Choukroun Yoni, Shtern Alon, Bronstein Alex, Kimmel Ron
IEEE Trans Vis Comput Graph. 2020 Feb;26(2):1320-1331. doi: 10.1109/TVCG.2018.2867513. Epub 2018 Aug 28.
Many shape analysis methods treat the geometry of an object as a metric space that can be captured by the Laplace-Beltrami operator. In this paper, we propose to adapt the classical Hamiltonian operator from quantum mechanics to the field of shape analysis. To this end, we study the addition of a potential function to the Laplacian as a generator for dual spaces in which shape processing is performed. We present general optimization approaches for solving variational problems involving the basis defined by the Hamiltonian using perturbation theory for its eigenvectors. The suggested operator is shown to produce better functional spaces to operate with, as demonstrated on different shape analysis tasks.
许多形状分析方法将物体的几何形状视为一个可由拉普拉斯 - 贝尔特拉米算子捕获的度量空间。在本文中，我们建议将量子力学中的经典哈密顿算子应用于形状分析领域。为此，我们研究了在拉普拉斯算子上添加一个势函数，作为执行形状处理的对偶空间的生成器。我们提出了一般的优化方法，用于使用哈密顿算子特征向量的微扰理论来解决涉及哈密顿定义的基的变分问题。如在不同形状分析任务中所示，所提出的算子能产生更好的可用于操作的函数空间。
