Matrix analysis
Manifolds, tensor analysis, and applications: 2nd edition
Manifolds, tensor analysis, and applications: 2nd edition
Matrix computations (3rd ed.)
Natural gradient works efficiently in learning
Neural Computation
Diffeomorphisms Groups and Pattern Matching in Image Analysis
International Journal of Computer Vision
The Geometry of Algorithms with Orthogonality Constraints
SIAM Journal on Matrix Analysis and Applications
International Journal of Computer 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
Fiber Tract Mapping from Diffusion Tensor MRI
VLSM '01 Proceedings of the IEEE Workshop on Variational and Level Set Methods (VLSM'01)
Variational Problems and PDE's on Implicit Surfaces
VLSM '01 Proceedings of the IEEE Workshop on Variational and Level Set Methods (VLSM'01)
A general framework for low level vision
IEEE Transactions on Image Processing
IEEE Transactions on Image Processing
A Riemannian Framework for Tensor Computing
International Journal of Computer Vision
Journal of Mathematical Imaging and Vision
Fast Anisotropic Smoothing of Multi-Valued Images using Curvature-Preserving PDE's
International Journal of Computer Vision
Journal of Mathematical Imaging and Vision
3-D Reconstruction of Shaded Objects from Multiple Images Under Unknown Illumination
International Journal of Computer Vision
Journal of Mathematical Imaging and Vision
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
Statistical Computing on Manifolds: From Riemannian Geometry to Computational Anatomy
Emerging Trends in Visual Computing
Fast GL(n)-Invariant Framework for Tensors Regularization
International Journal of Computer Vision
Image and Vision Computing
Coordinate-free diffusion over compact Lie-groups
SSVM'07 Proceedings of the 1st international conference on Scale space and variational methods in computer vision
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
Higher Order Positive Semidefinite Diffusion Tensor Imaging
SIAM Journal on Imaging Sciences
SIAM Journal on Imaging Sciences
Fast and simple calculus on tensors in the log-euclidean framework
MICCAI'05 Proceedings of the 8th international conference on Medical Image Computing and Computer-Assisted Intervention - Volume Part I
Denoising tensors via lie group flows
VLSM'05 Proceedings of the Third international conference on Variational, Geometric, and Level Set Methods in Computer Vision
Regularization of mappings between implicit manifolds of arbitrary dimension and codimension
VLSM'05 Proceedings of the Third international conference on Variational, Geometric, and Level Set Methods in Computer Vision
Curvature-Preserving regularization of multi-valued images using PDE's
ECCV'06 Proceedings of the 9th European conference on Computer Vision - Volume Part II
Nonnegative Diffusion Orientation Distribution Function
Journal of Mathematical Imaging and Vision
Anisotropy Preserving DTI Processing
International Journal of Computer Vision
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Nonlinear diffusion equations are now widely used to restore and enhance images. They allow to eliminate noise and artifacts while preserving large global features, such as object contours. In this context, we propose a differential-geometric framework to define PDEs acting on some manifold constrained datasets. We consider the case of images taking value into matrix manifolds defined by orthogonal and spectral constraints. We directly incorporate the geometry and natural metric of the underlying configuration space (viewed as a Lie group or a homogeneous space) in the design of the corresponding flows. Our numerical implementation relies on structure-preserving integrators that respect intrinsically the constraints geometry. The efficiency and versatility of this approach are illustrated through the anisotropic smoothing of diffusion tensor volumes in medical imaging.