Statistics on the Manifold of Multivariate Normal Distributions: Theory and Application to Diffusion Tensor MRI Processing

Authors:
Christophe Lenglet;Mikaël Rousson;Rachid Deriche;Olivier Faugeras
Affiliations:
I.N.R.I.A Sophia-Antipolis, Sophia-Antipolis, France;Siemens Corporate Research, Princeton, USA 08540;I.N.R.I.A Sophia-Antipolis, Sophia-Antipolis, France;I.N.R.I.A Sophia-Antipolis, Sophia-Antipolis, France
Venue:
Journal of Mathematical Imaging and Vision
Year:
2006

Citing 11
Cited 24

Fronts propagating with curvature-dependent speed: algorithms based on Hamilton-Jacobi formulations

Journal of Computational Physics
A distance between multivariate normal distributions based in an embedding into the Siegel group

Journal of Multivariate Analysis
Means and Averaging in the Group of Rotations

SIAM Journal on Matrix Analysis and Applications
A Variational Framework for Active and Adaptative Segmentation of Vector Valued Images

MOTION '02 Proceedings of the Workshop on Motion and Video Computing
Variational Frameworks for DT-MRI Estimation, Regularization and Visualization

ICCV '03 Proceedings of the Ninth IEEE International Conference on Computer Vision - Volume 2
Regularizing Flows for Constrained Matrix-Valued Images

Journal of Mathematical Imaging and Vision
A Differential Geometric Approach to the Geometric Mean of Symmetric Positive-Definite Matrices

SIAM Journal on Matrix Analysis and Applications
A Riemannian Framework for Tensor Computing

International Journal of Computer Vision
Intrinsic Statistics on Riemannian Manifolds: Basic Tools for Geometric Measurements

Journal of Mathematical Imaging and Vision
Statistics of shape via principal geodesic analysis on lie groups

CVPR'03 Proceedings of the 2003 IEEE computer society conference on Computer vision and pattern recognition
A riemannian approach to diffusion tensor images segmentation

IPMI'05 Proceedings of the 19th international conference on Information Processing in Medical Imaging

Intrinsic Statistics on Riemannian Manifolds: Basic Tools for Geometric Measurements

Journal of Mathematical Imaging and Vision
A Riemannian approach to anisotropic filtering of tensor fields

Signal Processing
Diffusion maps clustering for magnetic resonance Q-ball imaging segmentation

Journal of Biomedical Imaging - Recent Advances in Neuroimaging Methodology
Riemannian Framework for Estimating Symmetric Positive Definite 4th Order Diffusion Tensors

MICCAI '08 Proceedings of the 11th international conference on Medical Image Computing and Computer-Assisted Intervention - Part I
Regularizing Flows over Lie Groups

Journal of Mathematical Imaging and Vision
Information Theoretic Methods for Diffusion-Weighted MRI Analysis

Emerging Trends in Visual Computing
Statistical Computing on Manifolds: From Riemannian Geometry to Computational Anatomy

Emerging Trends in Visual Computing
Image segmentation based on GrabCut framework integrating multiscale nonlinear structure tensor

IEEE Transactions on Image Processing
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
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
Kernel-based manifold learning for statistical analysis of diffusion tensor images

IPMI'07 Proceedings of the 20th international conference on Information processing in medical imaging
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
Mixtures of Gaussians on tensor fields for DT-MRI segmentation

MICCAI'07 Proceedings of the 10th international conference on Medical image computing and computer-assisted intervention - Volume Part I
A New Tensorial Framework for Single-Shell High Angular Resolution Diffusion Imaging

Journal of Mathematical Imaging and Vision
Detection of brain functional-connectivity difference in post-stroke patients using group-level covariance modeling

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
The Riemannian Geometry of the Space of Positive-Definite Matrices and Its Application to the Regularization of Positive-Definite Matrix-Valued Data

Journal of Mathematical Imaging and Vision
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
Geodesics on the Manifold of Multivariate Generalized Gaussian Distributions with an Application to Multicomponent Texture Discrimination

International Journal of Computer Vision
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
On the Geometry of Multivariate Generalized Gaussian Models

Journal of Mathematical Imaging and Vision
A nonparametric Riemannian framework on tensor field with application to foreground segmentation

Pattern Recognition
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
Anisotropy Preserving DTI Processing

International Journal of Computer Vision

Quantified Score

Hi-index	0.00

Visualization

Abstract

This paper is dedicated to the statistical analysis of the space of multivariate normal distributions with an application to the processing of Diffusion Tensor Images (DTI). It relies on the differential geometrical properties of the underlying parameters space, endowed with a Riemannian metric, as well as on recent works that led to the generalization of the normal law on Riemannian manifolds. We review the geometrical properties of the space of multivariate normal distributions with zero mean vector and focus on an original characterization of the mean, covariance matrix and generalized normal law on that manifold. We extensively address the derivation of accurate and efficient numerical schemes to estimate these statistical parameters. A major application of the present work is related to the analysis and processing of DTI datasets and we show promising results on synthetic and real examples.