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
SIAM Review
Convergence of the Gradient Projection Method for Generalized Convex Minimization
Computational Optimization and Applications
Fast Approximate Energy Minimization via Graph Cuts
IEEE Transactions on Pattern Analysis and Machine Intelligence
FOCS '99 Proceedings of the 40th Annual Symposium on Foundations of Computer Science
Discrete Convex Analysis: Monographs on Discrete Mathematics and Applications 10
Discrete Convex Analysis: Monographs on Discrete Mathematics and Applications 10
Computing Geodesics and Minimal Surfaces via Graph Cuts
ICCV '03 Proceedings of the Ninth IEEE International Conference on Computer Vision - Volume 2
An Experimental Comparison of Min-Cut/Max-Flow Algorithms for Energy Minimization in Vision
IEEE Transactions on Pattern Analysis and Machine Intelligence
Smooth minimization of non-smooth functions
Mathematical Programming: Series A and B
What Metrics Can Be Approximated by Geo-Cuts, Or Global Optimization of Length/Area and Flux
ICCV '05 Proceedings of the Tenth IEEE International Conference on Computer Vision (ICCV'05) Volume 1 - Volume 01
Handbook of Mathematical Models in Computer Vision
Handbook of Mathematical Models in Computer Vision
Globally Minimal Surfaces by Continuous Maximal Flows
IEEE Transactions on Pattern Analysis and Machine Intelligence
Image Analysis, Random Fields and Markov Chain Monte Carlo Methods: A Mathematical Introduction (Stochastic Modelling and Applied Probability)
Approximate Labeling via Graph Cuts Based on Linear Programming
IEEE Transactions on Pattern Analysis and Machine Intelligence
Continuous Global Optimization in Multiview 3D Reconstruction
International Journal of Computer Vision
On Total Variation Minimization and Surface Evolution Using Parametric Maximum Flows
International Journal of Computer Vision
Some First-Order Algorithms for Total Variation Based Image Restoration
Journal of Mathematical Imaging and Vision
SSVM '09 Proceedings of the Second International Conference on Scale Space and Variational Methods in Computer Vision
An Unconstrained Multiphase Thresholding Approach for Image Segmentation
SSVM '09 Proceedings of the Second International Conference on Scale Space and Variational Methods in Computer Vision
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
A Variational Model for Interactive Shape Prior Segmentation and Real-Time Tracking
SSVM '09 Proceedings of the Second International Conference on Scale Space and Variational Methods in Computer Vision
Split Bregman Algorithm, Douglas-Rachford Splitting and Frame Shrinkage
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
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
Global Minimization for Continuous Multiphase Partitioning Problems Using a Dual Approach
International Journal of Computer Vision
A First-Order Primal-Dual Algorithm for Convex Problems with Applications to Imaging
Journal of Mathematical Imaging and Vision
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
EMMCVPR'11 Proceedings of the 8th international conference on Energy minimization methods in computer vision and pattern recognition
Global Solutions of Variational Models with Convex Regularization
SIAM Journal on Imaging Sciences
NESTA: A Fast and Accurate First-Order Method for Sparse Recovery
SIAM Journal on Imaging Sciences
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
Nonmetric priors for continuous multilabel optimization
ECCV'12 Proceedings of the 12th European conference on Computer Vision - Volume Part VII
Modelling Convex Shape Priors and Matching Based on the Gromov-Wasserstein Distance
Journal of Mathematical Imaging and Vision
Coupling Image Restoration and Segmentation: A Generalized Linear Model/Bregman Perspective
International Journal of Computer Vision
Optimality Bounds for a Variational Relaxation of the Image Partitioning Problem
Journal of Mathematical Imaging and Vision
Convex Relaxation of a Class of Vertex Penalizing Functionals
Journal of Mathematical Imaging and Vision
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We study convex relaxations of the image labeling problem on a continuous domain with regularizers based on metric interaction potentials. The generic framework ensures existence of minimizers and covers a wide range of relaxations of the original combinatorial problem. We focus on two specific relaxations that differ in flexibility and simplicity—one can be used to tightly relax any metric interaction potential, while the other covers only Euclidean metrics but requires less computational effort. For solving the nonsmooth discretized problem, we propose a globally convergent Douglas-Rachford scheme and show that a sequence of dual iterates can be recovered in order to provide a posteriori optimality bounds. In a quantitative comparison to two other first-order methods, the approach shows competitive performance on synthetic and real-world images. By combining the method with an improved rounding technique for nonstandard potentials, we were able to routinely recover integral solutions within $1\%$-$5\%$ of the global optimum for the combinatorial image labeling problem.