Symmetry and Orbit Detection via Lie-Algebra Voting

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Date
2016
Journal Title
Journal ISSN
Volume Title
Publisher
The Eurographics Association and John Wiley & Sons Ltd.
Abstract
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.
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@article{
10.1111:cgf.12978
, journal = {Computer Graphics Forum}, title = {{
Symmetry and Orbit Detection via Lie-Algebra Voting
}}, author = {
Shi, Zeyun
and
Alliez, Pierre
and
Desbrun, Mathieu
and
Bao, Hujun
and
Huang, Jin
}, year = {
2016
}, publisher = {
The Eurographics Association and John Wiley & Sons Ltd.
}, ISSN = {
1467-8659
}, DOI = {
10.1111/cgf.12978
} }
Citation