Convergence and stability properties of minimal polynomial and reduced rank extrapolation algorithms
SIAM Journal on Numerical Analysis
Extrapolation methods for vector sequences
SIAM Review
Scale-Space and Edge Detection Using Anisotropic Diffusion
IEEE Transactions on Pattern Analysis and Machine Intelligence
Efficient implementation of minimal polynomial and reduced rank extrapolation methods
Journal of Computational and Applied Mathematics
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
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
Bilateral Filtering for Gray and Color Images
ICCV '98 Proceedings of the Sixth International Conference on Computer Vision
Efficient Beltrami flow using a short time kernel
Scale Space'03 Proceedings of the 4th international conference on Scale space methods in computer vision
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
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
Denoising algorithm for jacquard image using Beltrami manifold technique
IITA'09 Proceedings of the 3rd international conference on Intelligent information technology application
Calcolo: a quarterly on numerical analysis and theory of computation
On Semi-implicit Splitting Schemes for the Beltrami Color Image Filtering
Journal of Mathematical Imaging and Vision
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The Beltrami image flow is an effective non-linear filter, often used in color image processing. It was shown to be closely related to the median, total variation, and bilateral filters. It treats the image as a 2D manifold embedded in a hybrid spatial-feature space. Minimization of the image area surface yields the Beltrami flow. The corresponding diffusion operator is anisotropic and strongly couples the spectral components. Thus, there is so far no implicit nor operator splitting based numerical scheme for the PDE that describes Beltrami flow in color. Usually, this flow is implemented by explicit schemes, which are stable only for very small time steps and therefore require many iterations. At the other end, vector extrapolation techniques accelerate the convergence of vector sequences, without explicit knowledge of the sequence generator. In this paper, we propose to use the minimum polynomial extrapolation (MPE) and reduced rank extrapolation (RRE) vector extrapolation methods for accelerating the convergence of the explicit schemes for the Beltrami flow. Experiments demonstrate their stability and efficiency compared to explicit schemes.