---
_id: '18440'
abstract:
- lang: eng
  text: In this paper, we explore the use of the diffusion geometry framework for
    the fusion of geometric and photometric information in local and global shape
    descriptors. Our construction is based on the definition of a diffusion process
    on the shape manifold embedded into a high-dimensional space where the embedding
    coordinates represent the photometric information. Experimental results show that
    such data fusion is useful in coping with different challenges of shape analysis
    where pure geometric and pure photometric methods fail.
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: Artiom
  full_name: Kovnatsky, Artiom
  last_name: Kovnatsky
- first_name: Dan
  full_name: Raviv, Dan
  last_name: Raviv
- 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, Kovnatsky A, Raviv D, Bronstein MM, Kimmel R. Geometric and
    photometric data fusion in non-rigid shape analysis. <i>Numerical Mathematics:
    Theory, Methods and Applications</i>. 2013;6(1):199-222. doi:<a href="https://doi.org/10.4208/nmtma.2013.mssvm11">10.4208/nmtma.2013.mssvm11</a>'
  apa: 'Bronstein, A. M., Kovnatsky, A., Raviv, D., Bronstein, M. M., &#38; Kimmel,
    R. (2013). Geometric and photometric data fusion in non-rigid shape analysis.
    <i>Numerical Mathematics: Theory, Methods and Applications</i>. Global Science
    Press. <a href="https://doi.org/10.4208/nmtma.2013.mssvm11">https://doi.org/10.4208/nmtma.2013.mssvm11</a>'
  chicago: 'Bronstein, Alex M., Artiom Kovnatsky, Dan Raviv, Michael M. Bronstein,
    and Ron Kimmel. “Geometric and Photometric Data Fusion in Non-Rigid Shape Analysis.”
    <i>Numerical Mathematics: Theory, Methods and Applications</i>. Global Science
    Press, 2013. <a href="https://doi.org/10.4208/nmtma.2013.mssvm11">https://doi.org/10.4208/nmtma.2013.mssvm11</a>.'
  ieee: 'A. M. Bronstein, A. Kovnatsky, D. Raviv, M. M. Bronstein, and R. Kimmel,
    “Geometric and photometric data fusion in non-rigid shape analysis,” <i>Numerical
    Mathematics: Theory, Methods and Applications</i>, vol. 6, no. 1. Global Science
    Press, pp. 199–222, 2013.'
  ista: 'Bronstein AM, Kovnatsky A, Raviv D, Bronstein MM, Kimmel R. 2013. Geometric
    and photometric data fusion in non-rigid shape analysis. Numerical Mathematics:
    Theory, Methods and Applications. 6(1), 199–222.'
  mla: 'Bronstein, Alex M., et al. “Geometric and Photometric Data Fusion in Non-Rigid
    Shape Analysis.” <i>Numerical Mathematics: Theory, Methods and Applications</i>,
    vol. 6, no. 1, Global Science Press, 2013, pp. 199–222, doi:<a href="https://doi.org/10.4208/nmtma.2013.mssvm11">10.4208/nmtma.2013.mssvm11</a>.'
  short: 'A.M. Bronstein, A. Kovnatsky, D. Raviv, M.M. Bronstein, R. Kimmel, Numerical
    Mathematics: Theory, Methods and Applications 6 (2013) 199–222.'
date_created: 2024-10-15T11:20:55Z
date_published: 2013-02-01T00:00:00Z
date_updated: 2024-12-19T15:09:21Z
day: '01'
doi: 10.4208/nmtma.2013.mssvm11
extern: '1'
fulldoi: https://doi.org/10.4208/nmtma.2013.mssvm11
intvolume: '         6'
issue: '1'
language:
- iso: eng
month: '02'
oa_version: None
page: 199-222
publication: 'Numerical Mathematics: Theory, Methods and Applications'
publication_identifier:
  eissn:
  - 2079-7338
  issn:
  - 1004-8979
publication_status: published
publisher: Global Science Press
quality_controlled: '1'
scopus_import: '1'
status: public
title: Geometric and photometric data fusion in non-rigid shape analysis
type: journal_article
user_id: 3E5EF7F0-F248-11E8-B48F-1D18A9856A87
volume: 6
year: '2013'
...
---
_id: '18441'
abstract:
- lang: eng
  text: Partial similarity of shapes is a challenging problem arising in many important
    applications in computer vision, shape analysis, and graphics, e.g. when one has
    to deal with partial information and acquisition artifacts. The problem is especially
    hard when the underlying shapes are non-rigid and are given up to a deformation.
    Partial matching is usually approached by computing local descriptors on a pair
    of shapes and then establishing a point-wise non-bijective correspondence between
    the two, taking into account possibly different parts. In this paper, we introduce
    an alternative correspondence-less approach to matching fragments to an entire
    shape undergoing a non-rigid deformation. We use region-wise local descriptors
    and optimize over the integration domains on which the integral descriptors of
    the two parts match. The problem is regularized using the Mumford-Shah functional.
    We show an efficient discretization based on the Ambrosio-Tortorelli approximation
    generalized to triangular point clouds and meshes, and present experiments demonstrating
    the success of the proposed method.
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: 'Jonathan '
  full_name: 'Pokrass, Jonathan '
  last_name: Pokrass
- first_name: Michael M.
  full_name: Bronstein, Michael M.
  last_name: Bronstein
citation:
  ama: 'Bronstein AM, Pokrass J, Bronstein MM. Partial shape matching without point-wise
    correspondence. <i>Numerical Mathematics: Theory, Methods and Applications</i>.
    2013;6(1):223-244. doi:<a href="https://doi.org/10.4208/nmtma.2013.mssvm12">10.4208/nmtma.2013.mssvm12</a>'
  apa: 'Bronstein, A. M., Pokrass, J., &#38; Bronstein, M. M. (2013). Partial shape
    matching without point-wise correspondence. <i>Numerical Mathematics: Theory,
    Methods and Applications</i>. Global Science Press. <a href="https://doi.org/10.4208/nmtma.2013.mssvm12">https://doi.org/10.4208/nmtma.2013.mssvm12</a>'
  chicago: 'Bronstein, Alex M., Jonathan  Pokrass, and Michael M. Bronstein. “Partial
    Shape Matching without Point-Wise Correspondence.” <i>Numerical Mathematics: Theory,
    Methods and Applications</i>. Global Science Press, 2013. <a href="https://doi.org/10.4208/nmtma.2013.mssvm12">https://doi.org/10.4208/nmtma.2013.mssvm12</a>.'
  ieee: 'A. M. Bronstein, J. Pokrass, and M. M. Bronstein, “Partial shape matching
    without point-wise correspondence,” <i>Numerical Mathematics: Theory, Methods
    and Applications</i>, vol. 6, no. 1. Global Science Press, pp. 223–244, 2013.'
  ista: 'Bronstein AM, Pokrass J, Bronstein MM. 2013. Partial shape matching without
    point-wise correspondence. Numerical Mathematics: Theory, Methods and Applications.
    6(1), 223–244.'
  mla: 'Bronstein, Alex M., et al. “Partial Shape Matching without Point-Wise Correspondence.”
    <i>Numerical Mathematics: Theory, Methods and Applications</i>, vol. 6, no. 1,
    Global Science Press, 2013, pp. 223–44, doi:<a href="https://doi.org/10.4208/nmtma.2013.mssvm12">10.4208/nmtma.2013.mssvm12</a>.'
  short: 'A.M. Bronstein, J. Pokrass, M.M. Bronstein, Numerical Mathematics: Theory,
    Methods and Applications 6 (2013) 223–244.'
date_created: 2024-10-15T11:20:55Z
date_published: 2013-02-01T00:00:00Z
date_updated: 2024-12-19T14:44:37Z
day: '01'
doi: 10.4208/nmtma.2013.mssvm12
extern: '1'
fulldoi: https://doi.org/10.4208/nmtma.2013.mssvm12
intvolume: '         6'
issue: '1'
language:
- iso: eng
month: '02'
oa_version: None
page: 223-244
publication: 'Numerical Mathematics: Theory, Methods and Applications'
publication_identifier:
  eissn:
  - 2079-7338
  issn:
  - 1004-8979
publication_status: published
publisher: Global Science Press
quality_controlled: '1'
scopus_import: '1'
status: public
title: Partial shape matching without point-wise correspondence
type: journal_article
user_id: 3E5EF7F0-F248-11E8-B48F-1D18A9856A87
volume: 6
year: '2013'
...