IEEE Transactions on Pattern Analysis and Machine Intelligence
Scale-Space and Edge Detection Using Anisotropic Diffusion
IEEE Transactions on Pattern Analysis and Machine Intelligence
Feature-oriented image enhancement using shock filters
SIAM Journal on Numerical Analysis
Biased anisotropic diffusion: a unified regularization and diffusion approach to edge detection
Image and Vision Computing - Special issue on the first ECCV 1990
Image selective smoothing and edge detection by nonlinear diffusion. II
SIAM Journal on Numerical Analysis
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
Three-dimensional computer vision: a geometric viewpoint
Three-dimensional computer vision: a geometric viewpoint
Image processing: flows under min/max curvature and mean curvature
Graphical Models and Image Processing
Computer Vision and Image Understanding
International Journal of Computer Vision
Proceedings of the 27th annual conference on Computer graphics and interactive techniques
Images as Embedded Maps and Minimal Surfaces: Movies, Color, Texture, and Volumetric Medical Images
International Journal of Computer Vision - Special issue on computer vision research at the Technion
Geometric partial differential equations and image analysis
Geometric partial differential equations and image analysis
Geometry-Driven Diffusion in Computer Vision
Geometry-Driven Diffusion in Computer Vision
Signal Processing for Computer Vision
Signal Processing for Computer Vision
A Theoretical Framework for Convex Regularizers in PDE-Based Computation of Image Motion
International Journal of Computer Vision
Linear Scale-Space has First been Proposed in Japan
Journal of Mathematical Imaging and 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
Regularization of MR Diffusion Tensor Maps for Tracking Brain White Matter Bundles
MICCAI '98 Proceedings of the First International Conference on Medical Image Computing and Computer-Assisted Intervention
From High Energy Physics to Low Level Vision
SCALE-SPACE '97 Proceedings of the First International Conference on Scale-Space Theory in Computer Vision
A Review of Nonlinear Diffusion Filtering
SCALE-SPACE '97 Proceedings of the First International Conference on Scale-Space Theory in Computer Vision
Non-linear operators in image restoration
CVPR '97 Proceedings of the 1997 Conference on Computer Vision and Pattern Recognition (CVPR '97)
CVPR '96 Proceedings of the 1996 Conference on Computer Vision and Pattern Recognition (CVPR '96)
A Common Framework for Curve Evolution, Segmentation and Anisotropic Diffusion
CVPR '96 Proceedings of the 1996 Conference on Computer Vision and Pattern Recognition (CVPR '96)
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)
Regularization of Orthonormal Vector Sets using Coupled PDE's
VLSM '01 Proceedings of the IEEE Workshop on Variational and Level Set Methods (VLSM'01)
Anisotropic diffusion of multivalued images with applications to color filtering
IEEE Transactions on Image Processing
IEEE Transactions on Image Processing
Multigrid anisotropic diffusion
IEEE Transactions on Image Processing
Color TV: total variation methods for restoration of vector-valued images
IEEE Transactions on Image Processing
Variational approach for edge-preserving regularization using coupled PDEs
IEEE Transactions on Image Processing
IEEE Transactions on Image Processing
Regularizing Flows for Constrained Matrix-Valued Images
Journal of Mathematical Imaging and Vision
Capture of hair geometry from multiple images
ACM SIGGRAPH 2004 Papers
Channel Smoothing: Efficient Robust Smoothing of Low-Level Signal Features
IEEE Transactions on Pattern Analysis and Machine Intelligence
A Riemannian Framework for Tensor Computing
International Journal of Computer Vision
Fast Anisotropic Smoothing of Multi-Valued Images using Curvature-Preserving PDE's
International Journal of Computer Vision
Curvature-Driven PDE Methods for Matrix-Valued Images
International Journal of Computer Vision
International Journal of Computer Vision
Connectivity-based parcellation of the cortical mantle using q-ball diffusion imaging
Journal of Biomedical Imaging - Recent Advances in Neuroimaging Methodology
Regularizing Flows over Lie Groups
Journal of Mathematical Imaging and Vision
A Nonlinear Structure Tensor with the Diffusivity Matrix Composed of the Image Gradient
Journal of Mathematical Imaging and Vision
Fast GL(n)-Invariant Framework for Tensors Regularization
International Journal of Computer Vision
Colour, texture, and motion in level set based segmentation and tracking
Image and Vision Computing
Image and Vision Computing
New Riemannian techniques for directional and tensorial image data
Pattern Recognition
Coordinate-free diffusion over compact Lie-groups
SSVM'07 Proceedings of the 1st international conference on Scale space and variational methods in computer vision
Smoothing of optical flow using robustified diffusion kernels
Image and Vision Computing
SIAM Journal on Imaging Sciences
Orientation-Matching Minimization for Image Denoising and Inpainting
International Journal of Computer Vision
Optical flow diffusion with robustified kernels
CAIP'05 Proceedings of the 11th international conference on Computer Analysis of Images and Patterns
3D curve inference for diffusion MRI regularization
MICCAI'05 Proceedings of the 8th 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
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
Lagrangian multipliers and split Bregman methods for minimization problems constrained on Sn-1
Journal of Visual Communication and Image Representation
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We are interested in regularizing fields of orthonormal vector sets, using constraint-preserving anisotropic diffusion PDE's. Each point of such a field is defined by multiple orthogonal and unitary vectors and can indeed represent a lot of interesting orientation features such as direction vectors or orthogonal matrices (among other examples). We first develop a general variational framework that solves this regularization problem, thanks to a constrained minimization of φ-functionals. This leads to a set of coupled vector-valued PDE's preserving the orthonormal constraints. Then, we focus on particular applications of this general framework, including the restoration of noisy direction fields, noisy chromaticity color images, estimated camera motions and DT-MRI (Diffusion Tensor MRI) datasets.