---
_id: '18380'
abstract:
- lang: eng
  text: This work presents a novel approach for detecting inliers in a given set of
    correspondences (matches). It does so without explicitly identifying any consensus
    set, based on a method for inlier rate estimation (IRE). Given such an estimator
    for the inlier rate, we also present an algorithm that detects a globally optimal
    transformation. We provide a theoretical analysis of the IRE method using a stochastic
    generative model on the continuous spaces of matches and transformations. This
    model allows rigorous investigation of the limits of our IRE method for the case
    of 2D-translation, further giving bounds and insights for the more general case.
    Our theoretical analysis is validated empirically and is shown to hold in practice
    for the more general case of 2D-affinities. In addition, we show that the combined
    framework works on challenging cases of 2D-homography estimation, with very few
    and possibly noisy inliers, where RANSAC generally fails.
article_number: '7299161'
article_processing_charge: No
author:
- first_name: Roee
  full_name: Litman, Roee
  last_name: Litman
- first_name: Simon
  full_name: Korman, Simon
  last_name: Korman
- first_name: Alexander
  full_name: Bronstein, Alexander
  id: 58f3726e-7cba-11ef-ad8b-e6e8cb3904e6
  last_name: Bronstein
  orcid: 0000-0001-9699-8730
- first_name: Shai
  full_name: Avidan, Shai
  last_name: Avidan
citation:
  ama: 'Litman R, Korman S, Bronstein AM, Avidan S. Inverting RANSAC: Global model
    detection via inlier rate estimation. In: <i>2015 IEEE Conference on Computer
    Vision and Pattern Recognition (CVPR)</i>. IEEE; 2015. doi:<a href="https://doi.org/10.1109/cvpr.2015.7299161">10.1109/cvpr.2015.7299161</a>'
  apa: 'Litman, R., Korman, S., Bronstein, A. M., &#38; Avidan, S. (2015). Inverting
    RANSAC: Global model detection via inlier rate estimation. In <i>2015 IEEE Conference
    on Computer Vision and Pattern Recognition (CVPR)</i>. Boston, MA, United States:
    IEEE. <a href="https://doi.org/10.1109/cvpr.2015.7299161">https://doi.org/10.1109/cvpr.2015.7299161</a>'
  chicago: 'Litman, Roee, Simon Korman, Alex M. Bronstein, and Shai Avidan. “Inverting
    RANSAC: Global Model Detection via Inlier Rate Estimation.” In <i>2015 IEEE Conference
    on Computer Vision and Pattern Recognition (CVPR)</i>. IEEE, 2015. <a href="https://doi.org/10.1109/cvpr.2015.7299161">https://doi.org/10.1109/cvpr.2015.7299161</a>.'
  ieee: 'R. Litman, S. Korman, A. M. Bronstein, and S. Avidan, “Inverting RANSAC:
    Global model detection via inlier rate estimation,” in <i>2015 IEEE Conference
    on Computer Vision and Pattern Recognition (CVPR)</i>, Boston, MA, United States,
    2015.'
  ista: 'Litman R, Korman S, Bronstein AM, Avidan S. 2015. Inverting RANSAC: Global
    model detection via inlier rate estimation. 2015 IEEE Conference on Computer Vision
    and Pattern Recognition (CVPR). IEEE Conference on Computer Vision and Pattern
    Recognition, 7299161.'
  mla: 'Litman, Roee, et al. “Inverting RANSAC: Global Model Detection via Inlier
    Rate Estimation.” <i>2015 IEEE Conference on Computer Vision and Pattern Recognition
    (CVPR)</i>, 7299161, IEEE, 2015, doi:<a href="https://doi.org/10.1109/cvpr.2015.7299161">10.1109/cvpr.2015.7299161</a>.'
  short: R. Litman, S. Korman, A.M. Bronstein, S. Avidan, in:, 2015 IEEE Conference
    on Computer Vision and Pattern Recognition (CVPR), IEEE, 2015.
conference:
  end_date: 2015-06-12
  location: Boston, MA, United States
  name: IEEE Conference on Computer Vision and Pattern Recognition
  start_date: 2015-06-07
date_created: 2024-10-15T11:20:54Z
date_published: 2015-10-15T00:00:00Z
date_updated: 2024-12-04T14:06:06Z
day: '15'
doi: 10.1109/cvpr.2015.7299161
extern: '1'
language:
- iso: eng
month: '10'
oa_version: None
publication: 2015 IEEE Conference on Computer Vision and Pattern Recognition (CVPR)
publication_identifier:
  eissn:
  - 1063-6919
  isbn:
  - '9781467369640'
publication_status: published
publisher: IEEE
quality_controlled: '1'
scopus_import: '1'
status: public
title: 'Inverting RANSAC: Global model detection via inlier rate estimation'
type: conference
user_id: 3E5EF7F0-F248-11E8-B48F-1D18A9856A87
year: '2015'
...
---
_id: '18378'
abstract:
- lang: eng
  text: 'In this work, we present intrinsic shape context (ISC) descriptors for 3D
    shapes. We generalize to surfaces the polar sampling of the image domain used
    in shape contexts: for this purpose, we chart the surface by shooting geodesic
    outwards from the point being analyzed; `angle'' is treated as tantamount to geodesic
    shooting direction, and radius as geodesic distance. To deal with orientation
    ambiguity, we exploit properties of the Fourier transform. Our charting method
    is intrinsic, i.e., invariant to isometric shape transformations. The resulting
    descriptor is a meta-descriptor that can be applied to any photometric or geometric
    property field defined on the shape, in particular, we can leverage recent developments
    in intrinsic shape analysis and construct ISC based on state-of-the-art dense
    shape descriptors such as heat kernel signatures. Our experiments demonstrate
    a notable improvement in shape matching on standard benchmarks.'
article_number: '6247671'
article_processing_charge: No
author:
- first_name: I.
  full_name: Kokkinos, I.
  last_name: Kokkinos
- first_name: M. M.
  full_name: Bronstein, M. M.
  last_name: Bronstein
- 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
citation:
  ama: 'Kokkinos I, Bronstein MM, Litman R, Bronstein AM. Intrinsic shape context
    descriptors for deformable shapes. In: <i>2012 IEEE Conference on Computer Vision
    and Pattern Recognition</i>. IEEE; 2012. doi:<a href="https://doi.org/10.1109/cvpr.2012.6247671">10.1109/cvpr.2012.6247671</a>'
  apa: 'Kokkinos, I., Bronstein, M. M., Litman, R., &#38; Bronstein, A. M. (2012).
    Intrinsic shape context descriptors for deformable shapes. In <i>2012 IEEE Conference
    on Computer Vision and Pattern Recognition</i>. Providence, RI, United States:
    IEEE. <a href="https://doi.org/10.1109/cvpr.2012.6247671">https://doi.org/10.1109/cvpr.2012.6247671</a>'
  chicago: Kokkinos, I., M. M. Bronstein, R. Litman, and Alex M. Bronstein. “Intrinsic
    Shape Context Descriptors for Deformable Shapes.” In <i>2012 IEEE Conference on
    Computer Vision and Pattern Recognition</i>. IEEE, 2012. <a href="https://doi.org/10.1109/cvpr.2012.6247671">https://doi.org/10.1109/cvpr.2012.6247671</a>.
  ieee: I. Kokkinos, M. M. Bronstein, R. Litman, and A. M. Bronstein, “Intrinsic shape
    context descriptors for deformable shapes,” in <i>2012 IEEE Conference on Computer
    Vision and Pattern Recognition</i>, Providence, RI, United States, 2012.
  ista: Kokkinos I, Bronstein MM, Litman R, Bronstein AM. 2012. Intrinsic shape context
    descriptors for deformable shapes. 2012 IEEE Conference on Computer Vision and
    Pattern Recognition. IEEE Conference on Computer Vision and Pattern Recognition,
    6247671.
  mla: Kokkinos, I., et al. “Intrinsic Shape Context Descriptors for Deformable Shapes.”
    <i>2012 IEEE Conference on Computer Vision and Pattern Recognition</i>, 6247671,
    IEEE, 2012, doi:<a href="https://doi.org/10.1109/cvpr.2012.6247671">10.1109/cvpr.2012.6247671</a>.
  short: I. Kokkinos, M.M. Bronstein, R. Litman, A.M. Bronstein, in:, 2012 IEEE Conference
    on Computer Vision and Pattern Recognition, IEEE, 2012.
conference:
  end_date: 2012-06-21
  location: Providence, RI, United States
  name: IEEE Conference on Computer Vision and Pattern Recognition
  start_date: 2012-06-16
date_created: 2024-10-15T11:20:54Z
date_published: 2012-07-26T00:00:00Z
date_updated: 2024-12-04T12:27:48Z
day: '26'
doi: 10.1109/cvpr.2012.6247671
extern: '1'
language:
- iso: eng
month: '07'
oa_version: None
publication: 2012 IEEE Conference on Computer Vision and Pattern Recognition
publication_identifier:
  eissn:
  - 1063-6919
  isbn:
  - '9781467312264'
publication_status: published
publisher: IEEE
quality_controlled: '1'
scopus_import: '1'
status: public
title: Intrinsic shape context descriptors for deformable shapes
type: conference
user_id: 3E5EF7F0-F248-11E8-B48F-1D18A9856A87
year: '2012'
...
---
_id: '18379'
abstract:
- lang: eng
  text: We consider the problem of minimum distortion intrinsic correspondence between
    deformable shapes, many useful formulations of which give rise to the NP-hard
    quadratic assignment problem (QAP). Previous attempts to use the spectral relaxation
    have had limited success due to the lack of sparsity of the obtained “fuzzy” solution.
    In this paper, we adopt the recently introduced alternative L 1 relaxation of
    the QAP based on the principles of game theory. We relate it to the Gromov and
    Lipschitz metrics between metric spaces and demonstrate on state-of-the-art benchmarks
    that the proposed approach is capable of finding very accurate sparse correspondences
    between deformable shapes.
article_number: '6247674'
article_processing_charge: No
author:
- first_name: E.
  full_name: Rodola, E.
  last_name: Rodola
- first_name: Alexander
  full_name: Bronstein, Alexander
  id: 58f3726e-7cba-11ef-ad8b-e6e8cb3904e6
  last_name: Bronstein
  orcid: 0000-0001-9699-8730
- first_name: A.
  full_name: Albarelli, A.
  last_name: Albarelli
- first_name: F.
  full_name: Bergamasco, F.
  last_name: Bergamasco
- first_name: A.
  full_name: Torsello, A.
  last_name: Torsello
citation:
  ama: 'Rodola E, Bronstein AM, Albarelli A, Bergamasco F, Torsello A. A game-theoretic
    approach to deformable shape matching. In: <i>2012 IEEE Conference on Computer
    Vision and Pattern Recognition</i>. IEEE; 2012. doi:<a href="https://doi.org/10.1109/cvpr.2012.6247674">10.1109/cvpr.2012.6247674</a>'
  apa: 'Rodola, E., Bronstein, A. M., Albarelli, A., Bergamasco, F., &#38; Torsello,
    A. (2012). A game-theoretic approach to deformable shape matching. In <i>2012
    IEEE Conference on Computer Vision and Pattern Recognition</i>. Providence, RI,
    United States: IEEE. <a href="https://doi.org/10.1109/cvpr.2012.6247674">https://doi.org/10.1109/cvpr.2012.6247674</a>'
  chicago: Rodola, E., Alex M. Bronstein, A. Albarelli, F. Bergamasco, and A. Torsello.
    “A Game-Theoretic Approach to Deformable Shape Matching.” In <i>2012 IEEE Conference
    on Computer Vision and Pattern Recognition</i>. IEEE, 2012. <a href="https://doi.org/10.1109/cvpr.2012.6247674">https://doi.org/10.1109/cvpr.2012.6247674</a>.
  ieee: E. Rodola, A. M. Bronstein, A. Albarelli, F. Bergamasco, and A. Torsello,
    “A game-theoretic approach to deformable shape matching,” in <i>2012 IEEE Conference
    on Computer Vision and Pattern Recognition</i>, Providence, RI, United States,
    2012.
  ista: Rodola E, Bronstein AM, Albarelli A, Bergamasco F, Torsello A. 2012. A game-theoretic
    approach to deformable shape matching. 2012 IEEE Conference on Computer Vision
    and Pattern Recognition. IEEE Conference on Computer Vision and Pattern Recognition,
    6247674.
  mla: Rodola, E., et al. “A Game-Theoretic Approach to Deformable Shape Matching.”
    <i>2012 IEEE Conference on Computer Vision and Pattern Recognition</i>, 6247674,
    IEEE, 2012, doi:<a href="https://doi.org/10.1109/cvpr.2012.6247674">10.1109/cvpr.2012.6247674</a>.
  short: E. Rodola, A.M. Bronstein, A. Albarelli, F. Bergamasco, A. Torsello, in:,
    2012 IEEE Conference on Computer Vision and Pattern Recognition, IEEE, 2012.
conference:
  end_date: 2012-06-21
  location: Providence, RI, United States
  name: IEEE Conference on Computer Vision and Pattern Recognition
  start_date: 2012-06-16
date_created: 2024-10-15T11:20:54Z
date_published: 2012-07-26T00:00:00Z
date_updated: 2024-12-04T12:22:03Z
day: '26'
doi: 10.1109/cvpr.2012.6247674
extern: '1'
language:
- iso: eng
month: '07'
oa_version: None
publication: 2012 IEEE Conference on Computer Vision and Pattern Recognition
publication_identifier:
  eissn:
  - 1063-6919
  isbn:
  - 978-1-4673-1226-4
publication_status: published
publisher: IEEE
quality_controlled: '1'
scopus_import: '1'
status: public
title: A game-theoretic approach to deformable shape matching
type: conference
user_id: 3E5EF7F0-F248-11E8-B48F-1D18A9856A87
year: '2012'
...
---
_id: '18377'
abstract:
- lang: eng
  text: We introduce an (equi-)affine invariant diffusion geometry by which surfaces
    that go through squeeze and shear transformations can still be properly analyzed.
    The definition of an affine invariant metric enables us to construct an invariant
    Laplacian from which local and global geometric structures are extracted. Applications
    of the proposed framework demonstrate its power in generalizing and enriching
    the existing set of tools for shape analysis.
article_number: '5995486'
article_processing_charge: No
arxiv: 1
author:
- first_name: Dan
  full_name: Raviv, Dan
  last_name: Raviv
- first_name: Michael M.
  full_name: Bronstein, Michael M.
  last_name: Bronstein
- first_name: Alexander
  full_name: Bronstein, Alexander
  id: 58f3726e-7cba-11ef-ad8b-e6e8cb3904e6
  last_name: Bronstein
  orcid: 0000-0001-9699-8730
- 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 MM, Bronstein AM, Kimmel R, Sochen N. Affine-invariant
    diffusion geometry for the analysis of deformable 3D shapes. In: <i>CVPR 2011</i>.
    IEEE; 2011. doi:<a href="https://doi.org/10.1109/cvpr.2011.5995486">10.1109/cvpr.2011.5995486</a>'
  apa: 'Raviv, D., Bronstein, M. M., Bronstein, A. M., Kimmel, R., &#38; Sochen, N.
    (2011). Affine-invariant diffusion geometry for the analysis of deformable 3D
    shapes. In <i>CVPR 2011</i>. Colorado Springs, CO, United States: IEEE. <a href="https://doi.org/10.1109/cvpr.2011.5995486">https://doi.org/10.1109/cvpr.2011.5995486</a>'
  chicago: Raviv, Dan, Michael M. Bronstein, Alex M. Bronstein, Ron Kimmel, and Nir
    Sochen. “Affine-Invariant Diffusion Geometry for the Analysis of Deformable 3D
    Shapes.” In <i>CVPR 2011</i>. IEEE, 2011. <a href="https://doi.org/10.1109/cvpr.2011.5995486">https://doi.org/10.1109/cvpr.2011.5995486</a>.
  ieee: D. Raviv, M. M. Bronstein, A. M. Bronstein, R. Kimmel, and N. Sochen, “Affine-invariant
    diffusion geometry for the analysis of deformable 3D shapes,” in <i>CVPR 2011</i>,
    Colorado Springs, CO, United States, 2011.
  ista: Raviv D, Bronstein MM, Bronstein AM, Kimmel R, Sochen N. 2011. Affine-invariant
    diffusion geometry for the analysis of deformable 3D shapes. CVPR 2011. IEEE Computer
    Vision and Pattern Recognition (CVPR) 2011, 5995486.
  mla: Raviv, Dan, et al. “Affine-Invariant Diffusion Geometry for the Analysis of
    Deformable 3D Shapes.” <i>CVPR 2011</i>, 5995486, IEEE, 2011, doi:<a href="https://doi.org/10.1109/cvpr.2011.5995486">10.1109/cvpr.2011.5995486</a>.
  short: D. Raviv, M.M. Bronstein, A.M. Bronstein, R. Kimmel, N. Sochen, in:, CVPR
    2011, IEEE, 2011.
conference:
  end_date: 2011-06-25
  location: Colorado Springs, CO, United States
  name: IEEE Computer Vision and Pattern Recognition (CVPR) 2011
  start_date: 2011-06-20
date_created: 2024-10-15T11:20:54Z
date_published: 2011-08-22T00:00:00Z
date_updated: 2024-12-05T14:15:22Z
day: '22'
doi: 10.1109/cvpr.2011.5995486
extern: '1'
external_id:
  arxiv:
  - '1012.5933'
language:
- iso: eng
main_file_link:
- open_access: '1'
  url: https://doi.org/10.48550/arXiv.1012.5933
month: '08'
oa: 1
oa_version: Preprint
publication: CVPR 2011
publication_identifier:
  eissn:
  - 1063-6919
  isbn:
  - '9781457703942'
publication_status: published
publisher: IEEE
quality_controlled: '1'
status: public
title: Affine-invariant diffusion geometry for the analysis of deformable 3D shapes
type: conference
user_id: 3E5EF7F0-F248-11E8-B48F-1D18A9856A87
year: '2011'
...