High Resolution Tracking of Non-Rigid Motion of Densely Sampled 3D Data Using Harmonic Maps
International Journal of Computer Vision
Analysis of Two-Dimensional Non-Rigid Shapes
International Journal of Computer Vision
Topology-Invariant Similarity of Nonrigid Shapes
International Journal of Computer Vision
Elastic Shape Models for Face Analysis Using Curvilinear Coordinates
Journal of Mathematical Imaging and Vision
Partial Similarity of Objects, or How to Compare a Centaur to a Horse
International Journal of Computer Vision
A Bag of Words Approach for 3D Object Categorization
MIRAGE '09 Proceedings of the 4th International Conference on Computer Vision/Computer Graphics CollaborationTechniques
Gromov-Hausdorff stable signatures for shapes using persistence
SGP '09 Proceedings of the Symposium on Geometry Processing
Squigraphs for fine and compact modeling of 3-D shapes
IEEE Transactions on Image Processing
Paretian similarity for partial comparison of non-rigid objects
SSVM'07 Proceedings of the 1st international conference on Scale space and variational methods in computer vision
ACM Transactions on Graphics (TOG)
Spectral-Driven Isometry-Invariant Matching of 3D Shapes
International Journal of Computer Vision
Ethnicity- and Gender-based Subject Retrieval Using 3-D Face-Recognition Techniques
International Journal of Computer Vision
International Journal of Computer Vision
International Journal of Computer Vision
Object recognition through topo-geometric shape models using error-tolerant subgraph isomorphisms
IEEE Transactions on Image Processing
Shape comparison through mutual distances of real functions
Proceedings of the ACM workshop on 3D object retrieval
Shape google: Geometric words and expressions for invariant shape retrieval
ACM Transactions on Graphics (TOG)
Geodesic Methods in Computer Vision and Graphics
Foundations and Trends® in Computer Graphics and Vision
Three-Dimensional Occlusion Detection and Restoration of Partially Occluded Faces
Journal of Mathematical Imaging and Vision
Short Communication to SMI 2011: Affine-invariant geodesic geometry of deformable 3D shapes
Computers and Graphics
A survey of geodesic paths on 3D surfaces
Computational Geometry: Theory and Applications
Metric structures on datasets: stability and classification of algorithms
CAIP'11 Proceedings of the 14th international conference on Computer analysis of images and patterns - Volume Part II
Computing the shape of brain networks using graph filtration and gromov-hausdorff metric
MICCAI'11 Proceedings of the 14th international conference on Medical image computing and computer-assisted intervention - Volume Part II
Non-rigid shape matching using geometry and photometry
ACCV'09 Proceedings of the 9th Asian conference on Computer Vision - Volume Part III
Image and Vision Computing
A comparison of methods for non-rigid 3D shape retrieval
Pattern Recognition
Isometry-invariant matching of point set surfaces
EG 3DOR'08 Proceedings of the 1st Eurographics conference on 3D Object Retrieval
SHREC'10 track: correspondence finding
EG 3DOR'10 Proceedings of the 3rd Eurographics conference on 3D Object Retrieval
ConTopo: non-rigid 3D object retrieval using topological information guided by conformal factors
EG 3DOR'11 Proceedings of the 4th Eurographics conference on 3D Object Retrieval
Intrinsic local symmetries: a computational framework
EG 3DOR'12 Proceedings of the 5th Eurographics conference on 3D Object Retrieval
Spectral analysis driven sparse matching of 3D shapes
EG 3DOR'12 Proceedings of the 5th Eurographics conference on 3D Object Retrieval
Scale Normalization for Isometric Shape Matching
Computer Graphics Forum
Equi-affine invariant geometries of articulated objects
Proceedings of the 15th international conference on Theoretical Foundations of Computer Vision: outdoor and large-scale real-world scene analysis
A parts-based approach for automatic 3D shape categorization using belief functions
ACM Transactions on Intelligent Systems and Technology (TIST) - Special section on agent communication, trust in multiagent systems, intelligent tutoring and coaching systems
Feature-Preserved 3D Canonical Form
International Journal of Computer Vision
PHOG: photometric and geometric functions for textured shape retrieval
SGP '13 Proceedings of the Eleventh Eurographics/ACMSIGGRAPH Symposium on Geometry Processing
Learning kernels on extended Reeb graphs for 3d shape classification and retrieval
3DOR '13 Proceedings of the Sixth Eurographics Workshop on 3D Object Retrieval
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We present an efficient computational framework for isometry-invariant comparison of smooth surfaces. We formulate the Gromov-Hausdorff distance as a multidimensional scaling-like continuous optimization problem. In order to construct an efficient optimization scheme, we develop a numerical tool for interpolating geodesic distances on a sampled surface from precomputed geodesic distances between the samples. For isometry-invariant comparison of surfaces in the case of partially missing data, we present the partial embedding distance, which is computed using a similar scheme. The main idea is finding a minimum-distortion mapping from one surface to another, while considering only relevant geodesic distances. We discuss numerical implementation issues and present experimental results that demonstrate its accuracy and efficiency.