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Quantum Simulation

Hamiltonian Operator for Spectral Shape Analysis.

PubMed
Authors: Choukroun Y, Shtern A, Bronstein A, Kimmel R

Year

2020

Paper ID

1472

Status

Peer-reviewed

Abstract Read

~2 min

Abstract Words

110

Citations

N/A

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.

Why This Paper Matters

  • This paper contributes to the Quantum Simulation research area in the Quantum Articles archive.
  • It adds a 2020 reference point for readers tracking recent quantum research.
  • Many shape analysis methods treat the geometry of an object as a metric space that can be captured by the Laplace-Beltrami operator.

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References & Citation Signals

[1] DOI https://doi.org/10.1109/TVCG.2018.2867513 [2] Publisher https://pubmed.ncbi.nlm.nih.gov/30176599/

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