---
_id: '18339'
abstract:
- lang: eng
  text: Automatic detection of symmetries, regularity, and repetitive structures in
    3D geometry is a fundamental problem in shape analysis and pattern recognition
    with applications in computer vision and graphics. Especially challenging is to
    detect intrinsic regularity, where the repetitions are on an intrinsic grid, without
    any apparent Euclidean pattern to describe the shape, but rising out of (near)
    isometric deformation of the underlying surface. In this paper, we employ multidimensional
    scaling to reduce the problem of intrinsic structure detection to a simpler problem
    of 2D grid detection. Potential 2D grids are then identified using an autocorrelation
    analysis, refined using local fitting, validated, and finally projected back to
    the spatial domain. We test the detection algorithm on a variety of scanned plaster
    models in presence of imperfections like missing data, noise and outliers. We
    also present a range of applications including scan completion, shape editing,
    super-resolution, and structural correspondence.
acknowledgement: We thank Helmut Pottmann and the anonymous reviewers for their comments
  and helpful suggestions. Niloy Mitra was partially supported by a Microsoft outstanding
  young faculty fellowship.
alternative_title:
- LNCS
article_processing_charge: No
author:
- first_name: Niloy J.
  full_name: Mitra, Niloy J.
  last_name: Mitra
- first_name: Alexander
  full_name: Bronstein, Alexander
  id: 58f3726e-7cba-11ef-ad8b-e6e8cb3904e6
  last_name: Bronstein
  orcid: 0000-0001-9699-8730
- first_name: Michael
  full_name: Bronstein, Michael
  last_name: Bronstein
citation:
  ama: 'Mitra NJ, Bronstein AM, Bronstein M. Intrinsic regularity detection in 3D
    geometry. In: <i>11th European Conference on Computer Vision</i>. Vol 6313. Springer
    Nature; 2010:398–410. doi:<a href="https://doi.org/10.1007/978-3-642-15558-1_29">10.1007/978-3-642-15558-1_29</a>'
  apa: 'Mitra, N. J., Bronstein, A. M., &#38; Bronstein, M. (2010). Intrinsic regularity
    detection in 3D geometry. In <i>11th European Conference on Computer Vision</i>
    (Vol. 6313, pp. 398–410). Heraklion, Greece: Springer Nature. <a href="https://doi.org/10.1007/978-3-642-15558-1_29">https://doi.org/10.1007/978-3-642-15558-1_29</a>'
  chicago: Mitra, Niloy J., Alex M. Bronstein, and Michael Bronstein. “Intrinsic Regularity
    Detection in 3D Geometry.” In <i>11th European Conference on Computer Vision</i>,
    6313:398–410. Springer Nature, 2010. <a href="https://doi.org/10.1007/978-3-642-15558-1_29">https://doi.org/10.1007/978-3-642-15558-1_29</a>.
  ieee: N. J. Mitra, A. M. Bronstein, and M. Bronstein, “Intrinsic regularity detection
    in 3D geometry,” in <i>11th European Conference on Computer Vision</i>, Heraklion,
    Greece, 2010, vol. 6313, pp. 398–410.
  ista: 'Mitra NJ, Bronstein AM, Bronstein M. 2010. Intrinsic regularity detection
    in 3D geometry. 11th European Conference on Computer Vision. ECCV: European Conference
    on Computer Vision, LNCS, vol. 6313, 398–410.'
  mla: Mitra, Niloy J., et al. “Intrinsic Regularity Detection in 3D Geometry.” <i>11th
    European Conference on Computer Vision</i>, vol. 6313, Springer Nature, 2010,
    pp. 398–410, doi:<a href="https://doi.org/10.1007/978-3-642-15558-1_29">10.1007/978-3-642-15558-1_29</a>.
  short: N.J. Mitra, A.M. Bronstein, M. Bronstein, in:, 11th European Conference on
    Computer Vision, Springer Nature, 2010, pp. 398–410.
conference:
  end_date: 2010-09-10
  location: Heraklion, Greece
  name: 'ECCV: European Conference on Computer Vision'
  start_date: 2010-09-05
date_created: 2024-10-15T11:20:54Z
date_published: 2010-01-01T00:00:00Z
date_updated: 2024-11-18T14:31:56Z
doi: 10.1007/978-3-642-15558-1_29
extern: '1'
intvolume: '      6313'
language:
- iso: eng
month: '01'
oa_version: None
page: 398–410
publication: 11th European Conference on Computer Vision
publication_identifier:
  isbn:
  - '9783642155574'
  - '9783642155581'
  issn:
  - 0302-9743
  - 1611-3349
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
scopus_import: '1'
status: public
title: Intrinsic regularity detection in 3D geometry
type: conference
user_id: ea97e931-d5af-11eb-85d4-e6957dddbf17
volume: 6313
year: '2010'
...