Hamiltonian operator for spectral shape analysis
This work addresses shape analysis for geometry processing, offering a novel operator that enhances functional spaces, though it appears incremental as it builds upon existing Laplacian-based methods.
The authors tackled the problem of shape analysis by adapting the Hamiltonian operator from quantum mechanics to generate better functional spaces, demonstrating improved performance on various shape analysis tasks.
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 a general optimization approach 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.