Principal curvatures from the integral invariant viewpoint
H. Pottmann, J. Wallner, Y.-L. Yang, Y.-K. Lai, and S.-M. Hu


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. The relation of the quantities computed by PCA with the surface's principal curvatures is investigated via an asymptotic analysis as the kernel radius tends to zero. This also allows to define multiscale principal curvatures which are consistent with the classical setting. A further advantage of this approach is numerical robustness. As to applications, we address computing principal curves and feature extraction on multiple scales.


author = "Helmut Pottmann and Johannes Wallner and
Yong-Liang Yang and Yu-Kun Lai and Shi-Min Hu",
title = "Principal curvatures from the integral invariant viewpoint",
journal = "Comput. Aided Geom. Design",
year = 2007,
volume = 24,
pages = 428-442",
publisher = "Elsevier",
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