Intrinsic Riemannian Metrics on Spaces of Curves: Theory and Computation.
Intrinsic Riemannian Metrics on Spaces of Curves: Theory and Computation.
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曲线空间的固有黎曼度量：理论与计算。
DOI：
10.1007/978-3-030-03009-4_87-1
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发表时间：
2021
期刊：
影响因子：
--
通讯作者：
Le Brigant, Alice
中科院分区：
文献类型：
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作者：
Bauer, Martin;Charon, Nicolas;Klassen, Eric;Le Brigant, Alice
这一章回顾了曲线模保形变换空间上基于固有黎曼度量计算的曲线形状比较和分析的一些过去和最近的发展。在考虑平方根速度度量的特殊情况之前，我们总结了欧氏曲线和非欧氏曲线的商弹性度量的一般结构和理论性质，对于平方根速度度量的结果距离的表达式通过特定的变换得到简化。然后，我们研究了在实践中估计这种距离的不同的数值方法，特别是在由此产生的最小化问题中的商输出曲线重新参数化。
This chapter reviews some past and recent developments in shape comparison and analysis of curves based on the computation of intrinsic Riemannian metrics on the space of curve modulo shape-preserving transformations. We summarize the general construction and theoretical properties of quotient elastic metrics for Euclidean as well as non-Euclidean curves before considering the special case of the square root velocity metric for which the expression of the resulting distance simplifies through a particular transformation. We then examine the different numerical approaches that have been proposed to estimate such distances in practice and in particular to quotient out curve reparametrization in the resulting minimization problems.