The Softassign Procrustes Matching Algorithm
IPMI '97 Proceedings of the 15th International Conference on Information Processing in Medical Imaging
Optimal Mass Transport for Registration and Warping
International Journal of Computer Vision
Shape Matching and Object Recognition Using Low Distortion Correspondences
CVPR '05 Proceedings of the 2005 IEEE Computer Society Conference on Computer Vision and Pattern Recognition (CVPR'05) - Volume 1 - Volume 01
Numerical Geometry of Non-Rigid Shapes
Numerical Geometry of Non-Rigid Shapes
Assignment Problems
Möbius voting for surface correspondence
ACM SIGGRAPH 2009 papers
Global intrinsic symmetries of shapes
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
Shape analysis using the auto diffusion function
SGP '09 Proceedings of the Symposium on Geometry Processing
Full and Partial Symmetries of Non-rigid Shapes
International Journal of Computer Vision
ACM SIGGRAPH 2011 papers
Functional maps: a flexible representation of maps between shapes
ACM Transactions on Graphics (TOG) - SIGGRAPH 2012 Conference Proceedings
An optimization approach for extracting and encoding consistent maps in a shape collection
ACM Transactions on Graphics (TOG) - Proceedings of ACM SIGGRAPH Asia 2012
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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The problem of mapping between two non-isometric surfaces admits ambiguities on both local and global scales. For instance, symmetries can make it possible for multiple maps to be equally acceptable, and stretching, slippage, and compression introduce difficulties deciding exactly where each point should go. Since most algorithms for point-to-point or even sparse mapping struggle to resolve these ambiguities, in this paper we introduce soft maps, a probabilistic relaxation of point-to-point correspondence that explicitly incorporates ambiguities in the mapping process. In addition to explaining a continuous theory of soft maps, we show how they can be represented using probability matrices and computed for given pairs of surfaces through a convex optimization explicitly trading off between continuity, conformity to geometric descriptors, and spread. Given that our correspondences are encoded in matrix form, we also illustrate how low-rank approximation and other linear algebraic tools can be used to analyze, simplify, and represent both individual and collections of soft maps. © 2012 Wiley Periodicals, Inc.