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
Oscillating Patterns in Image Processing and Nonlinear Evolution Equations: The Fifteenth Dean Jacqueline B. Lewis Memorial Lectures
Digital Picture Processing
Bilateral Filtering for Gray and Color Images
ICCV '98 Proceedings of the Sixth International Conference on Computer Vision
Geometric Partial Differential Equations and Image Analysis
Geometric Partial Differential Equations and Image Analysis
Image Processing And Analysis: Variational, Pde, Wavelet, And Stochastic Methods
Image Processing And Analysis: Variational, Pde, Wavelet, And Stochastic Methods
Mathematical Problems in Image Processing: Partial Differential Equations and the Calculus of Variations (Applied Mathematical Sciences)
Non-local Regularization of Inverse Problems
ECCV '08 Proceedings of the 10th European Conference on Computer Vision: Part III
Nonlocal Variational Image Deblurring Models in the Presence of Gaussian or Impulse Noise
SSVM '09 Proceedings of the Second International Conference on Scale Space and Variational Methods in Computer Vision
From Local Kernel to Nonlocal Multiple-Model Image Denoising
International Journal of Computer Vision
Image Recovery via Nonlocal Operators
Journal of Scientific Computing
Bregmanized Nonlocal Regularization for Deconvolution and Sparse Reconstruction
SIAM Journal on Imaging Sciences
Regularization on discrete spaces
PR'05 Proceedings of the 27th DAGM conference on Pattern Recognition
-SVD: An Algorithm for Designing Overcomplete Dictionaries for Sparse Representation
IEEE Transactions on Signal Processing
Non-local Methods with Shape-Adaptive Patches (NLM-SAP)
Journal of Mathematical Imaging and Vision
A general framework for low level vision
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 Nonlocal Version of the Osher-Solé-Vese Model
Journal of Mathematical Imaging and Vision
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Following ideas of Kindermann et al. (Multiscale Model. Simul. 4(4):1091---1115, 2005) and Gilboa and Osher (Multiscale Model. Simul. 7:1005---1028, 2008) we introduce new nonlocal operators to interpret the nonlocal means filter (NLM) as a regularization of the corresponding Dirichlet functional. Then we use these nonlocal operators to propose a new nonlocal H1 model, which is (slightly) different from the nonlocal H1 model of Gilboa and Osher (Multiscale Model. Simul. 6(2):595---630, 2007; Proc. SPIE 6498:64980U, 2007). The key point is that both the fidelity and the smoothing term are derived from the same geometric principle. We compare this model with the nonlocal H1 model of Gilboa and Osher and the nonlocal means filter, both theoretically and in computer experiments. The experiments show that this new nonlocal H1 model also provides good results in image denoising and closer to the nonlocal means filter than the H1 model of Gilboa and Osher. This means that the new nonlocal operators yield a better interpretation of the nonlocal means filter than the nonlocal operators given in Gilboa and Osher (Multiscale Model. Simul. 7:1005---1028, 2008).