论文标题
曲线空间上的固有的里曼尼亚指标：理论与计算
Intrinsic Riemannian metrics on spaces of curves: theory and computation
论文作者
论文摘要
本章回顾了形状比较和最近的一些过去和最新进展，并根据曲线模拟变形转换的固有性黎曼指标的计算计算了曲线。在考虑平方根速度度量的特殊情况之前，我们总结了欧几里得和非欧几里得曲线的商弹性指标的一般结构和理论特性。然后，我们研究了已提出的不同数值方法，以估算实践中的距离，尤其是在最小化问题中估算曲线的曲线重新构造。
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 curves 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 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.
