DG., Jin, Z., Li, G., Li, Y., Liu, A., Zhao, Y. (eds) New Advances in Statistics and Data Science. ICSA Book Series in Statistics. Springer, Cham. https://doi.org/10.1007/978-3-319-69416-0_12

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