Scale-Space and Edge Detection Using Anisotropic Diffusion
IEEE Transactions on Pattern Analysis and Machine Intelligence
Nonlinear total variation based noise removal algorithms
Proceedings of the eleventh annual international conference of the Center for Nonlinear Studies on Experimental mathematics : computational issues in nonlinear science: computational issues in nonlinear science
A nonlinear variational problem for image matching
SIAM Journal on Scientific Computing
Diffeomorphisms Groups and Pattern Matching in Image Analysis
International Journal of Computer Vision
International Journal of Computer Vision
Proceedings of the 27th annual conference on Computer graphics and interactive techniques
Geometric partial differential equations and image analysis
Geometric partial differential equations and image analysis
Variational problems and partial differential equations on implicit surfaces
Journal of Computational Physics
Signal Processing for Computer Vision
Signal Processing for Computer Vision
A Regularization Scheme for Diffusion Tensor Magnetic Resonance Images
IPMI '01 Proceedings of the 17th International Conference on Information Processing in Medical Imaging
Image Processing for Diffusion Tensor Magnetic Resonance Imaging
MICCAI '99 Proceedings of the Second International Conference on Medical Image Computing and Computer-Assisted Intervention
Optical-Flow Estimation while Preserving Its Discontinuities: A Variational Approach
ACCV '95 Invited Session Papers from the Second Asian Conference on Computer Vision: Recent Developments in Computer Vision
Non-linear operators in image restoration
CVPR '97 Proceedings of the 1997 Conference on Computer Vision and Pattern Recognition (CVPR '97)
Fiber Tract Mapping from Diffusion Tensor MRI
VLSM '01 Proceedings of the IEEE Workshop on Variational and Level Set Methods (VLSM'01)
Regularization of Orthonormal Vector Sets using Coupled PDE's
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
Variational principles, surface evolution, PDEs, level set methods, and the stereo problem
IEEE Transactions on Image Processing
IEEE Transactions on Image Processing
Orthonormal Vector Sets Regularization with PDE's and Applications
International Journal of Computer Vision
Regularizing Flows for Constrained Matrix-Valued Images
Journal of Mathematical Imaging and Vision
A Riemannian Framework for Tensor Computing
International Journal of Computer Vision
Journal of Mathematical Imaging and Vision
A Riemannian approach to anisotropic filtering of tensor fields
Signal Processing
Statistical Computing on Manifolds: From Riemannian Geometry to Computational Anatomy
Emerging Trends in Visual Computing
PDE-Driven Adaptive Morphology for Matrix Fields
SSVM '09 Proceedings of the Second International Conference on Scale Space and Variational Methods in Computer Vision
New Riemannian techniques for directional and tensorial image data
Pattern Recognition
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
An energy minimisation approach to attributed graph regularisation
EMMCVPR'07 Proceedings of the 6th international conference on Energy minimization methods in computer vision and pattern recognition
Adaptive Continuous-Scale Morphology for Matrix Fields
International Journal of Computer Vision
Simultaneous smoothing and estimation of the tensor field from diffusion tensor MRI
CVPR'03 Proceedings of the 2003 IEEE computer society conference on Computer vision and pattern recognition
Journal of Mathematical Imaging and Vision
Steerable deconvolution feature detection as an inverse problem
DAGM'11 Proceedings of the 33rd international conference on Pattern recognition
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
Flexible segmentation and smoothing of DT-MRI fields through a customizable structure tensor
ISVC'06 Proceedings of the Second international conference on Advances in Visual Computing - Volume Part I
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Nonlinear partial differential equations (PDE) are now widely used to regularize images. They allow to eliminate noise and artifacts while preserving large global features, such as object contours. In this context, we propose a geometric framework to design PDE flows acting on constrained datasets. We focus our interest on flows of matrix-valued functions undergoing orthogonal and spectral constraints. The corresponding evolution PDE's are found by minimization of cost functionals, and depend on the natural metrics of the underlying constrained manifolds (viewed as Lie groups or homogeneous spaces). Suitable numerical schemes that fit the constraints are also presented. We illustrate this theoretical framework through a recent and challenging problem in medical imaging: the regularization of diffusion tensor volumes (DTMRI).