Multiresolution analysis of arbitrary meshes
SIGGRAPH '95 Proceedings of the 22nd annual conference on Computer graphics and interactive techniques
A Metric for Distributions with Applications to Image Databases
ICCV '98 Proceedings of the Sixth International Conference on Computer Vision
Discrete exterior calculus
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
Diffusion Distance for Histogram Comparison
CVPR '06 Proceedings of the 2006 IEEE Computer Society Conference on Computer Vision and Pattern Recognition - Volume 1
Variational harmonic maps for space deformation
ACM SIGGRAPH 2009 papers
Möbius voting for surface correspondence
ACM SIGGRAPH 2009 papers
Deformation-driven shape correspondence
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
A simple geometric model for elastic deformations
ACM SIGGRAPH 2010 papers
ACM SIGGRAPH 2011 papers
Gromov–Wasserstein Distances and the Metric Approach to Object Matching
Foundations of Computational Mathematics
Functional maps: a flexible representation of maps between shapes
ACM Transactions on Graphics (TOG) - SIGGRAPH 2012 Conference Proceedings
Exploring collections of 3D models using fuzzy correspondences
ACM Transactions on Graphics (TOG) - SIGGRAPH 2012 Conference Proceedings
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
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Soft maps taking points on one surface to probability distributions on another are attractive for representing surface mappings in the presence of symmetry, ambiguity, and combinatorial complexity. Few techniques, however, are available to measure their continuity and other properties. To this end, we introduce a novel Dirichlet energy for soft maps generalizing the classical map Dirichlet energy, which measures distortion by computing how soft maps transport probabilistic mass from one distribution to another. We formulate the computation of the Dirichlet energy in terms of a differential equation and provide a finite elements discretization that enables all of the quantities introduced to be computed. We demonstrate the effectiveness of our framework for understanding soft maps arising from various sources. Furthermore, we suggest how these energies can be applied to generate continuous soft or point-to-point maps.