article

Accurate detection of symmetries in 3D shapes

Authors:

Aurélien Martinet,

Nicolas Holzschuch,

François X. SillionAuthors Info & Claims

ACM Transactions on Graphics (TOG), Volume 25, Issue 2

Pages 439 - 464

https://doi.org/10.1145/1138450.1138462

Published: 01 April 2006 Publication History

Abstract

We propose an automatic method for finding symmetries of 3D shapes, that is, isometric transforms which leave a shape globally unchanged. These symmetries are deterministically found through the use of an intermediate quantity: the generalized moments. By examining the extrema and spherical harmonic coefficients of these moments, we recover the parameters of the symmetries of the shape. The computation for large composite models is made efficient by using this information in an incremental algorithm capable of recovering the symmetries of a whole shape using the symmetries of its subparts. Applications of this work range from coherent remeshing of geometry with respect to the symmetries of a shape to geometric compression, intelligent mesh editing, and automatic instantiation.

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Cited By

Nagar R(2025)Robust extrinsic symmetry estimation in 3D point cloudsThe Visual Computer: International Journal of Computer Graphics10.1007/s00371-024-03313-641:1(115-128)Online publication date: 1-Jan-2025
https://dl.acm.org/doi/10.1007/s00371-024-03313-6
He YFang QZhang ZDai TWu KLiu LFu X(2024)Symmetric Piecewise Developable ApproximationsComputer Graphics Forum10.1111/cgf.1524243:7Online publication date: 24-Oct-2024
https://doi.org/10.1111/cgf.15242
Wang YLuo C(2024)Key-Axis-Based Localization of Symmetry Axes in 3D Objects Utilizing Geometry and TextureIEEE Transactions on Image Processing10.1109/TIP.2024.351580133(6720-6733)Online publication date: 1-Jan-2024
https://dl.acm.org/doi/10.1109/TIP.2024.3515801
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Index Terms

Accurate detection of symmetries in 3D shapes
1. Computing methodologies
  1. Computer graphics
    1. Shape modeling
      1. Parametric curve and surface models
      2. Volumetric models

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Published In

cover image ACM Transactions on Graphics

ACM Transactions on Graphics Volume 25, Issue 2

April 2006

288 pages

ISSN:0730-0301

EISSN:1557-7368

DOI:10.1145/1138450

Issue’s Table of Contents

Copyright © 2006 ACM.

Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected]

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Publication History

Published: 01 April 2006

Published in TOG Volume 25, Issue 2

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Citations

Cited By

Nagar R(2025)Robust extrinsic symmetry estimation in 3D point cloudsThe Visual Computer: International Journal of Computer Graphics10.1007/s00371-024-03313-641:1(115-128)Online publication date: 1-Jan-2025
https://dl.acm.org/doi/10.1007/s00371-024-03313-6
He YFang QZhang ZDai TWu KLiu LFu X(2024)Symmetric Piecewise Developable ApproximationsComputer Graphics Forum10.1111/cgf.1524243:7Online publication date: 24-Oct-2024
https://doi.org/10.1111/cgf.15242
Wang YLuo C(2024)Key-Axis-Based Localization of Symmetry Axes in 3D Objects Utilizing Geometry and TextureIEEE Transactions on Image Processing10.1109/TIP.2024.351580133(6720-6733)Online publication date: 1-Jan-2024
https://dl.acm.org/doi/10.1109/TIP.2024.3515801
Li RZhang LLi CLai YGao L(2023)E3Sym: Leveraging E(3) Invariance for Unsupervised 3D Planar Reflective Symmetry Detection2023 IEEE/CVF International Conference on Computer Vision (ICCV)10.1109/ICCV51070.2023.01337(14497-14507)Online publication date: 1-Oct-2023
https://doi.org/10.1109/ICCV51070.2023.01337
Niu WHuang XXiang HWang XJi SZhang F(2023)A symmetry-aware alignment method for photogrammetric 3D modelsISPRS Journal of Photogrammetry and Remote Sensing10.1016/j.isprsjprs.2023.09.004204(184-208)Online publication date: Oct-2023
https://doi.org/10.1016/j.isprsjprs.2023.09.004
Figueiredo LIvson PCeles W(2023)Unsupervised method for identifying shape instances on 3D CAD modelsComputers & Graphics10.1016/j.cag.2023.08.018116(228-238)Online publication date: Nov-2023
https://doi.org/10.1016/j.cag.2023.08.018
Nguyen TNguyen TTran T(2022)Projection of semi-shapes for rotational symmetry detection2022 26th International Conference on Pattern Recognition (ICPR)10.1109/ICPR56361.2022.9956227(196-202)Online publication date: 21-Aug-2022
https://doi.org/10.1109/ICPR56361.2022.9956227
Walter LFrancoeur M(2022)Orientation effects on near-field radiative heat transfer between complex-shaped dielectric particlesApplied Physics Letters10.1063/5.0116828121:18Online publication date: 3-Nov-2022
https://doi.org/10.1063/5.0116828
Hruda LKolingerová ILávička MMaňák M(2022)Rotational symmetry detection in 3D using reflectional symmetry candidates and quaternion-based rotation parameterizationComputer Aided Geometric Design10.1016/j.cagd.2022.10213898(102138)Online publication date: Oct-2022
https://doi.org/10.1016/j.cagd.2022.102138
Bizzarri MLávička MVršek J(2022)Approximate symmetries of perturbed planar discrete curvesComputer Aided Geometric Design10.1016/j.cagd.2022.10211596(102115)Online publication date: Jun-2022
https://doi.org/10.1016/j.cagd.2022.102115
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