Shape-Aware Matching of Implicit Surfaces Based on Thin Shell Energies
Shape-Aware Matching of Implicit Surfaces Based on Thin Shell Energies
复制标题
DOI：
10.1007/s10208-017-9357-9
复制
发表时间：
2015-09
期刊：
影响因子：
--
通讯作者：
José A. Iglesias;M. Rumpf;O. Scherzer
中科院分区：
文献类型：
--
作者：
José A. Iglesias;M. Rumpf;O. Scherzer
研究了一种形状敏感的变分方法，用于匹配被视为薄弹性壳的表面。要最小化的弹性函数考虑了两种不同类型的非线性能量：膜能量测量参考壳变形为模板壳时的切向变形率，弯曲能量测量变形下的弯曲，根据形状算子从未变形到变形配置的变化。变分法适用于描述为水平集的表面。它在数学上是适定的，并且给出了最佳匹配变形的存在性证明。变分模型是在高效的分层网格结构上使用有限元离散化与窄带方法相结合来实现的。对于优化，使用正则化非线性共轭梯度方案和级联多级策略。针对综合测试用例和几何处理示例集合研究了所提出方法的特征。
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.