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Symmetry and Orbit Detection via Lie-Algebra Voting

Shi, Zeyun and Alliez, Pierre and Desbrun, Mathieu and Bao, Hujun and Huang, Jin (2016) Symmetry and Orbit Detection via Lie-Algebra Voting. Computer Graphics Forum, 35 (5). pp. 217-227. ISSN 0167-7055. doi:10.1111/cgf.12978.

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In this paper, we formulate an automatic approach to the detection of partial, local, and global symmetries and orbits in arbitrary 3D datasets. We improve upon existing voting-based symmetry detection techniques by leveraging the Lie group structure of geometric transformations. In particular, we introduce a logarithmic mapping that ensures that orbits are mapped to linear subspaces, hence unifying and extending many existing mappings in a single Lie-algebra voting formulation. Compared to previous work, our resulting method offers significantly improved robustness as it guarantees that our symmetry detection of an input model is frame, scale, and reflection invariant. As a consequence, we demonstrate that our approach efficiently and reliably discovers symmetries and orbits of geometric datasets without requiring heavy parameter tuning.

Item Type:Article
Related URLs:
URLURL TypeDescription Material
Desbrun, Mathieu0000-0003-3424-6079
Additional Information:© 2016 The Author(s) Computer Graphics Forum © 2016 The Eurographics Association and John Wiley & Sons Ltd. Published by John Wiley & Sons Ltd. We would like to thank the anonymous reviewers for their valuable comments and suggestions. This work was partially supported by NSFC (No. 61522209, No. 61210007), the Fundamental Research Funds for the Central Universities (No. 2015XZZX004-19), the European Research Council (ERC Starting Grant “Robust Geometry Processing” #257474), and the National Science Foundation’s grant CCF-1011944.
Group:Applied Geometry
Funding AgencyGrant Number
National Science Foundation of China61522209
National Science Foundation of China61210007
Federal Research Funds for the Central Universities2015XZZX004-19
European Research Council (ERC)257474
Issue or Number:5
Record Number:CaltechAUTHORS:20160630-141056845
Persistent URL:
Official Citation:Shi, Z., Alliez, P., Desbrun, M., Bao, H. and Huang, J. (2016), Symmetry and Orbit Detection via Lie-Algebra Voting. Computer Graphics Forum, 35: 217–227. doi: 10.1111/cgf.12978
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:68791
Deposited By: Joy Painter
Deposited On:30 Jun 2016 21:51
Last Modified:11 Nov 2021 04:04

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