---
_id: '18349'
abstract:
- lang: eng
  text: The rapid development of 3D acquisition technology has brought with itself
    the need to perform standard signal processing operations such as filters on 3D
    data. It has been shown that the eigenfunctions of the Laplace-Beltrami operator
    (manifold harmonics) of a surface play the role of the Fourier basis in the Euclidean
    space; it is thus possible to formulate signal analysis and synthesis in the manifold
    harmonics basis. In particular, geometry filtering can be carried out in the manifold
    harmonics domain by decomposing the embedding coordinates of the shape in this
    basis. However, since the basis functions depend on the shape itself, such filtering
    is valid only for weak (near all-pass) filters, and produces severe artifacts
    otherwise. In this paper, we analyze this problem and propose the fractional filtering
    approach, wherein we apply iteratively weak fractional powers of the filter, followed
    by the update of the basis functions. Experimental results show that such a process
    produces more plausible and meaningful results.
alternative_title:
- LNCS
article_processing_charge: No
author:
- first_name: Artiom
  full_name: Kovnatsky, Artiom
  last_name: Kovnatsky
- 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
citation:
  ama: 'Kovnatsky A, Bronstein MM, Bronstein AM. Stable Spectral Mesh Filtering. In:
    <i>Computer Vision, ECCV 2012 - Workshops and Demonstrations</i>. Vol 7583. Springer
    Nature; 2012:83-91. doi:<a href="https://doi.org/10.1007/978-3-642-33863-2_9">10.1007/978-3-642-33863-2_9</a>'
  apa: 'Kovnatsky, A., Bronstein, M. M., &#38; Bronstein, A. M. (2012). Stable Spectral
    Mesh Filtering. In <i>Computer Vision, ECCV 2012 - Workshops and Demonstrations</i>
    (Vol. 7583, pp. 83–91). Florence, Italy: Springer Nature. <a href="https://doi.org/10.1007/978-3-642-33863-2_9">https://doi.org/10.1007/978-3-642-33863-2_9</a>'
  chicago: Kovnatsky, Artiom, Michael M. Bronstein, and Alex M. Bronstein. “Stable
    Spectral Mesh Filtering.” In <i>Computer Vision, ECCV 2012 - Workshops and Demonstrations</i>,
    7583:83–91. Springer Nature, 2012. <a href="https://doi.org/10.1007/978-3-642-33863-2_9">https://doi.org/10.1007/978-3-642-33863-2_9</a>.
  ieee: A. Kovnatsky, M. M. Bronstein, and A. M. Bronstein, “Stable Spectral Mesh
    Filtering,” in <i>Computer Vision, ECCV 2012 - Workshops and Demonstrations</i>,
    Florence, Italy, 2012, vol. 7583, no. Part 1, pp. 83–91.
  ista: 'Kovnatsky A, Bronstein MM, Bronstein AM. 2012. Stable Spectral Mesh Filtering.
    Computer Vision, ECCV 2012 - Workshops and Demonstrations. ECCV: European Conference
    on Computer Vision, LNCS, vol. 7583, 83–91.'
  mla: Kovnatsky, Artiom, et al. “Stable Spectral Mesh Filtering.” <i>Computer Vision,
    ECCV 2012 - Workshops and Demonstrations</i>, vol. 7583, no. Part 1, Springer
    Nature, 2012, pp. 83–91, doi:<a href="https://doi.org/10.1007/978-3-642-33863-2_9">10.1007/978-3-642-33863-2_9</a>.
  short: A. Kovnatsky, M.M. Bronstein, A.M. Bronstein, in:, Computer Vision, ECCV
    2012 - Workshops and Demonstrations, Springer Nature, 2012, pp. 83–91.
conference:
  end_date: 2012-10-13
  location: Florence, Italy
  name: 'ECCV: European Conference on Computer Vision'
  start_date: 2012-10-07
date_created: 2024-10-15T11:20:54Z
date_published: 2012-08-31T00:00:00Z
date_updated: 2025-01-16T11:49:13Z
day: '31'
doi: 10.1007/978-3-642-33863-2_9
extern: '1'
intvolume: '      7583'
issue: Part 1
language:
- iso: eng
month: '08'
oa_version: None
page: 83-91
publication: Computer Vision, ECCV 2012 - Workshops and Demonstrations
publication_identifier:
  isbn:
  - '9783642338625'
  - '9783642338632'
  issn:
  - 0302-9743
  - 1611-3349
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
scopus_import: '1'
status: public
title: Stable Spectral Mesh Filtering
type: conference
user_id: 3E5EF7F0-F248-11E8-B48F-1D18A9856A87
volume: 7583
year: '2012'
...