---
OA_type: closed access
_id: '18326'
abstract:
- lang: eng
  text: Nonrigid shapes are ubiquitous in nature and are encountered at all levels
    of life, from macro to nano. The need to model such shapes and understand their
    behavior arises in many applications in imaging sciences, pattern recognition,
    computer vision, and computer graphics. Of particular importance is understanding
    which properties of the shape are attributed to deformations and which are invariant,
    i.e., remain unchanged. This chapter presents an approach to nonrigid shapes from
    the point of view of metric geometry. Modeling shapes as metric spaces, one can
    pose the problem of shape similarity as the similarity of metric spaces and harness
    tools from theoretical metric geometry for the computation of such a similarity.
article_processing_charge: No
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
citation:
  ama: 'Bronstein AM, Bronstein MM. Manifold Intrinsic Similarity. In: Scherzer O,
    ed. <i>Handbook of Mathematical Methods in Imaging</i>. 2nd ed. New York: Springer
    Nature; 2015:1859-1908. doi:<a href="https://doi.org/10.1007/978-1-4939-0790-8_57">10.1007/978-1-4939-0790-8_57</a>'
  apa: 'Bronstein, A. M., &#38; Bronstein, M. M. (2015). Manifold Intrinsic Similarity.
    In O. Scherzer (Ed.), <i>Handbook of Mathematical Methods in Imaging</i> (2nd
    ed., pp. 1859–1908). New York: Springer Nature. <a href="https://doi.org/10.1007/978-1-4939-0790-8_57">https://doi.org/10.1007/978-1-4939-0790-8_57</a>'
  chicago: 'Bronstein, Alex M., and Michael M. Bronstein. “Manifold Intrinsic Similarity.”
    In <i>Handbook of Mathematical Methods in Imaging</i>, edited by Otmar Scherzer,
    2nd ed., 1859–1908. New York: Springer Nature, 2015. <a href="https://doi.org/10.1007/978-1-4939-0790-8_57">https://doi.org/10.1007/978-1-4939-0790-8_57</a>.'
  ieee: 'A. M. Bronstein and M. M. Bronstein, “Manifold Intrinsic Similarity,” in
    <i>Handbook of Mathematical Methods in Imaging</i>, 2nd ed., O. Scherzer, Ed.
    New York: Springer Nature, 2015, pp. 1859–1908.'
  ista: 'Bronstein AM, Bronstein MM. 2015.Manifold Intrinsic Similarity. In: Handbook
    of Mathematical Methods in Imaging. , 1859–1908.'
  mla: Bronstein, Alex M., and Michael M. Bronstein. “Manifold Intrinsic Similarity.”
    <i>Handbook of Mathematical Methods in Imaging</i>, edited by Otmar Scherzer,
    2nd ed., Springer Nature, 2015, pp. 1859–908, doi:<a href="https://doi.org/10.1007/978-1-4939-0790-8_57">10.1007/978-1-4939-0790-8_57</a>.
  short: A.M. Bronstein, M.M. Bronstein, in:, O. Scherzer (Ed.), Handbook of Mathematical
    Methods in Imaging, 2nd ed., Springer Nature, New York, 2015, pp. 1859–1908.
date_created: 2024-10-15T11:20:53Z
date_published: 2015-05-30T00:00:00Z
date_updated: 2024-10-22T08:12:57Z
day: '30'
doi: 10.1007/978-1-4939-0790-8_57
edition: '2'
editor:
- first_name: Otmar
  full_name: Scherzer, Otmar
  last_name: Scherzer
extern: '1'
fulldoi: https://doi.org/10.1007/978-1-4939-0790-8_57
language:
- iso: eng
month: '05'
oa_version: None
page: 1859-1908
place: New York
publication: Handbook of Mathematical Methods in Imaging
publication_identifier:
  eisbn:
  - '9781493907908'
  isbn:
  - '9781493907892'
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
scopus_import: '1'
status: public
title: Manifold Intrinsic Similarity
type: book_chapter
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
year: '2015'
...