Generating and generalizing models of visual objects
Artificial Intelligence
Hands: a pattern theoretic study of biological shapes
Hands: a pattern theoretic study of biological shapes
IEEE Transactions on Pattern Analysis and Machine Intelligence - Special issue on interpretation of 3-D scenes—part I
Fuzzy sets and fuzzy logic: theory and applications
Fuzzy sets and fuzzy logic: theory and applications
Object Matching Using Deformable Templates
IEEE Transactions on Pattern Analysis and Machine Intelligence
Fuzzy set theory—and its applications (3rd ed.)
Fuzzy set theory—and its applications (3rd ed.)
Shape Similarity Measure Based on Correspondence of Visual Parts
IEEE Transactions on Pattern Analysis and Machine Intelligence
Classification with Nonmetric Distances: Image Retrieval and Class Representation
IEEE Transactions on Pattern Analysis and Machine Intelligence
Measurement of Visual Motion
Vector-Valued Optimization Problems in Control Theory
Vector-Valued Optimization Problems in Control Theory
Computer Vision: A Modern Approach
Computer Vision: A Modern Approach
Distortion Invariant Object Recognition in the Dynamic Link Architecture
IEEE Transactions on Computers
IEEE Transactions on Pattern Analysis and Machine Intelligence
Shape Matching and Object Recognition Using Shape Contexts
IEEE Transactions on Pattern Analysis and Machine Intelligence
Representation and Self-Similarity of Shapes
IEEE Transactions on Pattern Analysis and Machine Intelligence
Tracking Points on Deformable Objects Using Curvature Information
ECCV '92 Proceedings of the Second European Conference on Computer Vision
On interactive visualization of high-dimensional data using the hyperbolic plane
Proceedings of the eighth ACM SIGKDD international conference on Knowledge discovery and data mining
A shock grammar for recognition
CVPR '96 Proceedings of the 1996 Conference on Computer Vision and Pattern Recognition (CVPR '96)
Pictorial Structures for Object Recognition
International Journal of Computer Vision
Representation and Detection of Deformable Shapes
IEEE Transactions on Pattern Analysis and Machine Intelligence
Three-Dimensional Face Recognition
International Journal of Computer Vision
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
Using the Inner-Distance for Classification of Articulated Shapes
CVPR '05 Proceedings of the 2005 IEEE Computer Society Conference on Computer Vision and Pattern Recognition (CVPR'05) - Volume 2 - Volume 02
Deformation Invariant Image Matching
ICCV '05 Proceedings of the Tenth IEEE International Conference on Computer Vision - Volume 2
A Theoretical and Computational Framework for Isometry Invariant Recognition of Point Cloud Data
Foundations of Computational Mathematics
Multi-class ROC analysis from a multi-objective optimisation perspective
Pattern Recognition Letters - Special issue: ROC analysis in pattern recognition
On Shape of Plane Elastic Curves
International Journal of Computer Vision
Generalized Gradients: Priors on Minimization Flows
International Journal of Computer Vision
Efficient Computation of Isometry-Invariant Distances Between Surfaces
SIAM Journal on Scientific Computing
SGP '05 Proceedings of the third Eurographics symposium on Geometry processing
The Representation and Matching of Pictorial Structures
IEEE Transactions on Computers
Numerical Geometry of Non-Rigid Shapes
Numerical Geometry of Non-Rigid Shapes
Optimal partial shape similarity
Image and Vision Computing
Expression-invariant 3D face recognition
AVBPA'03 Proceedings of the 4th international conference on Audio- and video-based biometric person authentication
Representation and matching of articulated shapes
CVPR'04 Proceedings of the 2004 IEEE computer society conference on Computer vision and pattern recognition
Facetoface: an isometric model for facial animation
AMDO'06 Proceedings of the 4th international conference on Articulated Motion and Deformable Objects
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
Using top-points as interest points for image matching
DSSCV'05 Proceedings of the First international conference on Deep Structure, Singularities, and Computer Vision
Isometric embedding of facial surfaces into S3
Scale-Space'05 Proceedings of the 5th international conference on Scale Space and PDE Methods in Computer Vision
Calculus of Nonrigid Surfaces for Geometry and Texture Manipulation
IEEE Transactions on Visualization and Computer Graphics
Design and analysis of planar shape deformation
Computational Geometry: Theory and Applications
The farthest point strategy for progressive image sampling
IEEE Transactions on Image Processing
Holographic representations of images
IEEE Transactions on Image Processing
Symmetry of Shapes Via Self-similarity
ISVC '08 Proceedings of the 4th International Symposium on Advances in Visual Computing, Part II
Topology-Invariant Similarity of Nonrigid Shapes
International Journal of Computer Vision
Partial Similarity of Objects, or How to Compare a Centaur to a Horse
International Journal of Computer Vision
Non-rigid registration under isometric deformations
SGP '08 Proceedings of the Symposium on Geometry Processing
Full and Partial Symmetries of Non-rigid Shapes
International Journal of Computer Vision
Recursive computation of moments of 2D objects represented by elliptic Fourier descriptors
Pattern Recognition Letters
Improving shape retrieval by spectral matching and meta similarity
IEEE Transactions on Image Processing
Volumetric heat kernel signatures
Proceedings of the ACM workshop on 3D object retrieval
Geodesic Methods in Computer Vision and Graphics
Foundations and Trends® in Computer Graphics and Vision
Balancing deformability and discriminability for shape matching
ECCV'10 Proceedings of the 11th European conference on computer vision conference on Computer vision: Part III
Matching 2D and 3D articulated shapes using the eccentricity transform
Computer Vision and Image Understanding
Shape description by bending invariant moments
CAIP'11 Proceedings of the 14th international conference on Computer analysis of images and patterns - Volume Part I
Persistent homology and partial similarity of shapes
Pattern Recognition Letters
Robust shape normalization of 3D articulated volumetric models
Computer-Aided Design
Local phase quantization descriptor for improving shape retrieval/classification
Pattern Recognition Letters
3D object classification using scale invariant heat kernels with collaborative classification
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
Perceptually motivated shape context which uses shape interiors
Pattern Recognition
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Analysis of deformable two-dimensional shapes is an important problem, encountered in numerous pattern recognition, computer vision and computer graphics applications. In this paper, we address three major problems in the analysis of non-rigid shapes: similarity, partial similarity, and correspondence. We present an axiomatic construction of similarity criteria for deformation-invariant shape comparison, based on intrinsic geometric properties of the shapes, and show that such criteria are related to the Gromov-Hausdorff distance. Next, we extend the problem of similarity computation to shapes which have similar parts but are dissimilar when considered as a whole, and present a construction of set-valued distances, based on the notion of Pareto optimality. Finally, we show that the correspondence between non-rigid shapes can be obtained as a byproduct of the non-rigid similarity problem. As a numerical framework, we use the generalized multidimensional scaling (GMDS) method, which is the numerical core of the three problems addressed in this paper.