How Good is Recursive Bisection?
SIAM Journal on Scientific Computing
A Multiphase Level Set Framework for Image Segmentation Using the Mumford and Shah Model
International Journal of Computer Vision
What Energy Functions Can Be Minimizedvia Graph Cuts?
IEEE Transactions on Pattern Analysis and Machine Intelligence
Graph based algorithms for scene reconstruction from two or more views
Graph based algorithms for scene reconstruction from two or more views
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
Minimizing Nonsubmodular Functions with Graph Cuts-A Review
IEEE Transactions on Pattern Analysis and Machine Intelligence
Fast Global Minimization of the Active Contour/Snake Model
Journal of Mathematical Imaging and Vision
Unsupervised multiphase segmentation: A recursive approach
Computer Vision and Image Understanding
SSVM '09 Proceedings of the Second International Conference on Scale Space and Variational Methods in Computer Vision
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
On two multigrid algorithms for modeling variational multiphase image segmentation
IEEE Transactions on Image Processing
Graph cut optimization for the Mumford-Shah model
VIIP '07 The Seventh IASTED International Conference on Visualization, Imaging and Image Processing
The piecewise smooth Mumford-Shah functional on an arbitrary graph
IEEE Transactions on Image Processing
Unsupervised hierarchical image segmentation with level set and additive operator splitting
Pattern Recognition Letters
A fast and exact algorithm for total variation minimization
IbPRIA'05 Proceedings of the Second Iberian conference on Pattern Recognition and Image Analysis - Volume Part I
Exact optimization for Markov random fields with convex priors
IEEE Transactions on Pattern Analysis and Machine Intelligence
IEEE Transactions on Image Processing
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The Mumford-Shah model has been one of the most powerful models in image segmentation and denoising. The optimization of the multiphase Mumford-Shah energy functional has been performed using level sets methods that optimize the Mumford-Shah energy by evolving the level sets via the gradient descent. These methods are very slow and prone to getting stuck in local optima due to the use of the gradient descent. After the reformulation of the bimodal Mumford-Shah functional on a graph, several groups investigated the hierarchical extension of the graph representation to multi class. These approaches, though more effective than level sets, provide approximate solutions and can diverge away from the optimal solution. In this paper, we present a discrete optimization for the multiphase Mumford Shah functional that directly minimizes the multiphase functional without recursive bisection on the labels. Our approach handles the nonsubmodularity of the multiphase energy function and provide a global optimum if prior information is provided.