A note on the gradient of a multi-image
Computer Vision, Graphics, and Image Processing - Lectures notes in computer science, Vol. 201 (G. Goos and J. Hartmanis, Eds.)
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
A Nonlinear Primal-Dual Method for Total Variation-Based Image Restoration
SIAM Journal on Scientific Computing
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
Digital Picture Processing
IEEE Transactions on Pattern Analysis and Machine Intelligence
Diffusions and Confusions in Signal and Image Processing
Journal of Mathematical Imaging and Vision
Bilateral Filtering for Gray and Color Images
ICCV '98 Proceedings of the Sixth International Conference on Computer Vision
Numerical Geometry of Images: Theory, Algorithms, and Applications
Numerical Geometry of Images: Theory, Algorithms, and Applications
An Algorithm for Total Variation Minimization and Applications
Journal of Mathematical Imaging and Vision
Vector-Valued Image Regularization with PDEs: A Common Framework for Different Applications
IEEE Transactions on Pattern Analysis and Machine Intelligence
International Journal of Computer Vision
A Fast Approximation of the Bilateral Filter Using a Signal Processing Approach
International Journal of Computer Vision
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
Augmented Lagrangian Method, Dual Methods and Split Bregman Iteration for ROF Model
SSVM '09 Proceedings of the Second International Conference on Scale Space and Variational Methods in Computer Vision
Efficient Beltrami Image Filtering via Vector Extrapolation Methods
SIAM Journal on Imaging Sciences
A New Alternating Minimization Algorithm for Total Variation Image Reconstruction
SIAM Journal on Imaging Sciences
Anisotropic diffusion of multivalued images with applications to color filtering
IEEE Transactions on Image Processing
Color TV: total variation methods for restoration of vector-valued images
IEEE Transactions on Image Processing
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
On the origin of the bilateral filter and ways to improve it
IEEE Transactions on Image Processing
Deblurring of Color Images Corrupted by Impulsive Noise
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 Laplace-Beltrami operator is an extension of the Laplacian from flat domains to curved manifolds. It was proven to be useful for color image processing as it models a meaningful coupling between the color channels. This coupling is naturally expressed in the Beltrami framework in which a color image is regarded as a two dimensional manifold embedded in a hybrid, five-dimensional, spatial-chromatic (x,y,R,G,B) space. The Beltrami filter defined by this framework minimizes the Polyakov action, adopted from high-energy physics, which measures the area of the image manifold. Minimization is usually obtained through a geometric heat equation defined by the Laplace-Beltrami operator. Though efficient simplifications such as the bilateral filter have been proposed for the single channel case, so far, the coupling between the color channel posed a non-trivial obstacle when designing fast Beltrami filters. Here, we propose to use an augmented Lagrangian approach to design an efficient and accurate regularization framework for color image processing by minimizing the Polyakov action. We extend the augmented Lagrangian framework for total variation (TV) image denoising to the more general Polyakov action case for color images, and apply the proposed framework to denoise and deblur color images.