Robust principal curvatures on multiple scales
Robust principal curvatures on multiple scales
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DOI：
10.2312/sgp/sgp06/223-226
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发表时间：
2006-06
期刊：
影响因子：
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通讯作者：
Yong-Liang Yang;Yu-Kun Lai;Shimin Hu;H. Pottmann
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文献类型：
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作者：
Yong-Liang Yang;Yu-Kun Lai;Shimin Hu;H. Pottmann
几何处理算法通常要求曲率信息的鲁棒提取。我们建议用局部邻域的主成分分析（PCA）来实现这一点，通过以给定表面为中心的球形核来定义Φ核球Br或其边界球Sr与以Φ为界的体积的交集导致所谓的球和球邻域。这些邻域的PCA获得的信息比之前使用的补丁邻域Br∩Φ的PCA具有更强的鲁棒性。当核半径r趋于零时，通过渐近分析揭示了主成分分析法计算的量与Φ主曲率的关系。这也允许我们以一种与经典设置一致的方式定义“尺度r”的主曲率。通过与正规循环和局部拟合结果的比较，讨论了新方法的优点；前一种方法在鲁棒性上有所欠缺，而后者在粗尺度上不能实现特征的一致行为。在应用方面，我们解决了多尺度的主曲线计算和特征提取问题。
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 Φ Intersection of a kernel ball Br or its boundary sphere Sr with the volume bounded by Φ 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∩Φ previously used. The relation of the quantities computed by PCA with the principal curvatures of Φ 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.