Robust regression and outlier detection
Robust regression and outlier detection
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
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
Signal and image restoration using shock filters and anisotropic diffusion
SIAM Journal on Numerical Analysis
SUSAN—A New Approach to Low Level Image Processing
International Journal of Computer Vision
Modern mathematical methods for physicists and engineers
Modern mathematical methods for physicists and engineers
Digital Picture Processing
A Note on Two Classical Enhancement Filters and Their Associated PDE's
International Journal of Computer Vision
Bilateral Filtering for Gray and Color Images
ICCV '98 Proceedings of the Sixth International Conference on Computer Vision
Integrated Edge and Junction Detection with the Boundary Tensor
ICCV '03 Proceedings of the Ninth IEEE International Conference on Computer Vision - Volume 2
Levelings, Image Simplification Filters for Segmentation
Journal of Mathematical Imaging and Vision
Vector-Valued Image Regularization with PDEs: A Common Framework for Different Applications
IEEE Transactions on Pattern Analysis and Machine Intelligence
A Non-Local Algorithm for Image Denoising
CVPR '05 Proceedings of the 2005 IEEE Computer Society Conference on Computer Vision and Pattern Recognition (CVPR'05) - Volume 2 - Volume 02
Unsupervised, Information-Theoretic, Adaptive Image Filtering for Image Restoration
IEEE Transactions on Pattern Analysis and Machine Intelligence
Edge-Preserving Image Denoising and Estimation of Discontinuous Surfaces
IEEE Transactions on Pattern Analysis and Machine Intelligence
Visualization and Processing of Tensor Fields (Mathematics and Visualization)
Visualization and Processing of Tensor Fields (Mathematics and Visualization)
Mathematical Problems in Image Processing: Partial Differential Equations and the Calculus of Variations (Applied Mathematical Sciences)
A Riemannian approach to anisotropic filtering of tensor fields
Signal Processing
Robust NL-means filter with optimal pixel-wise smoothing parameter for statistical image denoising
IEEE Transactions on Signal Processing
Image and Vision Computing
Principal neighborhood dictionaries for nonlocal means image denoising
IEEE Transactions on Image Processing
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
Rotationally invariant similarity measures for nonlocal image denoising
Journal of Visual Communication and Image Representation
Image enhancement and denoising by complex diffusion processes
IEEE Transactions on Pattern Analysis and Machine Intelligence
Efficient and reliable schemes for nonlinear diffusion filtering
IEEE Transactions on Image Processing
KCS-new kernel family with compact support in scale space: formulation and impact
IEEE Transactions on Image Processing
Optimal Spatial Adaptation for Patch-Based Image Denoising
IEEE Transactions on Image Processing
Kernel Regression for Image Processing and Reconstruction
IEEE Transactions on Image Processing
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Structure tensors are used in several PDE-based methods to estimate information on the local structure in the image, such as edge orientation. They have become a common tool in many image processing applications. To integrate the local data information, the structure tensor is based on a local regularization of a tensorial product. In this paper, we propose a new regularization model based on the non-local properties of the tensor product. The resulting non-local structure tensor is effective in the restitution of the non homogeneity of the local orientation of the structures. It is particularly efficient in texture regions where patches repeat non locally. The new tensor regularization also offers the advantage of automatically adapting the smoothing parameter to the local structures of the tensor product. Finally, we explain how this new adaptive structure tensor can be plugged into two PDEs: an anisotropic diffusion and a shock filter. Comparisons with other tensor regularization methods and other PDEs demonstrate the clear advantage of using the non-local structure tensor.