The Earth Mover's Distance as a Metric for Image Retrieval
International Journal of Computer Vision
Automatic three-dimensional modeling from reality
Automatic three-dimensional modeling from reality
A new point matching algorithm for non-rigid registration
Computer Vision and Image Understanding - Special issue on nonrigid image registration
Deformation transfer for triangle meshes
ACM SIGGRAPH 2004 Papers
ACM SIGGRAPH 2004 Papers
A global approach to automatic solution of jigsaw puzzles
Computational Geometry: Theory and Applications - Special issue on the 18th annual symposium on computational geometrySoCG2002
ACM SIGGRAPH 2005 Papers
A Theoretical and Computational Framework for Isometry Invariant Recognition of Point Cloud Data
Foundations of Computational Mathematics
Reassembling fractured objects by geometric matching
ACM SIGGRAPH 2006 Papers
Efficient MAP approximation for dense energy functions
ICML '06 Proceedings of the 23rd international conference on Machine learning
Möbius voting for surface correspondence
ACM SIGGRAPH 2009 papers
Technical Section: Consistent segmentation of 3D models
Computers and Graphics
An Analysis of Convex Relaxations for MAP Estimation of Discrete MRFs
The Journal of Machine Learning Research
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
Characterizing structural relationships in scenes using graph kernels
ACM SIGGRAPH 2011 papers
Probabilistic reasoning for assembly-based 3D modeling
ACM SIGGRAPH 2011 papers
ACM SIGGRAPH 2011 papers
Joint shape segmentation with linear programming
Proceedings of the 2011 SIGGRAPH Asia Conference
Unsupervised co-segmentation of a set of shapes via descriptor-space spectral clustering
Proceedings of the 2011 SIGGRAPH Asia Conference
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
Structure from motion for scenes with large duplicate structures
CVPR '11 Proceedings of the 2011 IEEE Conference on Computer Vision and Pattern Recognition
Computer Graphics Forum
Learning part-based templates from large collections of 3D shapes
ACM Transactions on Graphics (TOG) - SIGGRAPH 2013 Conference Proceedings
Fine-grained semi-supervised labeling of large shape collections
ACM Transactions on Graphics (TOG)
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 introduce a novel approach for computing high quality point-to-point maps among a collection of related shapes. The proposed approach takes as input a sparse set of imperfect initial maps between pairs of shapes and builds a compact data structure which implicitly encodes an improved set of maps between all pairs of shapes. These maps align well with point correspondences selected from initial maps; they map neighboring points to neighboring points; and they provide cycle-consistency, so that map compositions along cycles approximate the identity map. The proposed approach is motivated by the fact that a complete set of maps between all pairs of shapes that admits nearly perfect cycle-consistency are highly redundant and can be represented by compositions of maps through a single base shape. In general, multiple base shapes are needed to adequately cover a diverse collection. Our algorithm sequentially extracts such a small collection of base shapes and creates correspondences from each of these base shapes to all other shapes. These correspondences are found by global optimization on candidate correspondences obtained by diffusing initial maps. These are then used to create a compact graphical data structure from which globally optimal cycle-consistent maps can be extracted using simple graph algorithms. Experimental results on benchmark datasets show that the proposed approach yields significantly better results than state-of-the-art data-driven shape matching methods.