Total Variation on a Tree

@article{Kolmogorov2016TotalVO,
  title={Total Variation on a Tree},
  author={V. Kolmogorov and T. Pock and Michal Rolinek},
  journal={SIAM J. Imaging Sci.},
  year={2016},
  volume={9},
  pages={605-636}
}
We consider the problem of minimizing the continuous valued total variation subject to different unary terms on trees and propose fast direct algorithms based on dynamic programming to solve these problems. We treat both the convex and the nonconvex case and derive worst-case complexities that are equal to or better than existing methods. We show applications to total variation based two dimensional image processing and computer vision problems based on a Lagrangian decomposition approach. The… Expand
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References

SHOWING 1-10 OF 36 REFERENCES
Image Restoration with Discrete Constrained Total Variation Part I: Fast and Exact Optimization
  • J. Darbon, M. Sigelle
  • Mathematics, Computer Science
  • Journal of Mathematical Imaging and Vision
  • 2006
  • 246
  • PDF
Dynamic Programming and Graph Algorithms in Computer Vision
  • 175
  • PDF
Distance Transforms of Sampled Functions
  • 678
  • PDF
A First-Order Primal-Dual Algorithm for Convex Problems with Applications to Imaging
  • A. Chambolle, T. Pock
  • Mathematics, Computer Science
  • Journal of Mathematical Imaging and Vision
  • 2010
  • 3,232
  • Highly Influential
  • PDF
Nonlinear total variation based noise removal algorithms
  • 12,851
  • PDF
An efficient algorithm for image segmentation, Markov random fields and related problems
  • 160
  • Highly Influential
A Fast Iterative Shrinkage-Thresholding Algorithm for Linear Inverse Problems
  • 8,233
  • PDF
Modular Proximal Optimization for Multidimensional Total-Variation Regularization
  • 78
  • Highly Influential
  • PDF
A Method for Finding Projections onto the Intersection of Convex Sets in Hilbert Spaces
  • 402
...
1
2
3
4
...