Robust Principal Curvatures on Multiple Scales

Yang, Yong-Liang; Lai, Yu-Kun; Hu, Shi-Min; Pottmann, Helmut

Robust Principal Curvatures on Multiple Scales

Files

223-226.pdf (1.06 MB)

Date

2006

Authors

Yang, Yong-Liang
Lai, Yu-Kun
Hu, Shi-Min
Pottmann, Helmut

Publisher

The Eurographics Association

Abstract

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 F. Intersection of a kernel ball B(r) of radius r or its boundary sphere S(r) with the volume bounded by F 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 previously used. The relation of the quantities computed by PCA with the principal curvatures of F 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.

        @inproceedings{:10.2312/SGP/SGP06/223-226
,
booktitle = {Symposium on Geometry Processing
},
editor = {Alla Sheffer and Konrad Polthier
},
title = {{Robust Principal Curvatures on Multiple Scales
}},
author = {Yang, Yong-Liang and 
Lai, Yu-Kun and 
Hu, Shi-Min and 
Pottmann, Helmut
},
year = {2006
},
publisher = {The Eurographics Association
},
ISSN = {1727-8384
},
ISBN = {3-905673-24-X
},
DOI = {/10.2312/SGP/SGP06/223-226
}
}