Robust Principal Curvatures on Multiple Scales

Yong-Liang Yang Tsinghua University Yu-Kun Lai Tsinghua University Shi-Min Hu Tsinghua University Helmut Pottmann Vienna University of Technology

Geometric Modeling and Processing mathscidoc:1608.16059

Proceedings of 4th Eurographics Symposium on Geometry Processing , 223-226, 2006
Geometry processing algorithms often require the robust extraction of curvature information. We propose to achieve this with principal component analysis (PCA) of local neighborhoods, defined via spherical kernels centered on the given surface $\Phi$. Intersection of a kernel ball $B_r$ or its boundary sphere $S_r$ with the volume bounded by $\Phi$ leads to the so-called ball and sphere neighborhoods. Information obtained by PCA of these neighborhoods turns out to be more robust than PCA of the patch neighborhood $B_r \cap \Phi$ previously used. The relation of the quantities computed by PCA with the principal curvatures of $\Phi$ is revealed by an asymptotic analysis as the kernel radius $r$ tends to zero. This also allows us to define principal curvatures 'at scale $r$ in a way which is consistent with the classical setting. The advantages of the new approach are discussed in a comparison with results obtained by normal cycles and local fitting; whereas the former method somewhat lacks in robustness, the latter does not achieve a consistent behavior at features on coarse scales. As to applications, we address computing principal curves and feature extraction on multiple scales.
Principal Curvature, principal component analysis, feature extraction, multiple scales
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@inproceedings{yong-liang2006robust,
  title={Robust Principal Curvatures on Multiple Scales},
  author={Yong-Liang Yang, Yu-Kun Lai, Shi-Min Hu, and Helmut Pottmann},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20160824232057888171435},
  booktitle={Proceedings of 4th Eurographics Symposium on Geometry Processing },
  pages={223-226},
  year={2006},
}
Yong-Liang Yang, Yu-Kun Lai, Shi-Min Hu, and Helmut Pottmann. Robust Principal Curvatures on Multiple Scales. 2006. In Proceedings of 4th Eurographics Symposium on Geometry Processing . pp.223-226. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20160824232057888171435.
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