Robust Principal Curvatures on Multiple Scales

dc.contributor.authorYang, Yong-Liangen_US
dc.contributor.authorLai, Yu-Kunen_US
dc.contributor.authorHu, Shi-Minen_US
dc.contributor.authorPottmann, Helmuten_US
dc.contributor.editorAlla Sheffer and Konrad Polthieren_US
dc.date.accessioned2014-01-29T08:14:08Z
dc.date.available2014-01-29T08:14:08Z
dc.date.issued2006en_US
dc.description.abstractGeometry 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.en_US
dc.description.seriesinformationSymposium on Geometry Processingen_US
dc.identifier.isbn3-905673-24-Xen_US
dc.identifier.issn1727-8384en_US
dc.identifier.urihttps://doi.org/10.2312/SGP/SGP06/223-226en_US
dc.publisherThe Eurographics Associationen_US
dc.titleRobust Principal Curvatures on Multiple Scalesen_US
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