A finite algorithm for finding the projection of a point onto the Canonical simplex of Rn
Journal of Optimization Theory and Applications
Weakly differentiable functions
Weakly differentiable functions
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
Mathematical Programming: Series A and B
Iterative methods for total variation denoising
SIAM Journal on Scientific Computing - Special issue on iterative methods in numerical linear algebra; selected papers from the Colorado conference
Auxiliary variables and two-step iterative algorithms in computer vision problems
Journal of Mathematical Imaging and Vision
SIAM Review
A Nonlinear Primal-Dual Method for Total Variation-Based Image Restoration
SIAM Journal on Scientific Computing
Fast Approximate Energy Minimization via Graph Cuts
IEEE Transactions on Pattern Analysis and Machine Intelligence
Oscillating Patterns in Image Processing and Nonlinear Evolution Equations: The Fifteenth Dean Jacqueline B. Lewis Memorial Lectures
FOCS '99 Proceedings of the 40th Annual Symposium on Foundations of Computer Science
What Energy Functions Can Be Minimizedvia Graph Cuts?
IEEE Transactions on Pattern Analysis and Machine Intelligence
An Algorithm for Total Variation Minimization and Applications
Journal of Mathematical Imaging and Vision
An Experimental Comparison of Min-Cut/Max-Flow Algorithms for Energy Minimization in Vision
IEEE Transactions on Pattern Analysis and Machine Intelligence
SIAM Journal on Scientific Computing
Image Processing And Analysis: Variational, Pde, Wavelet, And Stochastic Methods
Image Processing And Analysis: Variational, Pde, Wavelet, And Stochastic Methods
A Convex Formulation of Continuous Multi-label Problems
ECCV '08 Proceedings of the 10th European Conference on Computer Vision: Part III
Total variation minimization and a class of binary MRF models
EMMCVPR'05 Proceedings of the 5th international conference on Energy Minimization Methods in Computer Vision and Pattern Recognition
A comparative study of energy minimization methods for markov random fields
ECCV'06 Proceedings of the 9th European conference on Computer Vision - Volume Part II
Exact optimization for Markov random fields with convex priors
IEEE Transactions on Pattern Analysis and Machine Intelligence
Anisotropic diffusion of multivalued images with applications to color filtering
IEEE Transactions on Image Processing
Nonlinear image recovery with half-quadratic regularization
IEEE Transactions on Image Processing
Efficient Global Minimization for the Multiphase Chan-Vese Model of Image Segmentation
EMMCVPR '09 Proceedings of the 7th International Conference on Energy Minimization Methods in Computer Vision and Pattern Recognition
Fast and exact primal-dual iterations for variational problems in computer vision
ECCV'10 Proceedings of the 11th European conference on Computer vision: Part II
A continuous max-flow approach to potts model
ECCV'10 Proceedings of the 11th European conference on Computer vision: Part VI
Global Minimization for Continuous Multiphase Partitioning Problems Using a Dual Approach
International Journal of Computer Vision
Globally optimal image partitioning by multicuts
EMMCVPR'11 Proceedings of the 8th international conference on Energy minimization methods in computer vision and pattern recognition
Optimality bounds for a variational relaxation of the image partitioning problem
EMMCVPR'11 Proceedings of the 8th international conference on Energy minimization methods in computer vision and pattern recognition
A Spatial Regularization Approach for Vector Quantization
Journal of Mathematical Imaging and Vision
Journal of Scientific Computing
Efficient minimization of the non-local potts model
SSVM'11 Proceedings of the Third international conference on Scale Space and Variational Methods in Computer Vision
Weakly convex coupling continuous cuts and shape priors
SSVM'11 Proceedings of the Third international conference on Scale Space and Variational Methods in Computer Vision
Completely Convex Formulation of the Chan-Vese Image Segmentation Model
International Journal of Computer Vision
Segmentation of images with separating layers by fuzzy c-means and convex optimization
Journal of Visual Communication and Image Representation
Continuous Multiclass Labeling Approaches and Algorithms
SIAM Journal on Imaging Sciences
Wehrli 2.0: an algorithm for "tidying up art"
ECCV'12 Proceedings of the 12th international conference on Computer Vision - Volume Part I
A multiple object geometric deformable model for image segmentation
Computer Vision and Image Understanding
Optimality Bounds for a Variational Relaxation of the Image Partitioning Problem
Journal of Mathematical Imaging and Vision
Journal of Mathematical Imaging and Vision
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Multi-class labeling is one of the core problems in image analysis. We show how this combinatorial problem can be approximately solved using tools from convex optimization. We suggest a novel functional based on a multidimensional total variation formulation, allowing for a broad range of data terms. Optimization is carried out in the operator splitting framework using Douglas-Rachford Splitting. In this connection, we compare two methods to solve the Rudin-Osher-Fatemi type subproblems and demonstrate the performance of our approach on single- and multichannel images.