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Visual Explanation of Deformation Theories in Shape Analysis

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  • Yukari Shirota
  • Takako Hashimoto

Abstract

In the paper we explain the deformation theories in shape analysis. The Geometry Driven Statistics offers a new horizon of the statistical methods. Using a thin-plate interpolation, the given configuration with landmark coordinates is featured by the principal warps which are eigenvectors of the bending energy matrix. In addition, the deformation between two configurations can be described by an affine transformation component and a non-affine transformation. The non-affine transformation can be described by partial warps. Seeing the partial warps help a lot us to understand the features of the deformation. We apply the deformation theories to a tiny economics deformation analysis. The concrete example will be helpful so that economics students can understand the deformation theories. In addition, the way of applying the shape analysis method is explained through the concrete example.

Suggested Citation

  • Yukari Shirota & Takako Hashimoto, 2017. "Visual Explanation of Deformation Theories in Shape Analysis," Gakushuin Economic Papers, Gakushuin University, Faculty of Economics, vol. 54(1), pages 1-12.
    • Handle: RePEc:abc:gakuep:54-1-1
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    File URL: http://www.gakushuin.ac.jp/univ/eco/gakkai/pdf_files/keizai_ronsyuu/contents/contents2017/5401/5401shirota/5401shirota.pdf
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    References listed on IDEAS

    as
    1. Kanti V. Mardia, 2013. "Statistical approaches to three key challenges in protein structural bioinformatics," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 62(3), pages 487-514, May.
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    Cited by:

    1. Catur Apriono & Riti Fitri Sari & Yuriko Yano & Yukari Shirota, 2017. "Economic Indicator Evaluation Based on Shape Deformation Analysis of Indonesian Provinces Statistics," Gakushuin Economic Papers, Gakushuin University, Faculty of Economics, vol. 54(3), pages 185-206.

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