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Robust 3D Shape Correspondence in the Spectral Domain
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Partial and approximate symmetry detection for 3D geometry
ACM SIGGRAPH 2006 Papers
SGP '05 Proceedings of the third Eurographics symposium on Geometry processing
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ACM SIGGRAPH 2008 papers
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Numerical Geometry of Non-Rigid Shapes
Möbius voting for surface correspondence
ACM SIGGRAPH 2009 papers
Partial intrinsic reflectional symmetry of 3D shapes
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SGP '08 Proceedings of the Symposium on Geometry Processing
Deformation-driven shape correspondence
SGP '08 Proceedings of the Symposium on Geometry Processing
Non-rigid registration under isometric deformations
SGP '08 Proceedings of the Symposium on Geometry Processing
A concise and provably informative multi-scale signature based on heat diffusion
SGP '09 Proceedings of the Symposium on Geometry Processing
Full and Partial Symmetries of Non-rigid Shapes
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ACM SIGGRAPH 2010 papers
International Journal of Computer Vision
ACM SIGGRAPH 2011 papers
Exploring collections of 3D models using fuzzy correspondences
ACM Transactions on Graphics (TOG) - SIGGRAPH 2012 Conference Proceedings
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ICCV '11 Proceedings of the 2011 International Conference on Computer Vision
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This paper proposes a novel algorithm that resolves the underlying ambiguity in shape correspondences between symmetric objects. Due to the equivocal nature of symmetry, each part of a symmetric object may have two or more correspondence candidates in another symmetric object, which may induce local inconsistencies in the correspondence of parts or global ambiguities in shape matching. As an effective approach for resolving these symmetric ambiguities, we find multiple probable solutions for consistent shape correspondences between two 3D symmetric objects and let the user select one of them for an application-specific purpose. We formulate the problem of 3D symmetric object correspondences with a Markov Random Field (MRF) and iteratively search multiple solutions by excluding previously found solutions using Linear Programming (LP). The consistency of each solution is provided by four-point correspondences as high-order measurements in our MRF network, with each node corresponding to a point pair and each edge corresponding to a pair of point pairs. By leveraging the properties of the symmetry structure of the 3D object, we further reduce the complexity of our MRF network while efficiently handling high-order measurements. Finally, we evaluate the proposed algorithm using real-world symmetric object datasets.