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Gaussian-curvature-derived invariants for isometry

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Abstract

Surface deformations without tearing or stretching, preserving the intrinsic properties, are called isometries. This paper presents a new definition of Gaussian curvature moments (GCMs) by the integral of n power of Gaussian curvature. Then a series of moment invariants, called Gaussian curvature moment invariants (GCMIs), are derived via GCMs. These moment invariants share many good properties under rigid transformations and isometric non-rigid transformations, and Gaussian-Bonnet theorem is a special case of GCMI. GCMIs are invariant under isometry and scaling transformations. We construct an invariant vector as a descriptor for a surface via GCMIs, and a modified χ 2 distance is defined as a measure of similarity. Finally, experiments show that it is a reliable descriptor for isometric non-rigid shape.

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Authors and Affiliations

  1. Institute of Computing Technology, Chinese Academy of Sciences, Beijing, 100190, China

    WeiGuo Cao, Ping Hu, Ming Gong & Hua Li

  2. Graduate University of Chinese Academy of Sciences, Beijing, 100190, China

    WeiGuo Cao, Ping Hu, Ming Gong & Hua Li

  3. School of Computer Science and Communication Engineering, China University of Petroleum, Dongying, 257061, China

    YuJie Liu

Authors
  1. WeiGuo Cao
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  2. Ping Hu
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  3. YuJie Liu
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  4. Ming Gong
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  5. Hua Li
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Corresponding authors

Correspondence to WeiGuo Cao or Ping Hu.

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Cao, W., Hu, P., Liu, Y. et al. Gaussian-curvature-derived invariants for isometry. Sci. China Inf. Sci. 56, 1–12 (2013). https://doi.org/10.1007/s11432-011-4453-y

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  • DOI: https://doi.org/10.1007/s11432-011-4453-y

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