Fronts propagating with curvature-dependent speed: algorithms based on Hamilton-Jacobi formulations
Journal of Computational Physics
Proximal Minimization Methods with Generalized Bregman Functions
SIAM Journal on Control and Optimization
Applied Numerical Mathematics
Convex analysis and variational problems
Convex analysis and variational problems
Markov random field modeling in image analysis
Markov random field modeling in image analysis
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
A Multiphase Level Set Framework for Image Segmentation Using the Mumford and Shah Model
International Journal of Computer Vision
Computing Geodesics and Minimal Surfaces via Graph Cuts
ICCV '03 Proceedings of the Ninth IEEE International Conference on Computer Vision - Volume 2
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
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
Convergent Tree-Reweighted Message Passing for Energy Minimization
IEEE Transactions on Pattern Analysis and Machine Intelligence
Clustering with Bregman Divergences
The Journal of Machine Learning Research
A Unified Continuous Optimization Framework for Center-Based Clustering Methods
The Journal of Machine Learning Research
Approximate Labeling via Graph Cuts Based on Linear Programming
IEEE Transactions on Pattern Analysis and Machine Intelligence
Fast Global Minimization of the Active Contour/Snake Model
Journal of Mathematical Imaging and Vision
A Convex Formulation of Continuous Multi-label Problems
ECCV '08 Proceedings of the 10th European Conference on Computer Vision: Part III
An Experimental Comparison of Discrete and Continuous Shape Optimization Methods
ECCV '08 Proceedings of the 10th European Conference on Computer Vision: Part I
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
P³ & Beyond: Move Making Algorithms for Solving Higher Order Functions
IEEE Transactions on Pattern Analysis and Machine Intelligence
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
An integral solution to surface evolution PDEs via geo-cuts
ECCV'06 Proceedings of the 9th European conference on Computer Vision - Volume Part III
MAP estimation via agreement on trees: message-passing and linear programming
IEEE Transactions on Information Theory
Exact optimization for Markov random fields with convex priors
IEEE Transactions on Pattern Analysis and Machine Intelligence
IEEE Transactions on Image Processing
A binary level set model and some applications to Mumford-Shah image segmentation
IEEE Transactions on Image Processing
A continuous max-flow approach to minimal partitions with label cost prior
SSVM'11 Proceedings of the Third international conference on Scale Space and Variational Methods in Computer Vision
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
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
A convex relaxation method for computing exact global solutions for multiplicative noise removal
Journal of Computational and Applied Mathematics
A multiple object geometric deformable model for image segmentation
Computer Vision and Image Understanding
Journal of Scientific Computing
Journal of Scientific Computing
Gradient competition anisotropy for centerline extraction and segmentation of spinal cords
IPMI'13 Proceedings of the 23rd international conference on Information Processing in Medical Imaging
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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This paper is devoted to the optimization problem of continuous multi-partitioning, or multi-labeling, which is based on a convex relaxation of the continuous Potts model. In contrast to previous efforts, which are tackling the optimal labeling problem in a direct manner, we first propose a novel dual model and then build up a corresponding duality-based approach. By analyzing the dual formulation, sufficient conditions are derived which show that the relaxation is often exact, i.e. there exists optimal solutions that are also globally optimal to the original nonconvex Potts model. In order to deal with the nonsmooth dual problem, we develop a smoothing method based on the log-sum exponential function and indicate that such a smoothing approach leads to a novel smoothed primal-dual model and suggests labelings with maximum entropy. Such a smoothing method for the dual model also yields a new thresholding scheme to obtain approximate solutions. An expectation maximization like algorithm is proposed based on the smoothed formulation which is shown to be superior in efficiency compared to earlier approaches from continuous optimization. Numerical experiments also show that our method outperforms several competitive approaches in various aspects, such as lower energies and better visual quality.