---
_id: '18287'
abstract:
- lang: eng
  text: Many algorithms for the computation of correspondences between deformable
    shapes rely on some variant of nearest neighbor matching in a descriptor space.
    Such are, for example, various point-wise correspondence recovery algorithms used
    as a post-processing stage in the functional correspondence framework. Such frequently
    used techniques implicitly make restrictive assumptions (e.g., nearisometry) on
    the considered shapes and in practice suffer from lack of accuracy and result
    in poor surjectivity. We propose an alternative recovery technique capable of
    guaranteeing a bijective correspondence and producing significantly higher accuracy
    and smoothness. Unlike other methods our approach does not depend on the assumption
    that the analyzed shapes are isometric. We derive the proposed method from the
    statistical framework of kernel density estimation and demonstrate its performance
    on several challenging deformable 3D shape matching datasets.
article_processing_charge: No
arxiv: 1
author:
- first_name: Matthias
  full_name: Vestner, Matthias
  last_name: Vestner
- first_name: Roee
  full_name: Litman, Roee
  last_name: Litman
- first_name: Emanuele
  full_name: Rodola, Emanuele
  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: Daniel
  full_name: Cremers, Daniel
  last_name: Cremers
citation:
  ama: 'Vestner M, Litman R, Rodola E, Bronstein AM, Cremers D. Product manifold filter:
    Non-rigid shape correspondence via kernel density estimation in the product space.
    In: <i>2017 IEEE Conference on Computer Vision and Pattern Recognition (CVPR)</i>.
    IEEE; 2017:6681-6690. doi:<a href="https://doi.org/10.1109/cvpr.2017.707">10.1109/cvpr.2017.707</a>'
  apa: 'Vestner, M., Litman, R., Rodola, E., Bronstein, A. M., &#38; Cremers, D. (2017).
    Product manifold filter: Non-rigid shape correspondence via kernel density estimation
    in the product space. In <i>2017 IEEE Conference on Computer Vision and Pattern
    Recognition (CVPR)</i> (pp. 6681–6690). Honolulu, HI, United States: IEEE. <a
    href="https://doi.org/10.1109/cvpr.2017.707">https://doi.org/10.1109/cvpr.2017.707</a>'
  chicago: 'Vestner, Matthias, Roee Litman, Emanuele Rodola, Alex M. Bronstein, and
    Daniel Cremers. “Product Manifold Filter: Non-Rigid Shape Correspondence via Kernel
    Density Estimation in the Product Space.” In <i>2017 IEEE Conference on Computer
    Vision and Pattern Recognition (CVPR)</i>, 6681–90. IEEE, 2017. <a href="https://doi.org/10.1109/cvpr.2017.707">https://doi.org/10.1109/cvpr.2017.707</a>.'
  ieee: 'M. Vestner, R. Litman, E. Rodola, A. M. Bronstein, and D. Cremers, “Product
    manifold filter: Non-rigid shape correspondence via kernel density estimation
    in the product space,” in <i>2017 IEEE Conference on Computer Vision and Pattern
    Recognition (CVPR)</i>, Honolulu, HI, United States, 2017, pp. 6681–6690.'
  ista: 'Vestner M, Litman R, Rodola E, Bronstein AM, Cremers D. 2017. Product manifold
    filter: Non-rigid shape correspondence via kernel density estimation in the product
    space. 2017 IEEE Conference on Computer Vision and Pattern Recognition (CVPR).
    30th IEEE Conference on Computer Vision and Pattern Recognition, 6681–6690.'
  mla: 'Vestner, Matthias, et al. “Product Manifold Filter: Non-Rigid Shape Correspondence
    via Kernel Density Estimation in the Product Space.” <i>2017 IEEE Conference on
    Computer Vision and Pattern Recognition (CVPR)</i>, IEEE, 2017, pp. 6681–90, doi:<a
    href="https://doi.org/10.1109/cvpr.2017.707">10.1109/cvpr.2017.707</a>.'
  short: M. Vestner, R. Litman, E. Rodola, A.M. Bronstein, D. Cremers, in:, 2017 IEEE
    Conference on Computer Vision and Pattern Recognition (CVPR), IEEE, 2017, pp.
    6681–6690.
conference:
  end_date: 2017-07-26
  location: Honolulu, HI, United States
  name: 30th IEEE Conference on Computer Vision and Pattern Recognition
  start_date: 2017-07-21
date_created: 2024-10-09T07:49:43Z
date_published: 2017-11-09T00:00:00Z
date_updated: 2024-12-05T14:20:16Z
day: '09'
doi: 10.1109/cvpr.2017.707
extern: '1'
external_id:
  arxiv:
  - '1701.00669'
language:
- iso: eng
main_file_link:
- open_access: '1'
  url: https://doi.org/10.48550/arXiv.1701.00669
month: '11'
oa: 1
oa_version: Preprint
page: 6681 - 6690
publication: 2017 IEEE Conference on Computer Vision and Pattern Recognition (CVPR)
publication_identifier:
  isbn:
  - '9781538604588'
  issn:
  - 1063-6919
publication_status: published
publisher: IEEE
quality_controlled: '1'
scopus_import: '1'
status: public
title: 'Product manifold filter: Non-rigid shape correspondence via kernel density
  estimation in the product space'
type: conference
user_id: 3E5EF7F0-F248-11E8-B48F-1D18A9856A87
year: '2017'
...