---
_id: '18429'
abstract:
- lang: eng
  text: We present an efficient computational framework for isometry‐invariant comparison
    of smooth surfaces. We formulate the Gromov–Hausdorff distance as a multidimensional
    scaling–like continuous optimization problem. In order to construct an efficient
    optimization scheme, we develop a numerical tool for interpolating geodesic distances
    on a sampled surface from precomputed geodesic distances between the samples.
    For isometry‐invariant comparison of surfaces in the case of partially missing
    data, we present the partial embedding distance, which is computed using a similar
    scheme. The main idea is finding a minimum‐distortion mapping from one surface
    to another, while considering only relevant geodesic distances. We discuss numerical
    implementation issues and present experimental results that demonstrate its accuracy
    and efficiency.
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
- first_name: Ron
  full_name: Kimmel, Ron
  last_name: Kimmel
citation:
  ama: Bronstein AM, Bronstein MM, Kimmel R. Efficient computation of isometry-invariant
    distances between surfaces. <i>SIAM Journal on Scientific Computing</i>. 2006;28(5):1812-1836.
    doi:<a href="https://doi.org/10.1137/050639296">10.1137/050639296</a>
  apa: Bronstein, A. M., Bronstein, M. M., &#38; Kimmel, R. (2006). Efficient computation
    of isometry-invariant distances between surfaces. <i>SIAM Journal on Scientific
    Computing</i>. Society for Industrial &#38; Applied Mathematics. <a href="https://doi.org/10.1137/050639296">https://doi.org/10.1137/050639296</a>
  chicago: Bronstein, Alex M., Michael M. Bronstein, and Ron Kimmel. “Efficient Computation
    of Isometry-Invariant Distances between Surfaces.” <i>SIAM Journal on Scientific
    Computing</i>. Society for Industrial &#38; Applied Mathematics, 2006. <a href="https://doi.org/10.1137/050639296">https://doi.org/10.1137/050639296</a>.
  ieee: A. M. Bronstein, M. M. Bronstein, and R. Kimmel, “Efficient computation of
    isometry-invariant distances between surfaces,” <i>SIAM Journal on Scientific
    Computing</i>, vol. 28, no. 5. Society for Industrial &#38; Applied Mathematics,
    pp. 1812–1836, 2006.
  ista: Bronstein AM, Bronstein MM, Kimmel R. 2006. Efficient computation of isometry-invariant
    distances between surfaces. SIAM Journal on Scientific Computing. 28(5), 1812–1836.
  mla: Bronstein, Alex M., et al. “Efficient Computation of Isometry-Invariant Distances
    between Surfaces.” <i>SIAM Journal on Scientific Computing</i>, vol. 28, no. 5,
    Society for Industrial &#38; Applied Mathematics, 2006, pp. 1812–36, doi:<a href="https://doi.org/10.1137/050639296">10.1137/050639296</a>.
  short: A.M. Bronstein, M.M. Bronstein, R. Kimmel, SIAM Journal on Scientific Computing
    28 (2006) 1812–1836.
date_created: 2024-10-15T11:20:55Z
date_published: 2006-10-01T00:00:00Z
date_updated: 2024-12-18T15:49:10Z
day: '01'
doi: 10.1137/050639296
extern: '1'
fulldoi: https://doi.org/10.1137/050639296
intvolume: '        28'
issue: '5'
language:
- iso: eng
month: '10'
oa_version: None
page: 1812-1836
publication: SIAM Journal on Scientific Computing
publication_identifier:
  eissn:
  - 1095-7197
  issn:
  - 1064-8275
publication_status: published
publisher: Society for Industrial & Applied Mathematics
quality_controlled: '1'
scopus_import: '1'
status: public
title: Efficient computation of isometry-invariant distances between surfaces
type: journal_article
user_id: 3E5EF7F0-F248-11E8-B48F-1D18A9856A87
volume: 28
year: '2006'
...