Iso-charts: stretch-driven mesh parameterization using spectral analysis
Proceedings of the 2004 Eurographics/ACM SIGGRAPH symposium on Geometry processing
Laplace-spectra as fingerprints for shape matching
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Three-Dimensional Face Recognition
International Journal of Computer Vision
The complexity of low-distortion embeddings between point sets
SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
Shape Classification Using the Inner-Distance
IEEE Transactions on Pattern Analysis and Machine Intelligence
A spectral approach to shape-based retrieval of articulated 3D models
Computer-Aided Design
Laplace spectra as fingerprints for image recognition
Computer-Aided Design
Pose-Oblivious Shape Signature
IEEE Transactions on Visualization and Computer Graphics
Generalized surface flows for mesh processing
SGP '07 Proceedings of the fifth Eurographics symposium on Geometry processing
Laplace-Beltrami eigenfunctions for deformation invariant shape representation
SGP '07 Proceedings of the fifth Eurographics symposium on Geometry processing
Quasi-isometric parameterization for texture mapping
Pattern Recognition
Quasi-isometric parameterization for texture mapping
Pattern Recognition
Expression-invariant face recognition by facial expression transformations
Pattern Recognition Letters
Topology-Invariant Similarity of Nonrigid Shapes
International Journal of Computer Vision
A linear-space algorithm for distance preserving graph embedding
Computational Geometry: Theory and Applications
Möbius voting for surface correspondence
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Partial Similarity of Objects, or How to Compare a Centaur to a Horse
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A Critical Assessment of 2D and 3D Face Recognition Algorithms
AVSS '09 Proceedings of the 2009 Sixth IEEE International Conference on Advanced Video and Signal Based Surveillance
Dense sampling and fast encoding for 3D model retrieval using bag-of-visual features
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Laplace-Beltrami spectra as 'Shape-DNA' of surfaces and solids
Computer-Aided Design
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Manifold based analysis of facial expression
Image and Vision Computing
Deformation-driven shape correspondence
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
From 3D mesh data hiding to 3D shape blind and robust watermarking: a survey
Transactions on data hiding and multimedia security II
IEEE Transactions on Signal Processing
Full and Partial Symmetries of Non-rigid Shapes
International Journal of Computer Vision
Nonlinear Dimensionality Reduction by Topologically Constrained Isometric Embedding
International Journal of Computer Vision
Face recognition by matching 2D and 3D geodesic distances
MCAM'07 Proceedings of the 2007 international conference on Multimedia content analysis and mining
Spectral-Driven Isometry-Invariant Matching of 3D Shapes
International Journal of Computer Vision
Shape Similarity for 3D Video Sequences of People
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
ACM SIGGRAPH 2010 Courses
Improving shape retrieval by spectral matching and meta similarity
IEEE Transactions on Image Processing
Inelastic deformation invariant modal representation for non-rigid 3D object recognition
AMDO'10 Proceedings of the 6th international conference on Articulated motion and deformable objects
Probabilistic expression analysis on manifolds
CVPR'04 Proceedings of the 2004 IEEE computer society conference on Computer vision and pattern recognition
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
Articulation-invariant representation of non-planar shapes
ECCV'10 Proceedings of the 11th European conference on computer vision conference on Computer vision: Part III
Efficient computation of scale-space features for deformable shape correspondences
ECCV'10 Proceedings of the 11th European conference on computer vision conference on Computer vision: Part III
Balancing deformability and discriminability for shape matching
ECCV'10 Proceedings of the 11th European conference on computer vision conference on Computer vision: Part III
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
Shape description by bending invariant moments
CAIP'11 Proceedings of the 14th international conference on Computer analysis of images and patterns - Volume Part I
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
2.5D face recognition using Patch Geodesic Moments
Pattern Recognition
Elements of geometry processing
SIGGRAPH Asia 2011 Courses
Acquisition of articulated human body models using multiple cameras
AMDO'06 Proceedings of the 4th international conference on Articulated Motion and Deformable Objects
Facial expression transformations for expression-invariant face recognition
ISVC'06 Proceedings of the Second international conference on Advances in Visual Computing - Volume Part I
Robust expression-invariant face recognition from partially missing data
ECCV'06 Proceedings of the 9th European conference on Computer Vision - Volume Part III
Non-rigid shape matching using geometry and photometry
ACCV'09 Proceedings of the 9th Asian conference on Computer Vision - Volume Part III
Isometric deformation invariant 3D shape recognition
Pattern Recognition
Shape-based retrieval of articulated 3d models using spectral embedding
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Hierarchical matching of non-rigid shapes
SSVM'11 Proceedings of the Third international conference on Scale Space and Variational Methods in Computer Vision
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Robotics and Autonomous Systems
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Image and Vision Computing
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Pattern Recognition
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Isometry-invariant matching of point set surfaces
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Global Non-rigid Alignment of Surface Sequences
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Isometric surfaces share the same geometric structure, also known as the "first fundamental form." For example, all possible bendings of a given surface that includes all length preserving deformations without tearing or stretching the surface are considered to be isometric. We present a method to construct a bending invariant signature for such surfaces. This invariant representation is an embedding of the geometric structure of the surface in a small dimensional Euclidean space in which geodesic distances are approximated by Euclidean ones. The bending invariant representation is constructed by first measuring the intergeodesic distances between uniformly distributed points on the surface. Next, a multidimensional scaling technique is applied to extract coordinates in a finite dimensional Euclidean space in which geodesic distances are replaced by Euclidean ones. Applying this transform to various surfaces with similar geodesic structures (first fundamental form) maps them into similar signature surfaces. We thereby translate the problem of matching nonrigid objects in various postures into a simpler problem of matching rigid objects. As an example, we show a simple surface classification method that uses our bending invariant signatures.