A Computational Approach to Edge Detection
IEEE Transactions on Pattern Analysis and Machine Intelligence
Scale-Space and Edge Detection Using Anisotropic Diffusion
IEEE Transactions on Pattern Analysis and Machine Intelligence
Image selective smoothing and edge detection by nonlinear diffusion
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
Numerical recipes in C (2nd ed.): the art of scientific computing
Numerical recipes in C (2nd ed.): the art of scientific computing
SIAM Journal on Applied Mathematics
A multigrid tutorial (2nd ed.)
A multigrid tutorial (2nd ed.)
Multigrid
An Algebraic Multigrid Approach for Image Analysis
SIAM Journal on Scientific Computing
A Review of Nonlinear Diffusion Filtering
SCALE-SPACE '97 Proceedings of the First International Conference on Scale-Space Theory in Computer Vision
Selection of Optimal Stopping Time for Nonlinear Diffusion Filtering
Scale-Space '01 Proceedings of the Third International Conference on Scale-Space and Morphology in Computer Vision
An Accurate Operator Splitting Scheme for Nonlinear Diffusion Filtering
Scale-Space '01 Proceedings of the Third International Conference on Scale-Space and Morphology in Computer Vision
Biased Anisotropic Diffusion--A Unified Regularization and Diffusion
Biased Anisotropic Diffusion--A Unified Regularization and Diffusion
An Algorithm for Total Variation Minimization and Applications
Journal of Mathematical Imaging and Vision
CVPR '05 Proceedings of the 2005 IEEE Computer Society Conference on Computer Vision and Pattern Recognition (CVPR'05) - Volume 1 - Volume 01
Noise Estimation from a Single Image
CVPR '06 Proceedings of the 2006 IEEE Computer Society Conference on Computer Vision and Pattern Recognition - Volume 1
Mathematical Problems in Image Processing: Partial Differential Equations and the Calculus of Variations (Applied Mathematical Sciences)
Nonlinear Scale Space with Spatially Varying Stopping Time
IEEE Transactions on Pattern Analysis and Machine Intelligence
SSVM '09 Proceedings of the Second International Conference on Scale Space and Variational Methods in Computer Vision
Multigrid anisotropic diffusion
IEEE Transactions on Image Processing
Efficient and reliable schemes for nonlinear diffusion filtering
IEEE Transactions on Image Processing
Image quality assessment: from error visibility to structural similarity
IEEE Transactions on Image Processing
Multigrid Geometric Active Contour Models
IEEE Transactions on Image Processing
On the choice of the parameters for anisotropic diffusion in image processing
Pattern Recognition
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Anisotropic diffusion methods are well known for giving good qualitative results for image denoising. This paper gives a review of the anisotropic diffusion methodology and its application to image denoising. We propose a fixed-point iteration using a multigrid solver to solve a regularized anisotropic diffusion equation, which is not only well-posed, but also has a nontrivial steady-state solution. A new regularization parameter-choice method (Brent-NCP), combining Brent's method and the normalized cumulative periodogram information of the misfit, is also introduced. We test our algorithm on several common test images with different noise levels. The experimental results demonstrate the effectiveness of the anisotropic diffusion with a multigrid approach and the broad applicability of the Brent-NCP parameter-choice algorithm.