Meshless geometric subdivision
Graphical Models
Analysis of Two-Dimensional Non-Rigid Shapes
International Journal of Computer Vision
Parallel algorithms for approximation of distance maps on parametric surfaces
ACM Transactions on Graphics (TOG)
Topology-Invariant Similarity of Nonrigid Shapes
International Journal of Computer Vision
An Intrinsic Framework for Analysis of Facial Surfaces
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
An Elasticity Approach to Principal Modes of Shape Variation
SSVM '09 Proceedings of the Second International Conference on Scale Space and Variational Methods in Computer Vision
Geodesics in Shape Space via Variational Time Discretization
EMMCVPR '09 Proceedings of the 7th International Conference on Energy Minimization Methods in Computer Vision and Pattern Recognition
Global intrinsic symmetries of shapes
SGP '08 Proceedings of the Symposium on Geometry Processing
Gromov-Hausdorff stable signatures for shapes using persistence
SGP '09 Proceedings of the Symposium on Geometry 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
Full and Partial Symmetries of Non-rigid Shapes
International Journal of Computer Vision
ACM Transactions on Graphics (TOG)
Spectral-Driven Isometry-Invariant Matching of 3D Shapes
International Journal of Computer Vision
International Journal of Computer Vision
International Journal of Computer Vision
Volumetric heat kernel signatures
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
Intrinsic regularity detection in 3D geometry
ECCV'10 Proceedings of the 11th European conference on computer vision conference on Computer vision: Part III
Defining, contouring, and visualizing scalar functions on point-sampled surfaces
Computer-Aided Design
An Elasticity-Based Covariance Analysis of Shapes
International Journal of Computer Vision
A Continuum Mechanical Approach to Geodesics in Shape Space
International Journal of Computer Vision
Matching 2D and 3D articulated shapes using the eccentricity transform
Computer Vision and Image Understanding
Face recognition using simplicial complexes
MCPR'10 Proceedings of the 2nd Mexican conference on Pattern recognition: Advances in pattern recognition
Short Communication to SMI 2011: Affine-invariant geodesic geometry of deformable 3D shapes
Computers and Graphics
Graph-based representations of point clouds
Graphical Models
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
Matching two-dimensional articulated shapes using generalized multidimensional scaling
AMDO'06 Proceedings of the 4th international conference on Articulated Motion and Deformable Objects
Robust expression-invariant face recognition from partially missing data
ECCV'06 Proceedings of the 9th European conference on Computer Vision - Volume Part III
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
A correspondence-less approach to matching of deformable shapes
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
Image and Vision Computing
Spaces and manifolds of shapes in computer vision: An overview
Image and Vision Computing
Non-rigid shape correspondence and description using geodesic field estimate distribution
ACM SIGGRAPH 2012 Posters
An optimization approach for extracting and encoding consistent maps in a shape collection
ACM Transactions on Graphics (TOG) - Proceedings of ACM SIGGRAPH Asia 2012
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
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
Detection, classification and estimation of individual shapes in 2D and 3D point clouds
Computational Statistics & Data Analysis
Statistical shape analysis for population studies via level-set based shape morphing
ECCV'12 Proceedings of the 12th international conference on Computer Vision - Volume Part I
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
Morphological analysis of the left ventricular endocardial surface and its clinical implications
MICCAI'12 Proceedings of the 15th international conference on Medical Image Computing and Computer-Assisted Intervention - Volume Part II
wFEM heat kernel: Discretization and applications to shape analysis and retrieval
Computer Aided Geometric Design
Feature-Preserved 3D Canonical Form
International Journal of Computer Vision
Modelling Convex Shape Priors and Matching Based on the Gromov-Wasserstein Distance
Journal of Mathematical Imaging and Vision
Invariant surface-based shape descriptor for dynamic surface encoding
ACCV'12 Proceedings of the 11th Asian conference on Computer Vision - Volume Part I
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Point clouds are one of the most primitive and fundamental manifold representations. Popular sources of point clouds are three-dimensional shape acquisition devices such as laser range scanners. Another important field where point clouds are found is in the representation of high-dimensional manifolds by samples. With the increasing popularity and very broad applications of this source of data, it is natural and important to work directly with this representation, without having to go through the intermediate and sometimes impossible and distorting steps of surface reconstruction. A geometric framework for comparing manifolds given by point clouds is presented in this paper. The underlying theory is based on Gromov-Hausdorff distances, leading to isometry invariant and completely geometric comparisons. This theory is embedded in a probabilistic setting as derived from random sampling of manifolds, and then combined with results on matrices of pairwise geodesic distances to lead to a computational implementation of the framework. The theoretical and computational results presented here are complemented with experiments for real three-dimensional shapes.