---
_id: '18257'
abstract:
- lang: eng
  text: We consider the problem of localizing relevant subsets of non-rigid geometric
    shapes given only a partial 3D query as the input. Such problems arise in several
    challenging tasks in 3D vision and graphics, including partial shape similarity,
    retrieval, and non-rigid correspondence. We phrase the problem as one of alignment
    between short sequences of eigenvalues of basic differential operators, which
    are constructed upon a scalar function defined on the 3D surfaces. Our method
    therefore seeks for a scalar function that entails this alignment. Differently
    from existing approaches, we do not require solving for a correspondence between
    the query and the target, therefore greatly simplifying the optimization process;
    our core technique is also descriptor-free, as it is driven by the geometry of
    the two objects as encoded in their operator spectra. We further show that our
    spectral alignment algorithm provides a remarkably simple alternative to the recent
    shape-from-spectrum reconstruction approaches. For both applications, we demonstrate
    improvement over the state-of-the-art either in terms of accuracy or computational
    cost.
article_number: '8886146'
article_processing_charge: No
arxiv: 1
author:
- first_name: Arianna
  full_name: Rampini, Arianna
  last_name: Rampini
- first_name: Irene
  full_name: Tallini, Irene
  last_name: Tallini
- first_name: Maks
  full_name: Ovsjanikov, Maks
  last_name: Ovsjanikov
- first_name: Alexander
  full_name: Bronstein, Alexander
  id: 58f3726e-7cba-11ef-ad8b-e6e8cb3904e6
  last_name: Bronstein
  orcid: 0000-0001-9699-8730
- first_name: Emanuele
  full_name: Rodola, Emanuele
  last_name: Rodola
citation:
  ama: 'Rampini A, Tallini I, Ovsjanikov M, Bronstein AM, Rodola E. Correspondence-free
    region localization for partial shape similarity via Hamiltonian spectrum alignment.
    In: <i>2019 International Conference on 3D Vision (3DV)</i>. IEEE; 2019. doi:<a
    href="https://doi.org/10.1109/3dv.2019.00014">10.1109/3dv.2019.00014</a>'
  apa: 'Rampini, A., Tallini, I., Ovsjanikov, M., Bronstein, A. M., &#38; Rodola,
    E. (2019). Correspondence-free region localization for partial shape similarity
    via Hamiltonian spectrum alignment. In <i>2019 International Conference on 3D
    Vision (3DV)</i>. Quebec City, QC, Canada: IEEE. <a href="https://doi.org/10.1109/3dv.2019.00014">https://doi.org/10.1109/3dv.2019.00014</a>'
  chicago: Rampini, Arianna, Irene Tallini, Maks Ovsjanikov, Alex M. Bronstein, and
    Emanuele Rodola. “Correspondence-Free Region Localization for Partial Shape Similarity
    via Hamiltonian Spectrum Alignment.” In <i>2019 International Conference on 3D
    Vision (3DV)</i>. IEEE, 2019. <a href="https://doi.org/10.1109/3dv.2019.00014">https://doi.org/10.1109/3dv.2019.00014</a>.
  ieee: A. Rampini, I. Tallini, M. Ovsjanikov, A. M. Bronstein, and E. Rodola, “Correspondence-free
    region localization for partial shape similarity via Hamiltonian spectrum alignment,”
    in <i>2019 International Conference on 3D Vision (3DV)</i>, Quebec City, QC, Canada,
    2019.
  ista: Rampini A, Tallini I, Ovsjanikov M, Bronstein AM, Rodola E. 2019. Correspondence-free
    region localization for partial shape similarity via Hamiltonian spectrum alignment.
    2019 International Conference on 3D Vision (3DV). 7th International Conference
    on 3D Vision, 8886146.
  mla: Rampini, Arianna, et al. “Correspondence-Free Region Localization for Partial
    Shape Similarity via Hamiltonian Spectrum Alignment.” <i>2019 International Conference
    on 3D Vision (3DV)</i>, 8886146, IEEE, 2019, doi:<a href="https://doi.org/10.1109/3dv.2019.00014">10.1109/3dv.2019.00014</a>.
  short: A. Rampini, I. Tallini, M. Ovsjanikov, A.M. Bronstein, E. Rodola, in:, 2019
    International Conference on 3D Vision (3DV), IEEE, 2019.
conference:
  end_date: 2019-09-19
  location: Quebec City, QC, Canada
  name: 7th International Conference on 3D Vision
  start_date: 2019-09-16
date_created: 2024-10-08T13:07:51Z
date_published: 2019-10-31T00:00:00Z
date_updated: 2024-12-05T15:49:06Z
day: '31'
doi: 10.1109/3dv.2019.00014
extern: '1'
external_id:
  arxiv:
  - '1906.06226'
fulldoi: https://doi.org/10.1109/3dv.2019.00014
language:
- iso: eng
main_file_link:
- open_access: '1'
  url: https://doi.org/10.48550/arXiv.1906.06226
month: '10'
oa: 1
oa_version: Preprint
publication: 2019 International Conference on 3D Vision (3DV)
publication_identifier:
  eissn:
  - 2475-7888
  isbn:
  - '9781728131320'
publication_status: published
publisher: IEEE
quality_controlled: '1'
scopus_import: '1'
status: public
title: Correspondence-free region localization for partial shape similarity via Hamiltonian
  spectrum alignment
type: conference
user_id: 3E5EF7F0-F248-11E8-B48F-1D18A9856A87
year: '2019'
...