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Symmetry and Orbit Detection via Lie‐Algebra Voting
Author(s) -
Shi Zeyun,
Alliez Pierre,
Desbrun Mathieu,
Bao Hujun,
Huang Jin
Publication year - 2016
Publication title -
computer graphics forum
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.578
H-Index - 120
eISSN - 1467-8659
pISSN - 0167-7055
DOI - 10.1111/cgf.12978
Subject(s) - homogeneous space , lie group , computer science , linear subspace , invariant (physics) , robustness (evolution) , logarithm , voting , lie algebra , transformation geometry , symmetry (geometry) , orbit (dynamics) , algebra over a field , algorithm , artificial intelligence , pure mathematics , mathematics , geometry , mathematical analysis , biochemistry , chemistry , engineering , politics , political science , law , mathematical physics , gene , aerospace engineering
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.