A shape sensitive, variational approach for the matching of surfaces considered as thin elastic shells is investigated. The elasticity functional to be minimized takes into account two different types of nonlinear energies: a membrane energy measuring the rate of tangential distortion when deforming the reference shell into the template shell, and a bending energy measuring the bending under the deformation in terms of the change of the shape operators from the undeformed into the deformed configuration. The variational method applies to surfaces described as level sets. It is mathematically well-posed, and an existence proof of an optimal matching deformation is given. The variational model is implemented using a finite element discretization combined with a narrow band approach on an efficient hierarchical grid structure. For the optimization, a regularized nonlinear conjugate gradient scheme and a cascadic multilevel strategy are used. The features of the proposed approach are studied for synthetic test cases and a collection of geometry processing examples.

中文翻译：

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基于薄壳能的隐式表面形状感知匹配。

研究了形状敏感的变形方法，用于匹配被认为是薄弹性壳的表面。要最小化的弹性函数考虑了两种不同类型的非线性能量：用于测量将参考壳变形为模板壳时的切向变形率的膜能量，以及用于测量变形下的弯曲在变化方面的弯曲能从未变形的形状算子到变形的形状。变分方法适用于描述为水平集的曲面。它在数学上是正确的，并给出了最佳匹配变形的存在证明。使用有限元离散化结合窄带方法在有效的分层网格结构上实现变分模型。为了优化，使用正则化非线性共轭梯度方案和级联多级策略。针对合成测试用例和几何处理示例的集合，研究了所提出方法的功能。