A Method for Registration of 3-D Shapes
IEEE Transactions on Pattern Analysis and Machine Intelligence - Special issue on interpretation of 3-D scenes—part II
SCAPE: shape completion and animation of people
ACM SIGGRAPH 2005 Papers
Laplace-Beltrami eigenfunctions for deformation invariant shape representation
SGP '07 Proceedings of the fifth Eurographics symposium on Geometry processing
Numerical Geometry of Non-Rigid Shapes
Numerical Geometry of Non-Rigid Shapes
Möbius voting for surface correspondence
ACM SIGGRAPH 2009 papers
Technical Section: Consistent segmentation of 3D models
Computers and Graphics
Global intrinsic symmetries of shapes
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
Learning 3D mesh segmentation and labeling
ACM SIGGRAPH 2010 papers
Style-content separation by anisotropic part scales
ACM SIGGRAPH Asia 2010 papers
ACM SIGGRAPH 2011 papers
Template-Based 3D Model Fitting Using Dual-Domain Relaxation
IEEE Transactions on Visualization and Computer Graphics
Joint shape segmentation with linear programming
Proceedings of the 2011 SIGGRAPH Asia Conference
A correspondence-less approach to matching of deformable shapes
SSVM'11 Proceedings of the Third international conference on Scale Space and Variational Methods in Computer Vision
Computer Graphics Forum
An optimization approach for extracting and encoding consistent maps in a shape collection
ACM Transactions on Graphics (TOG) - Proceedings of ACM SIGGRAPH Asia 2012
Fast nonrigid 3D retrieval using modal space transform
Proceedings of the 3rd ACM conference on International conference on multimedia retrieval
Map-based exploration of intrinsic shape differences and variability
ACM Transactions on Graphics (TOG) - SIGGRAPH 2013 Conference Proceedings
ACM Transactions on Graphics (TOG)
Diffusion pruning for rapidly and robustly selecting global correspondences using local isometry
ACM Transactions on Graphics (TOG)
Surface- and volume-based techniques for shape modeling and analysis
SIGGRAPH Asia 2013 Courses
Shape matching via quotient spaces
SGP '13 Proceedings of the Eleventh Eurographics/ACMSIGGRAPH Symposium on Geometry Processing
An operator approach to tangent vector field processing
SGP '13 Proceedings of the Eleventh Eurographics/ACMSIGGRAPH Symposium on Geometry Processing
Consistent shape maps via semidefinite programming
SGP '13 Proceedings of the Eleventh Eurographics/ACMSIGGRAPH Symposium on Geometry Processing
Dirichlet energy for analysis and synthesis of soft maps
SGP '13 Proceedings of the Eleventh Eurographics/ACMSIGGRAPH Symposium on Geometry Processing
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We present a novel representation of maps between pairs of shapes that allows for efficient inference and manipulation. Key to our approach is a generalization of the notion of map that puts in correspondence real-valued functions rather than points on the shapes. By choosing a multi-scale basis for the function space on each shape, such as the eigenfunctions of its Laplace-Beltrami operator, we obtain a representation of a map that is very compact, yet fully suitable for global inference. Perhaps more remarkably, most natural constraints on a map, such as descriptor preservation, landmark correspondences, part preservation and operator commutativity become linear in this formulation. Moreover, the representation naturally supports certain algebraic operations such as map sum, difference and composition, and enables a number of applications, such as function or annotation transfer without establishing point-to-point correspondences. We exploit these properties to devise an efficient shape matching method, at the core of which is a single linear solve. The new method achieves state-of-the-art results on an isometric shape matching benchmark. We also show how this representation can be used to improve the quality of maps produced by existing shape matching methods, and illustrate its usefulness in segmentation transfer and joint analysis of shape collections.