---
OA_type: closed access
_id: '18357'
abstract:
- lang: eng
  text: 'This paper explores the problem of similarity criteria between nonrigid shapes.
    Broadly speaking, such criteria are divided into intrinsic and extrinsic, the
    first referring to the metric structure of the object and the latter to how it
    is laid out in the Euclidean space. Both criteria have their advantages and disadvantages:
    extrinsic similarity is sensitive to nonrigid deformations, while intrinsic similarity
    is sensitive to topological noise. In this paper, we approach the problem from
    the perspective of metric geometry. We show that by unifying the extrinsic and
    intrinsic similarity criteria, it is possible to obtain a stronger topology-invariant
    similarity, suitable for comparing deformed shapes with different topology. We
    construct this new joint criterion as a tradeoff between the extrinsic and intrinsic
    similarity and use it as a set-valued distance. Numerical results demonstrate
    the efficiency of our approach in cases where using either extrinsic or intrinsic
    criteria alone would fail.'
article_processing_charge: No
article_type: original
author:
- first_name: Alexander
  full_name: Bronstein, Alexander
  id: 58f3726e-7cba-11ef-ad8b-e6e8cb3904e6
  last_name: Bronstein
  orcid: 0000-0001-9699-8730
- first_name: Michael M.
  full_name: Bronstein, Michael M.
  last_name: Bronstein
- first_name: Ron
  full_name: Kimmel, Ron
  last_name: Kimmel
citation:
  ama: Bronstein AM, Bronstein MM, Kimmel R. Topology-invariant similarity of nonrigid
    shapes. <i>International Journal of Computer Vision</i>. 2009;81(3):281-301. doi:<a
    href="https://doi.org/10.1007/s11263-008-0172-2">10.1007/s11263-008-0172-2</a>
  apa: Bronstein, A. M., Bronstein, M. M., &#38; Kimmel, R. (2009). Topology-invariant
    similarity of nonrigid shapes. <i>International Journal of Computer Vision</i>.
    Springer Nature. <a href="https://doi.org/10.1007/s11263-008-0172-2">https://doi.org/10.1007/s11263-008-0172-2</a>
  chicago: Bronstein, Alex M., Michael M. Bronstein, and Ron Kimmel. “Topology-Invariant
    Similarity of Nonrigid Shapes.” <i>International Journal of Computer Vision</i>.
    Springer Nature, 2009. <a href="https://doi.org/10.1007/s11263-008-0172-2">https://doi.org/10.1007/s11263-008-0172-2</a>.
  ieee: A. M. Bronstein, M. M. Bronstein, and R. Kimmel, “Topology-invariant similarity
    of nonrigid shapes,” <i>International Journal of Computer Vision</i>, vol. 81,
    no. 3. Springer Nature, pp. 281–301, 2009.
  ista: Bronstein AM, Bronstein MM, Kimmel R. 2009. Topology-invariant similarity
    of nonrigid shapes. International Journal of Computer Vision. 81(3), 281–301.
  mla: Bronstein, Alex M., et al. “Topology-Invariant Similarity of Nonrigid Shapes.”
    <i>International Journal of Computer Vision</i>, vol. 81, no. 3, Springer Nature,
    2009, pp. 281–301, doi:<a href="https://doi.org/10.1007/s11263-008-0172-2">10.1007/s11263-008-0172-2</a>.
  short: A.M. Bronstein, M.M. Bronstein, R. Kimmel, International Journal of Computer
    Vision 81 (2009) 281–301.
date_created: 2024-10-15T11:20:54Z
date_published: 2009-03-01T00:00:00Z
date_updated: 2024-10-22T07:27:15Z
day: '01'
doi: 10.1007/s11263-008-0172-2
extern: '1'
intvolume: '        81'
issue: '3'
language:
- iso: eng
month: '03'
oa_version: None
page: 281-301
publication: International Journal of Computer Vision
publication_identifier:
  eissn:
  - 1573-1405
  issn:
  - 0920-5691
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
scopus_import: '1'
status: public
title: Topology-invariant similarity of nonrigid shapes
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 81
year: '2009'
...