Geodesic Methods in Computer Vision and Graphics
Geodesic Methods in Computer Vision and Graphics
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DOI：
10.1561/0600000029
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发表时间：
2009-01-01
影响因子：
36.5
通讯作者：
Cohen, Laurent D.
中科院分区：
文献类型：
--
作者：
Peyre, Gabriel;Pechaud, Mickael;Cohen, Laurent D.
这本专着回顾了黎曼流形上测地距离的数值计算的理论和实践。黎曼流形的概念允许人们定义一个局部度量（对称的正张量场），它编码了人们希望解决的问题的信息。这考虑了局部各向同性成本（是否应该避免某个点）和局部各向异性（应该优选哪个方向）。使用这个局部张量场，测地线距离被用来解决许多实际感兴趣的问题，例如使用测地线球和Voronoi区域的分割，以规则的测地线距离采样点或用测地线Delaunay三角形网格化域。这个黎曼距离的最短路径，即所谓的测地线，也很重要，因为它们遵循域中的突出曲线结构。我们展示了几个应用程序的数值计算的测地线距离和最短路径的问题，在表面和形状处理，特别是分割，采样，网格化和比较的形状。本文中的所有图都可以通过信号处理的数值图尔斯之旅进行复制。
This monograph reviews both the theory and practice of the numerical computation of geodesic distances on Riemannian manifolds. The notion of Riemannian manifold allows one to define a local metric (a symmetric positive tensor field) that encodes the information about the problem one wishes to solve. This takes into account a local isotropic cost (whether some point should be avoided or not) and a local anisotropy (which direction should be preferred). Using this local tensor field, the geodesic distance is used to solve many problems of practical interest such as segmentation using geodesic balls and Voronoi regions, sampling points at regular geodesic distance or meshing a domain with geodesic Delaunay triangles. The shortest paths for this Riemannian distance, the so-called geodesics, are also important because they follow salient curvilinear structures in the domain. We show several applications of the numerical computation of geodesic distances and shortest paths to problems in surface and shape processing, in particular segmentation, sampling, meshing and comparison of shapes. All the figures from this review paper can be reproduced by following the Numerical Tours of Signal Processing.