一种用于比较具有一般弹性度量的平面曲线的非精确匹配方法
An inexact matching approach for the comparison of plane curves with general elastic metrics
AI总结：
针对浸入平面曲线的距离与测地线计算，提出结合一般简化弹性变换和参数化不变保真度松弛的非精确匹配方法，以简化优化并增强对噪声、不一致或损坏数据的处理能力。
摘要：
本文介绍了一种新的数学公式和数值方法，用于计算浸入平面曲线之间的距离和测地线。我们的方法将Kurtek和Needham最近提出的用于一阶弹性度量的一般简化变换，与使用参数化不变保真度度量对匹配约束进行的松弛相结合。该公式的主要优点是，它为离散化曲线带来了一个简单的优化问题，并提供了一种灵活的方法来处理含噪、不一致或损坏的数据。这些优势通过若干初步数值结果得到了说明。
英文摘要：
This paper introduces a new mathematical formulation and numerical approach for the computation of distances and geodesics between immersed planar curves. Our approach combines the general simplifying transform for first-order elastic metrics that was recently introduced by Kurtek and Needham, together with a relaxation of the matching constraint using parametrization-invariant fidelity metrics. The main advantages of this formulation are that it leads to a simple optimization problem for discretized curves, and that it provides a flexible approach to deal with noisy, inconsistent or corrupted data. These benefits are illustrated via a few preliminary numerical results.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
