A finite algorithm for finding the projection of a point onto the Canonical simplex of Rn
Journal of Optimization Theory and Applications
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
International Journal of Computer Vision
A Nonlinear Primal-Dual Method for Total Variation-Based Image Restoration
SIAM Journal on Scientific Computing
A Multiphase Level Set Framework for Image Segmentation Using the Mumford and Shah Model
International Journal of Computer Vision
Diffusion Snakes: Introducing Statistical Shape Knowledge into the Mumford-Shah Functional
International Journal of Computer Vision
Wavelet Algorithms for High-Resolution Image Reconstruction
SIAM Journal on Scientific Computing
Discrete exterior calculus
An Algorithm for Total Variation Minimization and Applications
Journal of Mathematical Imaging and Vision
Globally Minimal Surfaces by Continuous Maximal Flows
IEEE Transactions on Pattern Analysis and Machine Intelligence
Fast Global Minimization of the Active Contour/Snake Model
Journal of Mathematical Imaging and Vision
Diffusion Equations over Arbitrary Triangulated Surfaces for Filtering and Texture Applications
IEEE Transactions on Visualization and Computer Graphics
A Convex Formulation of Continuous Multi-label Problems
ECCV '08 Proceedings of the 10th European Conference on Computer Vision: Part III
Convex Multi-class Image Labeling by Simplex-Constrained Total Variation
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 Schemes for Total Variation Minimization Under Constraints in Image Processing
SIAM Journal on Scientific Computing
Bregman Iterative Algorithms for $\ell_1$-Minimization with Applications to Compressed Sensing
SIAM Journal on Imaging Sciences
A Fast Iterative Shrinkage-Thresholding Algorithm for Linear Inverse Problems
SIAM Journal on Imaging Sciences
A Fast Iterative Shrinkage-Thresholding Algorithm for Linear Inverse Problems
SIAM Journal on Imaging Sciences
The Split Bregman Method for L1-Regularized Problems
SIAM Journal on Imaging Sciences
Scale-Space Analysis of Discrete Filtering over Arbitrary Triangulated Surfaces
SIAM Journal on Imaging Sciences
A New Alternating Minimization Algorithm for Total Variation Image Reconstruction
SIAM Journal on Imaging Sciences
Geometric Applications of the Split Bregman Method: Segmentation and Surface Reconstruction
Journal of Scientific Computing
A Unified Primal-Dual Algorithm Framework Based on Bregman Iteration
Journal of Scientific Computing
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
IEEE Transactions on Image Processing
IEEE Transactions on Image Processing
An EM algorithm for wavelet-based image restoration
IEEE Transactions on Image Processing
A binary level set model and some applications to Mumford-Shah image segmentation
IEEE Transactions on Image Processing
An Iterative Shrinkage Approach to Total-Variation Image Restoration
IEEE Transactions on Image Processing
Group-Valued regularization for analysis of articulated motion
ECCV'12 Proceedings of the 12th international conference on Computer Vision - Volume Part I
Variational structure-texture image decomposition on manifolds
Signal Processing
Journal of Scientific Computing
A fixed-point augmented Lagrangian method for total variation minimization problems
Journal of Visual Communication and Image Representation
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Recently total variation (TV) regularization has been proven very successful in image restoration and segmentation. In image restoration, TV based models offer a good edge preservation property. In image segmentation, TV (or vectorial TV) helps to obtain convex formulations of the problems and thus provides global minimizations. Due to these advantages, TV based models have been extended to image restoration and data segmentation on manifolds. However, TV based restoration and segmentation models are difficult to solve, due to the nonlinearity and non-differentiability of the TV term. Inspired by the success of operator splitting and the augmented Lagrangian method (ALM) in 2D planar image processing, we extend the method to TV and vectorial TV based image restoration and segmentation on triangulated surfaces, which are widely used in computer graphics and computer vision. In particular, we will focus on the following problems. First, several Hilbert spaces will be given to describe TV and vectorial TV based variational models in the discrete setting. Second, we present ALM applied to TV and vectorial TV image restoration on mesh surfaces, leading to efficient algorithms for both gray and color image restoration. Third, we discuss ALM for vectorial TV based multi-region image segmentation, which also works for both gray and color images. The proposed method benefits from fast solvers for sparse linear systems and closed form solutions to subproblems. Experiments on both gray and color images demonstrate the efficiency of our algorithms.