Group Representation of Global Intrinsic Symmetries

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dc.contributor.authorWang, Huien_US
dc.contributor.authorHuang, Huien_US
dc.contributor.editorJernej Barbic and Wen-Chieh Lin and Olga Sorkine-Hornungen_US
dc.date.accessioned2017-10-16T05:23:48Z
dc.date.available2017-10-16T05:23:48Z
dc.date.issued2016
dc.description.abstractGlobal intrinsic symmetry detection of 3D shapes has received considerable attentions in recent years. However, unlike extrinsic symmetry that can be represented compactly as a combination of an orthogonal matrix and a translation vector, representing the global intrinsic symmetry itself is still challenging. Most previous works based on point-to-point representations of global intrinsic symmetries can only find reflectional symmetries, and are inadequate for describing the structure of a global intrinsic symmetry group. In this paper, we propose a novel group representation of global intrinsic symmetries, which describes each global intrinsic symmetry as a linear transformation of functional space on shapes. If the eigenfunctions of the Laplace-Beltrami operator on shapes are chosen as the basis of functional space, the group representation has a block diagonal structure. We thus prove that the group representation of each symmetry can be uniquely determined from a small number of symmetric pairs of points under certain conditions, where the number of pairs is equal to the maximum multiplicity of eigenvalues of the Laplace- Beltrami operator. Based on solid theoretical analysis, we propose an efficient global intrinsic symmetry detection method, which is the first one able to detect all reflectional and rotational global intrinsic symmetries with a clear group structure description. Experimental results demonstrate the effectiveness of our approach.en_US
dc.description.number7
dc.description.sectionheadersAnalyzing Geometries
dc.description.seriesinformationComputer Graphics Forum
dc.description.volume36
dc.identifier.doi10.1111/cgf.13271
dc.identifier.issn1467-8659
dc.identifier.pages51-61
dc.identifier.urihttps://doi.org/10.1111/cgf.13271
dc.identifier.urihttps://diglib.eg.org:443/handle/10.1111/cgf13271
dc.publisherThe Eurographics Association and John Wiley & Sons Ltd.en_US
dc.subjectI.3.5 [Computer Graphics]
dc.subjectComputer Graphics/Computational Geometry and Object Modeling
dc.subject[Geometric algorithms
dc.subjectlanguages
dc.subjectand systems]
dc.titleGroup Representation of Global Intrinsic Symmetriesen_US
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