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
Recovery of blocky images from noisy and blurred data
SIAM Journal on Applied Mathematics
SUSAN—A New Approach to Low Level Image Processing
International Journal of Computer Vision
Digital Picture Processing
High-Order Total Variation-Based Image Restoration
SIAM Journal on Scientific Computing
Total variation image restoration: numerical methods and extensions
ICIP '97 Proceedings of the 1997 International Conference on Image Processing (ICIP '97) 3-Volume Set-Volume 3 - Volume 3
Texture Synthesis by Non-Parametric Sampling
ICCV '99 Proceedings of the International Conference on Computer Vision-Volume 2 - Volume 2
TV Based Image Restoration with Local Constraints
Journal of Scientific Computing
Bilateral Filtering for Gray and Color Images
ICCV '98 Proceedings of the Sixth International Conference on Computer Vision
An Algorithm for Total Variation Minimization and Applications
Journal of Mathematical Imaging and Vision
Journal of Mathematical Imaging and Vision
Image Decomposition into a Bounded Variation Component and an Oscillating Component
Journal of Mathematical Imaging and Vision
Higher-Order Image Statistics for Unsupervised, Information-Theoretic, Adaptive, Image Filtering
CVPR '05 Proceedings of the 2005 IEEE Computer Society Conference on Computer Vision and Pattern Recognition (CVPR'05) - Volume 2 - Volume 02
Total Variation Wavelet Inpainting
Journal of Mathematical Imaging and Vision
Image Restoration with Discrete Constrained Total Variation Part I: Fast and Exact Optimization
Journal of Mathematical Imaging and Vision
Image decomposition combining staircase reduction and texture extraction
Journal of Visual Communication and Image Representation
A TV Based Restoration Model with Local Constraints
Journal of Scientific Computing
Local Adaptivity to Variable Smoothness for Exemplar-Based Image Regularization and Representation
International Journal of Computer Vision
Some First-Order Algorithms for Total Variation Based Image Restoration
Journal of Mathematical Imaging and Vision
Efficient Schemes for Total Variation Minimization Under Constraints in Image Processing
SIAM Journal on Scientific Computing
From Local Kernel to Nonlocal Multiple-Model Image Denoising
International Journal of Computer Vision
Iterated nonlocal means for texture restoration
SSVM'07 Proceedings of the 1st international conference on Scale space and variational methods in computer vision
Total variation minimization and a class of binary MRF models
EMMCVPR'05 Proceedings of the 5th international conference on Energy Minimization Methods in Computer Vision and Pattern Recognition
A fast and exact algorithm for total variation minimization
IbPRIA'05 Proceedings of the Second Iberian conference on Pattern Recognition and Image Analysis - Volume Part I
Total variation blind deconvolution
IEEE Transactions on Image Processing
Region filling and object removal by exemplar-based image inpainting
IEEE Transactions on Image Processing
The staircasing effect in neighborhood filters and its solution
IEEE Transactions on Image Processing
Kernel Regression for Image Processing and Reconstruction
IEEE Transactions on Image Processing
Pointwise Shape-Adaptive DCT for High-Quality Denoising and Deblocking of Grayscale and Color Images
IEEE Transactions on Image Processing
Image Denoising by Sparse 3-D Transform-Domain Collaborative Filtering
IEEE Transactions on Image Processing
A Bias-Variance Approach for the Nonlocal Means
SIAM Journal on Imaging Sciences
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In the Rudin-Osher-Fatemi (ROF) image denoising model, total variation (TV) is used as a global regularization term. However, as we observe, the local interactions induced by TV do not propagate much at long distances in practice, so that the ROF model is not far from being a local filter. In this paper, we propose building a purely local filter by considering the ROF model in a given neighborhood of each pixel. We show that appropriate weights are required to avoid aliasing-like effects, and we provide an explicit convergence criterion for an associated dual minimization algorithm based on Chambolle's work. We study theoretical properties of the obtained local filter and show that this localization of the ROF model brings an interesting optimization of the bias-variance trade-off, and a strong reduction of an ROF drawback called the “staircasing effect.” Finally, we present a new denoising algorithm, TV-means, that efficiently combines the idea of local TV-filtering with the nonlocal means patch-based method.