Symmetry and Orbit Detection via Lie-Algebra Voting

Zeyun Shi (1) , Pierre Alliez (2) , Mathieu Desbrun (3) , Hujun Bao (1) , Jin Huang (1)

1 State Key Lab CAD&CG [HangZhou]
2 TITANE - Geometric Modeling of 3D Environments
3 CS CALTECH - Computer Science Department

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.

Domaines: Géométrie algorithmique [cs.CG]

Zeyun Shi, Pierre Alliez, Mathieu Desbrun, Hujun Bao, Jin Huang. Symmetry and Orbit Detection via Lie-Algebra Voting. Computer Graphics Forum, 2016, Proceedings of EUROGRAPHICS Symposium on Geometry Processing, pp.12. ⟨hal-01344293⟩