In this article, we introduce a family of elastic metrics on the space of parametrized surfaces in 3D space using a corresponding family of metrics on the space of vector-valued one-forms. We provide a numerical framework for the computation of geodesics with respect to these metrics. The family of metrics is invariant under rigid motions and reparametrizations; hence, it induces a metric on the “shape space” of surfaces. This new class of metrics generalizes a previously studied family of elastic metrics and includes in particular the Square Root Normal Field (SRNF) metric, which has been proven successful in various applications. We demonstrate our framework by showing several examples of geodesics and compare our results with earlier results obtained from the SRNF framework.

中文翻译：

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使用通用弹性度量的曲面形状分析

在本文中，我们使用向量值单一形式空间上的相应度量标准系列，介绍了3D空间中参数化曲面空间的弹性度量标准系列。我们为有关这些度量的测地线计算提供了一个数值框架。在僵硬的运动和重新设定参数的情况下，度量标准的族是不变的。因此，它在曲面的“形状空间”上引入了度量。这类新的度量标准概括了先前研究的弹性度量标准系列，尤其是包括平方根正态场（SRNF）度量标准，该标准已在各种应用中证明是成功的。我们通过显示一些测地线示例来演示我们的框架，并将我们的结果与从SRNF框架获得的早期结果进行比较。