---
_id: '18364'
abstract:
- lang: eng
  text: Region feature detectors and descriptors have become a successful and popular
    alternative to point descriptors in image analysis due to their high robustness
    and repeatability, leading to a significant interest in the shape analysis community
    in finding analogous approaches in the 3D world. Recent works have successfully
    extended the maximally stable extremal region (MSER) detection algorithm to surfaces.
    In many applications, however, a volumetric shape model is more appropriate, and
    modeling shape deformations as approximate isometries of the volume of an object,
    rather than its boundary, better captures natural behavior of non-rigid deformations.
    In this paper, we formulate a diffusion-geometric framework for volumetric stable
    component detection and description in deformable shapes. An evaluation of our
    method on the SHREC'11 feature detection benchmark and SCAPE human body scans
    shows its potential as a source of high-quality features. Examples demonstrating
    the drawbacks of surface stable components and the advantage of their volumetric
    counterparts are also presented.
article_processing_charge: No
article_type: original
author:
- first_name: R.
  full_name: Litman, R.
  last_name: Litman
- first_name: Alexander
  full_name: Bronstein, Alexander
  id: 58f3726e-7cba-11ef-ad8b-e6e8cb3904e6
  last_name: Bronstein
  orcid: 0000-0001-9699-8730
- first_name: M.M.
  full_name: Bronstein, M.M.
  last_name: Bronstein
citation:
  ama: Litman R, Bronstein AM, Bronstein MM. Stable volumetric features in deformable
    shapes. <i>Computers &#38; Graphics</i>. 2012;36(5):569-576. doi:<a href="https://doi.org/10.1016/j.cag.2012.03.034">10.1016/j.cag.2012.03.034</a>
  apa: Litman, R., Bronstein, A. M., &#38; Bronstein, M. M. (2012). Stable volumetric
    features in deformable shapes. <i>Computers &#38; Graphics</i>. Elsevier. <a href="https://doi.org/10.1016/j.cag.2012.03.034">https://doi.org/10.1016/j.cag.2012.03.034</a>
  chicago: Litman, R., Alex M. Bronstein, and M.M. Bronstein. “Stable Volumetric Features
    in Deformable Shapes.” <i>Computers &#38; Graphics</i>. Elsevier, 2012. <a href="https://doi.org/10.1016/j.cag.2012.03.034">https://doi.org/10.1016/j.cag.2012.03.034</a>.
  ieee: R. Litman, A. M. Bronstein, and M. M. Bronstein, “Stable volumetric features
    in deformable shapes,” <i>Computers &#38; Graphics</i>, vol. 36, no. 5. Elsevier,
    pp. 569–576, 2012.
  ista: Litman R, Bronstein AM, Bronstein MM. 2012. Stable volumetric features in
    deformable shapes. Computers &#38; Graphics. 36(5), 569–576.
  mla: Litman, R., et al. “Stable Volumetric Features in Deformable Shapes.” <i>Computers
    &#38; Graphics</i>, vol. 36, no. 5, Elsevier, 2012, pp. 569–76, doi:<a href="https://doi.org/10.1016/j.cag.2012.03.034">10.1016/j.cag.2012.03.034</a>.
  short: R. Litman, A.M. Bronstein, M.M. Bronstein, Computers &#38; Graphics 36 (2012)
    569–576.
date_created: 2024-10-15T11:20:54Z
date_published: 2012-08-01T00:00:00Z
date_updated: 2024-11-12T08:42:27Z
day: '01'
doi: 10.1016/j.cag.2012.03.034
extern: '1'
intvolume: '        36'
issue: '5'
language:
- iso: eng
month: '08'
oa_version: None
page: 569-576
publication: Computers & Graphics
publication_identifier:
  issn:
  - 0097-8493
publication_status: published
publisher: Elsevier
quality_controlled: '1'
scopus_import: '1'
status: public
title: Stable volumetric features in deformable shapes
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 36
year: '2012'
...
---
OA_place: repository
OA_type: green
_id: '18362'
abstract:
- lang: eng
  text: Maximally stable component detection is a very popular method for feature
    analysis in images, mainly due to its low computation cost and high repeatability.
    With the recent advance of feature-based methods in geometric shape analysis,
    there is significant interest in finding analogous approaches in the 3D world.
    In this paper, we formulate a diffusion-geometric framework for stable component
    detection in non-rigid 3D shapes, which can be used for geometric feature detection
    and description. A quantitative evaluation of our method on the SHREC’10 feature
    detection benchmark shows its potential as a source of high-quality features.
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Roee
  full_name: Litman, Roee
  last_name: Litman
- 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: Litman R, Bronstein AM, Bronstein MM. Diffusion-geometric maximally stable
    component detection in deformable shapes. <i>Computers &#38; Graphics</i>. 2011;35(3):549-560.
    doi:<a href="https://doi.org/10.1016/j.cag.2011.03.011">10.1016/j.cag.2011.03.011</a>
  apa: Litman, R., Bronstein, A. M., &#38; Bronstein, M. M. (2011). Diffusion-geometric
    maximally stable component detection in deformable shapes. <i>Computers &#38;
    Graphics</i>. Elsevier. <a href="https://doi.org/10.1016/j.cag.2011.03.011">https://doi.org/10.1016/j.cag.2011.03.011</a>
  chicago: Litman, Roee, Alex M. Bronstein, and Michael M. Bronstein. “Diffusion-Geometric
    Maximally Stable Component Detection in Deformable Shapes.” <i>Computers &#38;
    Graphics</i>. Elsevier, 2011. <a href="https://doi.org/10.1016/j.cag.2011.03.011">https://doi.org/10.1016/j.cag.2011.03.011</a>.
  ieee: R. Litman, A. M. Bronstein, and M. M. Bronstein, “Diffusion-geometric maximally
    stable component detection in deformable shapes,” <i>Computers &#38; Graphics</i>,
    vol. 35, no. 3. Elsevier, pp. 549–560, 2011.
  ista: Litman R, Bronstein AM, Bronstein MM. 2011. Diffusion-geometric maximally
    stable component detection in deformable shapes. Computers &#38; Graphics. 35(3),
    549–560.
  mla: Litman, Roee, et al. “Diffusion-Geometric Maximally Stable Component Detection
    in Deformable Shapes.” <i>Computers &#38; Graphics</i>, vol. 35, no. 3, Elsevier,
    2011, pp. 549–60, doi:<a href="https://doi.org/10.1016/j.cag.2011.03.011">10.1016/j.cag.2011.03.011</a>.
  short: R. Litman, A.M. Bronstein, M.M. Bronstein, Computers &#38; Graphics 35 (2011)
    549–560.
date_created: 2024-10-15T11:20:54Z
date_published: 2011-06-01T00:00:00Z
date_updated: 2024-11-12T08:40:40Z
day: '01'
doi: 10.1016/j.cag.2011.03.011
extern: '1'
external_id:
  arxiv:
  - '1012.3951'
intvolume: '        35'
issue: '3'
language:
- iso: eng
main_file_link:
- open_access: '1'
  url: https://doi.org/10.48550/arXiv.1012.3951
month: '06'
oa: 1
oa_version: Preprint
page: 549-560
publication: Computers & Graphics
publication_identifier:
  issn:
  - 0097-8493
publication_status: published
publisher: Elsevier
quality_controlled: '1'
scopus_import: '1'
status: public
title: Diffusion-geometric maximally stable component detection in deformable shapes
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 35
year: '2011'
...
---
OA_place: repository
OA_type: green
_id: '18363'
abstract:
- lang: eng
  text: "Natural objects can be subject to various transformations yet still preserve
    properties that we refer to as invariants. Here, we use definitions of affine-invariant
    arclength for surfaces in \r\n in order to extend the set of existing non-rigid
    shape analysis tools. We show that by re-defining the surface metric as its equi-affine
    version, the surface with its modified metric tensor can be treated as a canonical
    Euclidean object on which most classical Euclidean processing and analysis tools
    can be applied. The new definition of a metric is used to extend the fast marching
    method technique for computing geodesic distances on surfaces, where now, the
    distances are defined with respect to an affine-invariant arclength. Applications
    of the proposed framework demonstrate its invariance, efficiency, and accuracy
    in shape analysis."
article_processing_charge: No
article_type: letter_note
arxiv: 1
author:
- first_name: Dan
  full_name: Raviv, Dan
  last_name: Raviv
- 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
- first_name: Nir
  full_name: Sochen, Nir
  last_name: Sochen
citation:
  ama: Raviv D, Bronstein AM, Bronstein MM, Kimmel R, Sochen N. Affine-invariant geodesic
    geometry of deformable 3D shapes. <i>Computers &#38; Graphics</i>. 2011;35(3):692-697.
    doi:<a href="https://doi.org/10.1016/j.cag.2011.03.030">10.1016/j.cag.2011.03.030</a>
  apa: Raviv, D., Bronstein, A. M., Bronstein, M. M., Kimmel, R., &#38; Sochen, N.
    (2011). Affine-invariant geodesic geometry of deformable 3D shapes. <i>Computers
    &#38; Graphics</i>. Elsevier. <a href="https://doi.org/10.1016/j.cag.2011.03.030">https://doi.org/10.1016/j.cag.2011.03.030</a>
  chicago: Raviv, Dan, Alex M. Bronstein, Michael M. Bronstein, Ron Kimmel, and Nir
    Sochen. “Affine-Invariant Geodesic Geometry of Deformable 3D Shapes.” <i>Computers
    &#38; Graphics</i>. Elsevier, 2011. <a href="https://doi.org/10.1016/j.cag.2011.03.030">https://doi.org/10.1016/j.cag.2011.03.030</a>.
  ieee: D. Raviv, A. M. Bronstein, M. M. Bronstein, R. Kimmel, and N. Sochen, “Affine-invariant
    geodesic geometry of deformable 3D shapes,” <i>Computers &#38; Graphics</i>, vol.
    35, no. 3. Elsevier, pp. 692–697, 2011.
  ista: Raviv D, Bronstein AM, Bronstein MM, Kimmel R, Sochen N. 2011. Affine-invariant
    geodesic geometry of deformable 3D shapes. Computers &#38; Graphics. 35(3), 692–697.
  mla: Raviv, Dan, et al. “Affine-Invariant Geodesic Geometry of Deformable 3D Shapes.”
    <i>Computers &#38; Graphics</i>, vol. 35, no. 3, Elsevier, 2011, pp. 692–97, doi:<a
    href="https://doi.org/10.1016/j.cag.2011.03.030">10.1016/j.cag.2011.03.030</a>.
  short: D. Raviv, A.M. Bronstein, M.M. Bronstein, R. Kimmel, N. Sochen, Computers
    &#38; Graphics 35 (2011) 692–697.
date_created: 2024-10-15T11:20:54Z
date_published: 2011-06-01T00:00:00Z
date_updated: 2024-11-12T08:37:24Z
day: '01'
doi: 10.1016/j.cag.2011.03.030
extern: '1'
external_id:
  arxiv:
  - '1012.5936'
intvolume: '        35'
issue: '3'
language:
- iso: eng
main_file_link:
- open_access: '1'
  url: https://doi.org/10.48550/arXiv.1012.5936
month: '06'
oa: 1
oa_version: Preprint
page: 692-697
publication: Computers & Graphics
publication_identifier:
  issn:
  - 0097-8493
publication_status: published
publisher: Elsevier
quality_controlled: '1'
scopus_import: '1'
status: public
title: Affine-invariant geodesic geometry of deformable 3D shapes
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 35
year: '2011'
...