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.

中文翻译：

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用于比较平面曲线与一般弹性度量的不精确匹配方法

本文介绍了一种新的数学公式和数值方法，用于计算浸没平面曲线之间的距离和测地线。我们的方法结合了 Kurtek 和 Needham 最近引入的一阶弹性度量的一般简化变换，以及使用参数化不变保真度度量来放松匹配约束。这种公式的主要优点是它导致了离散曲线的简单优化问题，并且它提供了一种灵活的方法来处理嘈杂、不一致或损坏的数据。这些好处通过一些初步的数值结果来说明。