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
SUSAN—A New Approach to Low Level Image Processing
International Journal of Computer Vision
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
IEEE Transactions on Pattern Analysis and Machine Intelligence
Diffusions and Confusions in Signal and Image Processing
Journal of Mathematical Imaging and Vision
Coherence-Enhancing Diffusion Filtering
International Journal of Computer Vision
From High Energy Physics to Low Level Vision
SCALE-SPACE '97 Proceedings of the First International Conference on Scale-Space Theory in Computer Vision
Non-Linear Gaussian Filters Performing Edge Preserving Diffusion
Mustererkennung 1995, 17. DAGM-Symposium
Journal of Mathematical Imaging and Vision
Bilateral Filtering for Gray and Color Images
ICCV '98 Proceedings of the Sixth International Conference on Computer Vision
Smoothing by Example: Mesh Denoising by Averaging with Similarity-Based Weights
SMI '06 Proceedings of the IEEE International Conference on Shape Modeling and Applications 2006
On Semi-implicit Splitting Schemes for the Beltrami Color Flow
SSVM '09 Proceedings of the Second International Conference on Scale Space and Variational Methods in Computer Vision
Efficient Beltrami filtering of color images via vector extrapolation
SSVM'07 Proceedings of the 1st international conference on Scale space and variational methods in computer vision
A fast approximation of the bilateral filter using a signal processing approach
ECCV'06 Proceedings of the 9th European conference on Computer Vision - Volume Part IV
Color image deblurring with impulsive noise
VLSM'05 Proceedings of the Third international conference on Variational, Geometric, and Level Set Methods in Computer Vision
A general framework for low level vision
IEEE Transactions on Image Processing
Modified curvature motion for image smoothing and enhancement
IEEE Transactions on Image Processing
Efficient and reliable schemes for nonlinear diffusion filtering
IEEE Transactions on Image Processing
On the origin of the bilateral filter and ways to improve it
IEEE Transactions on Image Processing
A Short- Time Beltrami Kernel for Smoothing Images and Manifolds
IEEE Transactions on Image Processing
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The Beltrami flow is an efficient nonlinear filter, that was shown to be effective for color image processing. The corresponding anisotropic diffusion operator strongly couples the spectral components. Usually, this flow is implemented by explicit schemes, that are stable only for very small time steps and therefore require many iterations. In this paper we introduce a semi-implicit Crank-Nicolson scheme based on locally one-dimensional (LOD)/additive operator splitting (AOS) for implementing the anisotropic Beltrami operator. The mixed spatial derivatives are treated explicitly, while the non-mixed derivatives are approximated in an implicit manner. In case of constant coefficients, the LOD splitting scheme is proven to be unconditionally stable. Numerical experiments indicate that the proposed scheme is also stable in more general settings. Stability, accuracy, and efficiency of the splitting schemes are tested in applications such as the Beltrami-based scale-space, Beltrami denoising and Beltrami deblurring. In order to further accelerate the convergence of the numerical scheme, the reduced rank extrapolation (RRE) vector extrapolation technique is employed.