Fronts propagating with curvature-dependent speed: algorithms based on Hamilton-Jacobi formulations
Journal of Computational Physics
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
A Multiphase Level Set Framework for Image Segmentation Using the Mumford and Shah Model
International Journal of Computer Vision
An Algorithm for Total Variation Minimization and Applications
Journal of Mathematical Imaging and Vision
Threshold dynamics for the piecewise constant Mumford-Shah functional
Journal of Computational Physics
Fast Global Minimization of the Active Contour/Snake Model
Journal of Mathematical Imaging and Vision
Γ-Convergence approximation to piecewise constant mumford-shah segmentation
ACIVS'05 Proceedings of the 7th international conference on Advanced Concepts for Intelligent Vision Systems
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
IEEE Transactions on Image Processing
A binary level set model and some applications to Mumford-Shah image segmentation
IEEE Transactions on Image Processing
Sulci detection in photos of the human cortex based on learned discriminative dictionaries
SSVM'11 Proceedings of the Third international conference on Scale Space and Variational Methods in Computer Vision
Continuous Multiclass Labeling Approaches and Algorithms
SIAM Journal on Imaging Sciences
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In this paper we provide a method to find global minimizers of certain non-convex 2-phase image segmentation problems. This is achieved by formulating a convex minimization problem whose minimizers are also minimizers of the initial non-convex segmentation problem, similar to the approach proposed by Nikolova, Esedo***lu and Chan. The key difference to the latter model is that the new model does not involve any constraint in the convex formulation that needs to be respected when minimizing the convex functional, neither explicitly nor by an artificial penalty term. This approach is related to recent results by Chambolle. Eliminating the constraint considerably simplifies the computational difficulties, and even a straightforward gradient descent scheme leads to a reliable computation of the global minimizer. Furthermore, the model is extended to multiphase segmentation along the lines of Vese and Chan. Numerical results of the model applied to the classical piecewise constant Mumford-Shah functional for two, four and eight phase segmentation are shown.