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.

中文翻译：

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光谱形状分析的哈密顿算子

许多形状分析方法将对象的几何形状视为可以由Laplace-Beltrami运算符捕获的度量空间。在本文中，我们建议将经典的哈密顿算子从量子力学中应用到形状分析领域。为此，我们研究了将潜在函数添加到Laplacian，作为生成空间的双重空间生成器。我们提出了解决变分问题的通用优化方法，该方法涉及哈密顿量使用其特征向量的扰动理论定义的基础。如在不同的形状分析任务上所示，建议的操作员将产生更好的功能空间来进行操作。