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
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
A Riemannian approach to anisotropic filtering of tensor fields
Signal Processing
MICCAI '08 Proceedings of the 11th international conference on Medical Image Computing and Computer-Assisted Intervention - Part I
MICCAI '08 Proceedings of the 11th International Conference on Medical Image Computing and Computer-Assisted Intervention, Part II
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
Object Tracking via Multi-region Covariance and Particle Swarm Optimization
AVSS '09 Proceedings of the 2009 Sixth IEEE International Conference on Advanced Video and Signal Based Surveillance
Tensor-Based Analysis of Genetic Influences on Brain Integrity Using DTI in 100 Twins
MICCAI '09 Proceedings of the 12th International Conference on Medical Image Computing and Computer-Assisted Intervention: Part I
The multivariate A/C/E model and the genetics of fiber architecture
ISBI'09 Proceedings of the Sixth IEEE international conference on Symposium on Biomedical Imaging: From Nano to Macro
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
ISBI'09 Proceedings of the Sixth IEEE international conference on Symposium on Biomedical Imaging: From Nano to Macro
Statistical comparison of cardiac fibre architectures
FIMH'07 Proceedings of the 4th international conference on Functional imaging and modeling of the heart
A generic approach to the filtering of matrix fields with singular PDEs
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
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
Multivariate variance-components analysis in DTI
ISBI'10 Proceedings of the 2010 IEEE international conference on Biomedical imaging: from nano to Macro
Region covariance matrix-based object tracking with occlusions handling
ICCVG'10 Proceedings of the 2010 international conference on Computer vision and graphics: Part I
Multi-class classification on Riemannian manifolds for video surveillance
ECCV'10 Proceedings of the 11th European conference on Computer vision: Part II
A novel consistency regularizer for meshless nonrigid image registration
ISVC'10 Proceedings of the 6th international conference on Advances in visual computing - Volume Part II
A meshless method for variational nonrigid 2-D shape registration
ISVC'10 Proceedings of the 6th international conference on Advances in visual computing - Volume Part II
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
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
A log-euclidean framework for statistics on diffeomorphisms
MICCAI'06 Proceedings of the 9th international conference on Medical Image Computing and Computer-Assisted Intervention - Volume Part I
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
Computational anatomy and computational physiology for medical image analysis
CVBIA'05 Proceedings of the First international conference on Computer Vision for Biomedical Image Applications
A log-euclidean polyaffine framework for locally rigid or affine registration
WBIR'06 Proceedings of the Third international conference on Biomedical Image Registration
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
Patient-specific models of cardiac biomechanics
Journal of Computational Physics
A novel sparse group Gaussian graphical model for functional connectivity estimation
IPMI'13 Proceedings of the 23rd international conference on Information Processing in Medical Imaging
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Computations on tensors have become common with the use of DT-MRI. But the classical Euclidean framework has many defects, and affine-invariant Riemannian metrics have been proposed to correct them. These metrics have excellent theoretical properties but lead to complex and slow algorithms. To remedy this limitation, we propose new metrics called Log-Euclidean. They also have excellent theoretical properties and yield similar results in practice, but with much simpler and faster computations. Indeed, Log-Euclidean computations are Euclidean computations in the domain of matrix logarithms. Theoretical aspects are presented and experimental results for multilinear interpolation and regularization of tensor fields are shown on synthetic and real DTI data.