Hamiltonian operator for spectral shape analysis

Yoni Choukroun, Alon Shtern, Alex Bronstein, Ron Kimmel

Research output: Contribution to journalArticlepeer-review

Abstract

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.

Original languageEnglish
Article number8449121
Pages (from-to)1320-1331
Number of pages12
JournalIEEE Transactions on Visualization and Computer Graphics
Volume26
Issue number2
DOIs
StatePublished - 1 Feb 2020
Externally publishedYes

Keywords

  • Compressed manifold modes
  • Hamiltonian
  • Mesh representation
  • Shape analysis
  • Shape matching

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