---
OA_place: repository
OA_type: green
_id: '18250'
abstract:
- lang: eng
  text: 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.
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Yoni
  full_name: Choukroun, Yoni
  last_name: Choukroun
- first_name: Alon
  full_name: Shtern, Alon
  last_name: Shtern
- first_name: Alexander
  full_name: Bronstein, Alexander
  id: 58f3726e-7cba-11ef-ad8b-e6e8cb3904e6
  last_name: Bronstein
  orcid: 0000-0001-9699-8730
- first_name: Ron
  full_name: Kimmel, Ron
  last_name: Kimmel
citation:
  ama: Choukroun Y, Shtern A, Bronstein AM, Kimmel R. Hamiltonian operator for spectral
    shape analysis. <i>IEEE Transactions on Visualization and Computer Graphics</i>.
    2020;26(2):1320-1331. doi:<a href="https://doi.org/10.1109/tvcg.2018.2867513">10.1109/tvcg.2018.2867513</a>
  apa: Choukroun, Y., Shtern, A., Bronstein, A. M., &#38; Kimmel, R. (2020). Hamiltonian
    operator for spectral shape analysis. <i>IEEE Transactions on Visualization and
    Computer Graphics</i>. Institute of Electrical and Electronics Engineers. <a href="https://doi.org/10.1109/tvcg.2018.2867513">https://doi.org/10.1109/tvcg.2018.2867513</a>
  chicago: Choukroun, Yoni, Alon Shtern, Alex M. Bronstein, and Ron Kimmel. “Hamiltonian
    Operator for Spectral Shape Analysis.” <i>IEEE Transactions on Visualization and
    Computer Graphics</i>. Institute of Electrical and Electronics Engineers, 2020.
    <a href="https://doi.org/10.1109/tvcg.2018.2867513">https://doi.org/10.1109/tvcg.2018.2867513</a>.
  ieee: Y. Choukroun, A. Shtern, A. M. Bronstein, and R. Kimmel, “Hamiltonian operator
    for spectral shape analysis,” <i>IEEE Transactions on Visualization and Computer
    Graphics</i>, vol. 26, no. 2. Institute of Electrical and Electronics Engineers,
    pp. 1320–1331, 2020.
  ista: Choukroun Y, Shtern A, Bronstein AM, Kimmel R. 2020. Hamiltonian operator
    for spectral shape analysis. IEEE Transactions on Visualization and Computer Graphics.
    26(2), 1320–1331.
  mla: Choukroun, Yoni, et al. “Hamiltonian Operator for Spectral Shape Analysis.”
    <i>IEEE Transactions on Visualization and Computer Graphics</i>, vol. 26, no.
    2, Institute of Electrical and Electronics Engineers, 2020, pp. 1320–31, doi:<a
    href="https://doi.org/10.1109/tvcg.2018.2867513">10.1109/tvcg.2018.2867513</a>.
  short: Y. Choukroun, A. Shtern, A.M. Bronstein, R. Kimmel, IEEE Transactions on
    Visualization and Computer Graphics 26 (2020) 1320–1331.
date_created: 2024-10-08T13:05:41Z
date_published: 2020-02-01T00:00:00Z
date_updated: 2024-10-15T09:43:31Z
day: '01'
doi: 10.1109/tvcg.2018.2867513
extern: '1'
external_id:
  arxiv:
  - '1611.01990'
  pmid:
  - '30176599'
intvolume: '        26'
issue: '2'
language:
- iso: eng
main_file_link:
- open_access: '1'
  url: 'https://doi.org/10.48550/arXiv.1611.01990 '
month: '02'
oa: 1
oa_version: Preprint
page: 1320-1331
pmid: 1
publication: IEEE Transactions on Visualization and Computer Graphics
publication_identifier:
  eissn:
  - 2160-9306
  issn:
  - 1077-2626
publication_status: published
publisher: Institute of Electrical and Electronics Engineers
quality_controlled: '1'
scopus_import: '1'
status: public
title: Hamiltonian operator for spectral shape analysis
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 26
year: '2020'
...