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
Using Spin Images for Efficient Object Recognition in Cluttered 3D Scenes
IEEE Transactions on Pattern Analysis and Machine Intelligence
The Earth Mover's Distance as a Metric for Image Retrieval
International Journal of Computer Vision
Spherical parametrization and remeshing
ACM SIGGRAPH 2003 Papers
The space of human body shapes: reconstruction and parameterization from range scans
ACM SIGGRAPH 2003 Papers
A new point matching algorithm for non-rigid registration
Computer Vision and Image Understanding - Special issue on nonrigid image registration
Distinctive Image Features from Scale-Invariant Keypoints
International Journal of Computer Vision
Deformation transfer for triangle meshes
ACM SIGGRAPH 2004 Papers
Optimal Global Conformal Surface Parameterization
VIS '04 Proceedings of the conference on Visualization '04
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
SCAPE: shape completion and animation of people
ACM SIGGRAPH 2005 Papers
Linear rotation-invariant coordinates for meshes
ACM SIGGRAPH 2005 Papers
Robust spherical parameterization of triangular meshes
Computing - Geometric modelling dagstuhl 2002
Conformal Geometry and Its Applications on 3D Shape Matching, Recognition, and Stitching
IEEE Transactions on Pattern Analysis and Machine Intelligence
Global non-rigid alignment of 3-D scans
ACM SIGGRAPH 2007 papers
ACM SIGGRAPH 2007 papers
Example-based 3D scan completion
SGP '05 Proceedings of the third Eurographics symposium on Geometry processing
SGP '05 Proceedings of the third Eurographics symposium on Geometry processing
Partial matching of 3D shapes with priority-driven search
SGP '06 Proceedings of the fourth Eurographics symposium on Geometry processing
Generalized surface flows for mesh processing
SGP '07 Proceedings of the fifth Eurographics symposium on Geometry processing
On Linear Variational Surface Deformation Methods
IEEE Transactions on Visualization and Computer Graphics
Numerical Geometry of Non-Rigid Shapes
Numerical Geometry of Non-Rigid Shapes
3D Non-rigid Surface Matching and Registration Based on Holomorphic Differentials
ECCV '08 Proceedings of the 10th European Conference on Computer Vision: Part III
Mesh parameterization: theory and practice
ACM SIGGRAPH ASIA 2008 courses
Global intrinsic symmetries of shapes
SGP '08 Proceedings of the Symposium on Geometry Processing
Global correspondence optimization for non-rigid registration of depth scans
SGP '08 Proceedings of the Symposium on Geometry Processing
Non-rigid registration under isometric deformations
SGP '08 Proceedings of the Symposium on Geometry Processing
Calculus of Nonrigid Surfaces for Geometry and Texture Manipulation
IEEE Transactions on Visualization and Computer Graphics
On bending invariant signatures for surfaces
IEEE Transactions on Pattern Analysis and Machine Intelligence
Symmetry factored embedding and distance
ACM SIGGRAPH 2010 papers
Style-content separation by anisotropic part scales
ACM SIGGRAPH Asia 2010 papers
Shape analysis of planar objects with arbitrary topologies using conformal geometry
ECCV'10 Proceedings of the 11th European conference on Computer vision: Part V
Shape google: Geometric words and expressions for invariant shape retrieval
ACM Transactions on Graphics (TOG)
ACM SIGGRAPH 2011 papers
Facial cartography: interactive scan correspondence
SCA '11 Proceedings of the 2011 ACM SIGGRAPH/Eurographics Symposium on Computer Animation
Shape- and pose-invariant correspondences using probabilistic geodesic surface embedding
DAGM'11 Proceedings of the 33rd international conference on Pattern recognition
3D shape restoration via matrix recovery
ACCV'10 Proceedings of the 2010 international conference on Computer vision - Volume part II
Computer-Aided Design
Animation cartography—intrinsic reconstruction of shape and motion
ACM Transactions on Graphics (TOG)
Measuring geodesic distances via the uniformization theorem
SSVM'11 Proceedings of the Third international conference on Scale Space and Variational Methods in Computer Vision
Discrete minimum distortion correspondence problems for non-rigid shape matching
SSVM'11 Proceedings of the Third international conference on Scale Space and Variational Methods in Computer Vision
Hierarchical matching of non-rigid shapes
SSVM'11 Proceedings of the Third international conference on Scale Space and Variational Methods in Computer Vision
Schelling points on 3D surface meshes
ACM Transactions on Graphics (TOG) - SIGGRAPH 2012 Conference Proceedings
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
Constructing common base domain by cues from Voronoi diagram
Graphical Models
Image and Vision Computing
The hitchhiker's guide to the galaxy of mathematical tools for shape analysis
ACM SIGGRAPH 2012 Courses
Finding Surface Correspondences Using Symmetry Axis Curves
Computer Graphics Forum
Computer Graphics Forum
Nonrigid Matching of Undersampled Shapes via Medial Diffusion
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
Scale Normalization for Isometric Shape Matching
Computer Graphics Forum
Correspondences of persistent feature points on near-isometric surfaces
ECCV'12 Proceedings of the 12th international conference on Computer Vision - Volume Part I
ECCV'12 Proceedings of the 12th European conference on Computer Vision - Volume Part IV
Transformed polynomials for global registration of point clouds
Proceedings of the 27th Spring Conference on Computer Graphics
ElastiFace: matching and blending textured faces
Proceedings of the Symposium on Non-Photorealistic Animation and Rendering
Skeleton-based intrinsic symmetry detection on point clouds
Graphical Models
Fuzzy Sets and Systems
ACM Transactions on Graphics (TOG)
ACM Transactions on Graphics (TOG)
Diffusion pruning for rapidly and robustly selecting global correspondences using local isometry
ACM Transactions on Graphics (TOG)
Technical Section: Automatic pose-independent 3D garment fitting
Computers and Graphics
3D human motion analysis framework for shape similarity and retrieval
Image and Vision Computing
Shape matching via quotient spaces
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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The goal of our work is to develop an efficient, automatic algorithm for discovering point correspondences between surfaces that are approximately and/or partially isometric. Our approach is based on three observations. First, isometries are a subset of the Möbius group, which has low-dimensionality -- six degrees of freedom for topological spheres, and three for topological discs. Second, computing the Möbius transformation that interpolates any three points can be computed in closed-form after a mid-edge flattening to the complex plane. Third, deviations from isometry can be modeled by a transportation-type distance between corresponding points in that plane. Motivated by these observations, we have developed a Möbius Voting algorithm that iteratively: 1) samples a triplet of three random points from each of two point sets, 2) uses the Möbius transformations defined by those triplets to map both point sets into a canonical coordinate frame on the complex plane, and 3) produces "votes" for predicted correspondences between the mutually closest points with magnitude representing their estimated deviation from isometry. The result of this process is a fuzzy correspondence matrix, which is converted to a permutation matrix with simple matrix operations and output as a discrete set of point correspondences with confidence values. The main advantage of this algorithm is that it can find intrinsic point correspondences in cases of extreme deformation. During experiments with a variety of data sets, we find that it is able to find dozens of point correspondences between different object types in different poses fully automatically.