A finite algorithm for finding the projection of a point onto the Canonical simplex of Rn
Journal of Optimization Theory and Applications
Fast Approximate Energy Minimization via Graph Cuts
IEEE Transactions on Pattern Analysis and Machine Intelligence
Digital Picture Processing
Texture Synthesis by Non-Parametric Sampling
ICCV '99 Proceedings of the International Conference on Computer Vision-Volume 2 - Volume 2
Bilateral Filtering for Gray and Color Images
ICCV '98 Proceedings of the Sixth International Conference on Computer Vision
Smooth minimization of non-smooth functions
Mathematical Programming: Series A and B
Adaptive Support-Weight Approach for Correspondence Search
IEEE Transactions on Pattern Analysis and Machine Intelligence
Graph Cuts and Efficient N-D Image Segmentation
International Journal of Computer Vision
Fast Global Minimization of the Active Contour/Snake Model
Journal of Mathematical Imaging and Vision
Nonlocal Image and Movie Denoising
International Journal of Computer Vision
Some First-Order Algorithms for Total Variation Based Image Restoration
Journal of Mathematical Imaging and 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
Efficient Schemes for Total Variation Minimization Under Constraints in Image Processing
SIAM Journal on Scientific Computing
A Fast Iterative Shrinkage-Thresholding Algorithm for Linear Inverse Problems
SIAM Journal on Imaging Sciences
A Fast Iterative Shrinkage-Thresholding Algorithm for Linear Inverse Problems
SIAM Journal on Imaging Sciences
Global Minimization for Continuous Multiphase Partitioning Problems Using a Dual Approach
International Journal of Computer Vision
Interactive multi-label segmentation
ACCV'10 Proceedings of the 10th Asian conference on Computer vision - Volume Part I
A First-Order Primal-Dual Algorithm for Convex Problems with Applications to Imaging
Journal of Mathematical Imaging and Vision
Global Solutions of Variational Models with Convex Regularization
SIAM Journal on Imaging Sciences
Exact optimization for Markov random fields with convex priors
IEEE Transactions on Pattern Analysis and Machine Intelligence
IEEE Transactions on Image Processing
Efficient Nonlocal Means for Denoising of Textural Patterns
IEEE Transactions on Image Processing
High accuracy TOF and stereo sensor fusion at interactive rates
ECCV'12 Proceedings of the 12th international conference on Computer Vision - Volume 2
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The Potts model is a well established approach to solve different multi-label problems. The classical Potts prior penalizes the total interface length to obtain regular boundaries. Although the Potts prior works well for many problems, it does not preserve fine details of the boundaries. In recent years, non-local regularizers have been proposed to improve different variational models. The basic idea is to consider pixel interactions within a larger neighborhood. This can for example be used to incorporate low-level segmentation into the regularizer which leads to improved boundaries. In this work we study such an extension for the multi-label Potts model. Due to the increased model complexity, the main challenge is the development of an efficient minimization algorithm. We show that an accelerated first-order algorithm of Nesterov is well suited for this problem, due to its low memory requirements and its potential for massive parallelism. Our algorithm allows us to minimize the non-local Potts model with several hundred labels within a few minutes. This makes the non-local Potts model applicable for computer vision problems with many labels, such as multi-label image segmentation and stereo.