Pose space deformation: a unified approach to shape interpolation and skeleton-driven deformation
Proceedings of the 27th annual conference on Computer graphics and interactive techniques
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Proceedings of the 27th annual conference on Computer graphics and interactive techniques
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Deformation transfer for triangle meshes
ACM SIGGRAPH 2004 Papers
ACM SIGGRAPH 2005 Papers
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SMI '06 Proceedings of the IEEE International Conference on Shape Modeling and Applications 2006
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ACM SIGGRAPH 2006 Papers
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IEEE Transactions on Visualization and Computer Graphics
Robust on-line computation of Reeb graphs: simplicity and speed
ACM SIGGRAPH 2007 papers
Geometric modeling in shape space
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ACM SIGGRAPH 2007 papers
Laplace-Beltrami eigenfunctions for deformation invariant shape representation
SGP '07 Proceedings of the fifth Eurographics symposium on Geometry processing
Shape Deformation Using a Skeleton to Drive Simplex Transformations
IEEE Transactions on Visualization and Computer Graphics
Harmonic 1-form based skeleton extraction from examples
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Salient spectral geometric features for shape matching and retrieval
The Visual Computer: International Journal of Computer Graphics
A Minimal Contouring Approach to the Computation of the Reeb Graph
IEEE Transactions on Visualization and Computer Graphics
Multiresolution Mean Shift Clustering Algorithm for Shape Interpolation
IEEE Transactions on Visualization and Computer Graphics
Laplace-Beltrami spectra as 'Shape-DNA' of surfaces and solids
Computer-Aided Design
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MICCAI'07 Proceedings of the 10th international conference on Medical image computing and computer-assisted intervention - Volume Part I
International Journal of Computer Vision
Convergence, stability, and discrete approximation of Laplace spectra
SODA '10 Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms
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We propose a novel method to analyze a set of poses of 3D models that are represented with triangle meshes and unregistered. Different shapes of poses are transformed from the 3D spatial domain to a geometry spectrum domain that is defined by Laplace---Beltrami operator. During this space-spectrum transform, all near-isometric deformations, mesh triangulations and Euclidean transformations are filtered away. The different spatial poses from a 3D model are represented with near-isometric deformations; therefore, they have similar behaviors in the spectral domain. Semantic parts of that model are then determined based on the computed geometric properties of all the mapped vertices in the geometry spectrum domain. Semantic skeleton can be automatically built with joints detected as well. The Laplace---Beltrami operator is proved to be invariant to isometric deformations and Euclidean transformations such as translation and rotation. It also can be invariant to scaling with normalization. The discrete implementation also makes the Laplace---Beltrami operator straightforward to be applied on triangle meshes despite triangulations. Our method turns a rather difficult spatial problem into a spectral problem that is much easier to solve. The applications show that our 3D pose analysis method leads to a registration-free pose analysis and a high-level semantic part understanding of 3D shapes.