Symmetry and Orbit Detection via Lie-Algebra Voting

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dc.contributor.authorShi, Zeyunen_US
dc.contributor.authorAlliez, Pierreen_US
dc.contributor.authorDesbrun, Mathieuen_US
dc.contributor.authorBao, Hujunen_US
dc.contributor.authorHuang, Jinen_US
dc.contributor.editorMaks Ovsjanikov and Daniele Panozzoen_US
dc.date.accessioned2016-06-17T14:12:09Z
dc.date.available2016-06-17T14:12:09Z
dc.date.issued2016en_US
dc.description.abstractIn 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.en_US
dc.description.number5en_US
dc.description.sectionheadersStructuresen_US
dc.description.seriesinformationComputer Graphics Forumen_US
dc.description.volume35en_US
dc.identifier.doi10.1111/cgf.12978en_US
dc.identifier.issn1467-8659en_US
dc.identifier.pages217-227en_US
dc.identifier.urihttps://doi.org/10.1111/cgf.12978en_US
dc.publisherThe Eurographics Association and John Wiley & Sons Ltd.en_US
dc.subjecten_US
dc.titleSymmetry and Orbit Detection via Lie-Algebra Votingen_US
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35-Issue 5
SGP16: Eurographics Symposium on Geometry Processing (CGF 35-5)