Scale-Space and Edge Detection Using Anisotropic Diffusion
IEEE Transactions on Pattern Analysis and Machine Intelligence
A Framework for Uncertainty and Validation of 3-D RegistrationMethods Based on Points and Frames
International Journal of Computer Vision
Uniform Distribution, Distance and Expectation Problems for Geometric Features Processing
Journal of Mathematical Imaging and Vision
Geometric partial differential equations and image analysis
Geometric partial differential equations and image analysis
Orthonormal Vector Sets Regularization with PDE's and Applications
International Journal of Computer Vision
Constrained Flows of Matrix-Valued Functions: Application to Diffusion Tensor Regularization
ECCV '02 Proceedings of the 7th European Conference on Computer Vision-Part I
Regularizing Flows for Constrained Matrix-Valued Images
Journal of Mathematical Imaging and Vision
Natural neighbor coordinates of points on a surface
Computational Geometry: Theory and Applications
Intrinsic Statistics on Riemannian Manifolds: Basic Tools for Geometric Measurements
Journal of Mathematical Imaging and Vision
Journal of Mathematical Imaging and Vision
A Riemannian approach to anisotropic filtering of tensor fields
Signal Processing
International Journal of Computer Vision
Variational Deconvolution of Multi-channel Images with Inequality Constraints
IbPRIA '07 Proceedings of the 3rd Iberian conference on Pattern Recognition and Image Analysis, Part I
Unsupervised Riemannian Clustering of Probability Density Functions
ECML PKDD '08 Proceedings of the 2008 European Conference on Machine Learning and Knowledge Discovery in Databases - Part I
MICCAI '08 Proceedings of the 11th International Conference on Medical Image Computing and Computer-Assisted Intervention, Part II
Regularizing Flows over Lie Groups
Journal of Mathematical Imaging and Vision
A Fast and Log-Euclidean Polyaffine Framework for Locally Linear Registration
Journal of Mathematical Imaging and Vision
Speech Emotion Classification on a Riemannian Manifold
PCM '08 Proceedings of the 9th Pacific Rim Conference on Multimedia: Advances in Multimedia Information Processing
Statistical Computing on Manifolds: From Riemannian Geometry to Computational Anatomy
Emerging Trends in Visual Computing
Nonlinear Mean Shift over Riemannian Manifolds
International Journal of Computer Vision
Kernel Based Multi-object Tracking Using Gabor Functions Embedded in a Region Covariance Matrix
IbPRIA '09 Proceedings of the 4th Iberian Conference on Pattern Recognition and Image Analysis
Fast GL(n)-Invariant Framework for Tensors Regularization
International Journal of Computer Vision
Image segmentation based on GrabCut framework integrating multiscale nonlinear structure tensor
IEEE Transactions on Image Processing
Intrinsic Regression Models for Manifold-Valued Data
MICCAI '09 Proceedings of the 12th International Conference on Medical Image Computing and Computer-Assisted Intervention: Part II
A Riemannian Framework for Orientation Distribution Function Computing
MICCAI '09 Proceedings of the 12th International Conference on Medical Image Computing and Computer-Assisted Intervention: Part I
Design and Construction of a Realistic DWI Phantom for Filtering Performance Assessment
MICCAI '09 Proceedings of the 12th International Conference on Medical Image Computing and Computer-Assisted Intervention: Part I
4th order diffusion tensor interpolation with divergence and curl constrained Bézier patches
ISBI'09 Proceedings of the Sixth IEEE international conference on Symposium on Biomedical Imaging: From Nano to Macro
New Riemannian techniques for directional and tensorial image data
Pattern Recognition
A tensorial framework for color images
Pattern Recognition Letters
Visual Tracking via Particle Filtering on the Affine Group
International Journal of Robotics Research
Speculation on the generality of the backward stepwise view of PCA
Proceedings of the international conference on Multimedia information retrieval
Statistical comparison of cardiac fibre architectures
FIMH'07 Proceedings of the 4th international conference on Functional imaging and modeling of the heart
Coordinate-free diffusion over compact Lie-groups
SSVM'07 Proceedings of the 1st international conference on Scale space and variational methods in computer vision
Riemannian curvature-driven flows for tensor-valued data
SSVM'07 Proceedings of the 1st international conference on Scale space and variational methods in computer vision
A fuzzy, nonparametric segmentation framework for DTI and MRI analysis
IPMI'07 Proceedings of the 20th international conference on Information processing in medical imaging
Symmetric positive 4th order tensors & their estimation from diffusion weighted MRI
IPMI'07 Proceedings of the 20th international conference on Information processing in medical imaging
Efficient texture representation using multi-scale regions
ACCV'07 Proceedings of the 8th Asian conference on Computer vision - Volume Part I
Non-local means variants for denoising of diffusion-weighted and diffusion tensor MRI
MICCAI'07 Proceedings of the 10th international conference on Medical image computing and computer-assisted intervention
Geodesic-loxodromes for diffusion tensor interpolation and difference measurement
MICCAI'07 Proceedings of the 10th international conference on Medical image computing and computer-assisted intervention - Volume Part I
Fuzzy nonparametric DTI segmentation for robust cingulum-tract extraction
MICCAI'07 Proceedings of the 10th international conference on Medical image computing and computer-assisted intervention - Volume Part I
Measuring brain variability via sulcal lines registration: a diffeomorphic approach
MICCAI'07 Proceedings of the 10th international conference on Medical image computing and computer-assisted intervention - Volume Part I
DTI noise reduction using anisotropic filtering
IITA'09 Proceedings of the 3rd international conference on Intelligent information technology application
A kernel particle filter multi-object tracking using Gabor-based region covariance matrices
ICIP'09 Proceedings of the 16th IEEE international conference on Image processing
Diffusion tensor images edge-directed interpolation
ISBI'10 Proceedings of the 2010 IEEE international conference on Biomedical imaging: from nano to Macro
ISBI'10 Proceedings of the 2010 IEEE international conference on Biomedical imaging: from nano to Macro
Animation wrinkling: augmenting coarse cloth simulations with realistic-looking wrinkles
ACM SIGGRAPH Asia 2010 papers
A New Tensorial Framework for Single-Shell High Angular Resolution Diffusion Imaging
Journal of Mathematical Imaging and Vision
SSPR&SPR'10 Proceedings of the 2010 joint IAPR international conference on Structural, syntactic, and statistical pattern recognition
Tensor sparse coding for region covariances
ECCV'10 Proceedings of the 11th European conference on Computer vision: Part IV
ECCV'10 Proceedings of the 11th European conference on Computer vision: Part VI
Riemannian Metric and Geometric Mean for Positive Semidefinite Matrices of Fixed Rank
SIAM Journal on Matrix Analysis and Applications
Differential feedback of MIMO channel gram matrices based on geodesic curves
IEEE Transactions on Wireless Communications
Free form face recognition using kernel sparse representation
Proceedings of the Seventh Indian Conference on Computer Vision, Graphics and Image Processing
Nearest-neighbor search algorithms on non-Euclidean manifolds for computer vision applications
Proceedings of the Seventh Indian Conference on Computer Vision, Graphics and Image Processing
MICCAI'10 Proceedings of the 13th international conference on Medical image computing and computer-assisted intervention: Part I
Statistical analysis of tensor fields
MICCAI'10 Proceedings of the 13th international conference on Medical image computing and computer-assisted intervention: Part I
Higher Order Positive Semidefinite Diffusion Tensor Imaging
SIAM Journal on Imaging Sciences
SIAM Journal on Imaging Sciences
Journal of Mathematical Imaging and Vision
Riemannian elasticity: a statistical regularization framework for non-linear registration
MICCAI'05 Proceedings of the 8th international conference on Medical image computing and computer-assisted intervention - Volume Part II
Information-geometric graph indexing from bags of partial node coverages
GbRPR'11 Proceedings of the 8th international conference on Graph-based representations in pattern recognition
A probabilistic framework to infer brain functional connectivity from anatomical connections
IPMI'11 Proceedings of the 22nd international conference on Information processing in medical imaging
Horoball hulls and extents in positive definite space
WADS'11 Proceedings of the 12th international conference on Algorithms and data structures
Voxelwise multivariate statistics and brain-wide machine learning using the full diffusion tensor
MICCAI'11 Proceedings of the 14th international conference on Medical image computing and computer-assisted intervention - Volume Part II
Diffeomorphism invariant riemannian framework for ensemble average propagator computing
MICCAI'11 Proceedings of the 14th international conference on Medical image computing and computer-assisted intervention - Volume Part II
Visual tracking based on Log-Euclidean Riemannian sparse representation
ISVC'11 Proceedings of the 7th international conference on Advances in visual computing - Volume Part I
Smoothing tensor-valued images using anisotropic geodesic diffusion
SSPR'06/SPR'06 Proceedings of the 2006 joint IAPR international conference on Structural, Syntactic, and Statistical Pattern Recognition
Rician noise removal in diffusion tensor MRI
MICCAI'06 Proceedings of the 9th international conference on Medical Image Computing and Computer-Assisted Intervention - Volume Part I
MICCAI'06 Proceedings of the 9th international conference on Medical Image Computing and Computer-Assisted Intervention - Volume Part I
Towards a statistical atlas of cardiac fiber structure
MICCAI'06 Proceedings of the 9th international conference on Medical Image Computing and Computer-Assisted Intervention - Volume Part I
Extrapolation of sparse tensor fields: application to the modeling of brain variability
IPMI'05 Proceedings of the 19th international conference on Information Processing in Medical Imaging
Riemannian graph diffusion for DT-MRI regularization
MICCAI'06 Proceedings of the 9th international conference on Medical Image Computing and Computer-Assisted Intervention - Volume Part II
Improved correspondence for DTI population studies via unbiased atlas building
MICCAI'06 Proceedings of the 9th international conference on Medical Image Computing and Computer-Assisted Intervention - Volume Part II
Multiplicative Calculus in Biomedical Image Analysis
Journal of Mathematical Imaging and Vision
ECCV'06 Proceedings of the 9th European conference on Computer Vision - Volume Part III
Face recognition via AAM and multi-features fusion on riemannian manifolds
ACCV'09 Proceedings of the 9th Asian conference on Computer Vision - Volume Part III
A riemannian framework for the processing of tensor-valued images
DSSCV'05 Proceedings of the First international conference on Deep Structure, Singularities, and Computer Vision
Denoising tensors via lie group flows
VLSM'05 Proceedings of the Third international conference on Variational, Geometric, and Level Set Methods in Computer Vision
Computational anatomy and computational physiology for medical image analysis
CVBIA'05 Proceedings of the First international conference on Computer Vision for Biomedical Image Applications
Regularization of positive definite matrix fields based on multiplicative calculus
SSVM'11 Proceedings of the Third international conference on Scale Space and Variational Methods in Computer Vision
On the Geometry of Multivariate Generalized Gaussian Models
Journal of Mathematical Imaging and Vision
Image and Vision Computing
Conjugate gradient on Grassmann manifolds for robust subspace estimation
Image and Vision Computing
Fitting smoothing splines to time-indexed, noisy points on nonlinear manifolds
Image and Vision Computing
Boosted human re-identification using Riemannian manifolds
Image and Vision Computing
Advances in matrix manifolds for computer vision
Image and Vision Computing
Approximating Symmetric Positive Semidefinite Tensors of Even Order
SIAM Journal on Imaging Sciences
Tensor scale: An analytic approach with efficient computation and applications
Computer Vision and Image Understanding
An optimization-based framework for anisotropic simplex mesh adaptation
Journal of Computational Physics
Fast regularization of matrix-valued images
ECCV'12 Proceedings of the 12th European conference on Computer Vision - Volume Part III
Local log-euclidean covariance matrix (L2ECM) for image representation and its applications
ECCV'12 Proceedings of the 12th European conference on Computer Vision - Volume Part III
Learning to match appearances by correlations in a covariance metric space
ECCV'12 Proceedings of the 12th European conference on Computer Vision - Volume Part III
ECCV'12 Proceedings of the 12th European conference on Computer Vision - Volume Part VII
Linear invariant tensor interpolation applied to cardiac diffusion tensor MRI
MICCAI'12 Proceedings of the 15th international conference on Medical Image Computing and Computer-Assisted Intervention - Volume Part II
A new optimal seam finding method based on tensor analysis for automatic panorama construction
Pattern Recognition Letters
Sparse Adaptive Parameterization of Variability in Image Ensembles
International Journal of Computer Vision
Analysis of Scalar Maps for the Segmentation of the Corpus Callosum in Diffusion Tensor Fields
Journal of Mathematical Imaging and Vision
ICCCI'12 Proceedings of the 4th international conference on Computational Collective Intelligence: technologies and applications - Volume Part I
Unscented Kalman Filtering on Riemannian Manifolds
Journal of Mathematical Imaging and Vision
Patient-specific models of cardiac biomechanics
Journal of Computational Physics
Information-Theoretic dissimilarities for graphs
SIMBAD'13 Proceedings of the Second international conference on Similarity-Based Pattern Recognition
Anisotropy Preserving DTI Processing
International Journal of Computer Vision
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Tensors are nowadays a common source of geometric information. In this paper, we propose to endow the tensor space with an affine-invariant Riemannian metric. We demonstrate that it leads to strong theoretical properties: the cone of positive definite symmetric matrices is replaced by a regular and complete manifold without boundaries (null eigenvalues are at the infinity), the geodesic between two tensors and the mean of a set of tensors are uniquely defined, etc.We have previously shown that the Riemannian metric provides a powerful framework for generalizing statistics to manifolds. In this paper, we show that it is also possible to generalize to tensor fields many important geometric data processing algorithms such as interpolation, filtering, diffusion and restoration of missing data. For instance, most interpolation and Gaussian filtering schemes can be tackled efficiently through a weighted mean computation. Linear and anisotropic diffusion schemes can be adapted to our Riemannian framework, through partial differential evolution equations, provided that the metric of the tensor space is taken into account. For that purpose, we provide intrinsic numerical schemes to compute the gradient and Laplace-Beltrami operators. Finally, to enforce the fidelity to the data (either sparsely distributed tensors or complete tensors fields) we propose least-squares criteria based on our invariant Riemannian distance which are particularly simple and efficient to solve.