Computable elastic distances between shapes
SIAM Journal on Applied Mathematics
Dynamic Programming Generation of Curves on Brain Surfaces
IEEE Transactions on Pattern Analysis and Machine Intelligence
Two- and three-dimensional patterns of the face
Two- and three-dimensional patterns of the face
Geometry and topology for mesh generation
Geometry and topology for mesh generation
Topology matching for fully automatic similarity estimation of 3D shapes
Proceedings of the 28th annual conference on Computer graphics and interactive techniques
Surface Coding Based on Morse Theory
IEEE Computer Graphics and Applications
IEEE Transactions on Pattern Analysis and Machine Intelligence
Matching 3D Models with Shape Distributions
SMI '01 Proceedings of the International Conference on Shape Modeling & Applications
Analysis of Planar Shapes Using Geodesic Paths on Shape Spaces
IEEE Transactions on Pattern Analysis and Machine Intelligence
An Evaluation of Multimodal 2D+3D Face Biometrics
IEEE Transactions on Pattern Analysis and Machine Intelligence
Fast and robust detection of crest lines on meshes
Proceedings of the 2005 ACM symposium on Solid and physical modeling
Three-Dimensional Face Recognition
International Journal of Computer Vision
Fast exact and approximate geodesics on meshes
ACM SIGGRAPH 2005 Papers
A Theoretical and Computational Framework for Isometry Invariant Recognition of Point Cloud Data
Foundations of Computational Mathematics
3D Surface Matching and Recognition Using Conformal Geometry
CVPR '06 Proceedings of the 2006 IEEE Computer Society Conference on Computer Vision and Pattern Recognition - Volume 2
Multiple Nose Region Matching for 3D Face Recognition under Varying Facial Expression
IEEE Transactions on Pattern Analysis and Machine Intelligence
Intrinsic Statistics on Riemannian Manifolds: Basic Tools for Geometric Measurements
Journal of Mathematical Imaging and Vision
Three-Dimensional Face Recognition Using Shapes of Facial Curves
IEEE Transactions on Pattern Analysis and Machine Intelligence
The implicit structure of ridges of a smooth parametric surface
Computer Aided Geometric Design
On Shape of Plane Elastic Curves
International Journal of Computer Vision
Laplace-Beltrami eigenfunctions for deformation invariant shape representation
SGP '07 Proceedings of the fifth Eurographics symposium on Geometry processing
Enhancing 3D mesh topological skeletons with discrete contour constrictions
The Visual Computer: International Journal of Computer Graphics
Elastic Shape Models for Face Analysis Using Curvilinear Coordinates
Journal of Mathematical Imaging and Vision
CVPR'04 Proceedings of the 2004 IEEE computer society conference on Computer vision and pattern recognition
Geodesics between 3d closed curves using path-straightening
ECCV'06 Proceedings of the 9th European conference on Computer Vision - Volume Part I
IPMI'05 Proceedings of the 19th international conference on Information Processing in Medical Imaging
Elastic Shape Models for Face Analysis Using Curvilinear Coordinates
Journal of Mathematical Imaging and Vision
A 3D face matching framework for facial curves
Graphical Models
Nasal Region Contribution in 3D Face Biometrics Using Shape Analysis Framework
ICB '09 Proceedings of the Third International Conference on Advances in Biometrics
Elastic Morphing of 2D and 3D Objects on a Shape Manifold
ICIAR '09 Proceedings of the 6th International Conference on Image Analysis and Recognition
Technical Section: Expression modeling for expression-invariant face recognition
Computers and Graphics
Anthropometric 3D Face Recognition
International Journal of Computer Vision
Local visual patch for 3d shape retrieval
Proceedings of the ACM workshop on 3D object retrieval
Elastic radial curves to model 3D facial deformations
Proceedings of the ACM workshop on 3D object retrieval
Shape analysis of local facial patches for 3D facial expression recognition
Pattern Recognition
Image and Vision Computing
Person independent 3D facial expression recognition by a selected ensemble of SIFT descriptors
EG 3DOR'10 Proceedings of the 3rd Eurographics conference on 3D Object Retrieval
Selecting 3D curves on the nasal surface using AdaBoost for person authentication
EG 3DOR'11 Proceedings of the 4th Eurographics conference on 3D Object Retrieval
3D Face Reconstruction from Two Orthogonal Images for Face Recognition Applications
International Journal of Digital Library Systems
Automatic facial expression recognition in real-time from dynamic sequences of 3D face scans
The Visual Computer: International Journal of Computer Graphics
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A statistical analysis of shapes of facial surfaces can play an important role in biometric authentication and other face-related applications. The main difficulty in developing such an analysis comes from the lack of a canonical system to represent and compare all facial surfaces. This paper suggests a specific, yet natural, coordinate system on facial surfaces, that enables comparisons of their shapes. Here a facial surface is represented as an indexed collection of closed curves, called facial curves, that are level curves of a surface distance function from the tip of the nose. Defining the space of all such representations of face, this paper studies its differential geometry and endows it with a Riemannian metric. It presents numerical techniques for computing geodesic paths between facial surfaces in that space. This Riemannian framework is then used to: (i) compute distances between faces to quantify differences in their shapes, (ii) find optimal deformations between faces, and (iii) define and compute average of a given set of faces. Experimental results generated using laser-scanned faces are presented to demonstrate these ideas.