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 Br or its boundary sphere Sr 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 Br Ç F 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.
Bibtex:
@inproceedings{yang-2006-rpc,
author = "Yong-Liang Yang and Yu-Kun Lai and Shi-Min Hu and
Helmut Pottmann",
title = "Robust Principal Curvatures on Multiple Scales",
booktitle = {{SGP} 2006: 4th Eurographics Symposium on
Geometry processing},
publisher = {Eurographics Association},
editor = "Konrad Polthier and Alla Sheffer",
url = "http://www.geometrie.tugraz.at/wallner/sgp06-electronic.pdf",
year = 2006,
pages = "223-226",
}
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