# Convergent Tree-Reweighted Message Passing for Energy Minimization

@article{Kolmogorov2006ConvergentTM, title={Convergent Tree-Reweighted Message Passing for Energy Minimization}, author={Vladimir Kolmogorov}, journal={IEEE Transactions on Pattern Analysis and Machine Intelligence}, year={2006}, volume={28}, pages={1568-1583} }

Algorithms for discrete energy minimization are of fundamental importance in computer vision. In this paper, we focus on the recent technique proposed by Wainwright et al. (Nov. 2005)- tree-reweighted max-product message passing (TRW). It was inspired by the problem of maximizing a lower bound on the energy. However, the algorithm is not guaranteed to increase this bound - it may actually go down. In addition, TRW does not always converge. We develop a modification of this algorithm which we…

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## References

SHOWING 1-10 OF 46 REFERENCES

An experimental comparison of min-cut/max- flow algorithms for energy minimization in vision

- Computer ScienceIEEE Transactions on Pattern Analysis and Machine Intelligence
- 2004

The goal of this paper is to provide an experimental comparison of the efficiency of min-cut/max flow algorithms for applications in vision, comparing the running times of several standard algorithms, as well as a new algorithm that is recently developed.

On the Optimality of Tree-reweighted Max-product Message-passing

- Computer ScienceUAI
- 2005

This paper demonstrates how it is possible to identify part of the optimal solution—i.e., a provably optimal solution for a subset of nodes— without knowing a complete solution, and establishes that for submodular functions, a WTA fixed point always yields a globally optimal solution.

Efficient Belief Propagation for Early Vision

- Computer ScienceProceedings of the 2004 IEEE Computer Society Conference on Computer Vision and Pattern Recognition, 2004. CVPR 2004.
- 2004

Algorithmic techniques are presented that substantially improve the running time of the loopy belief propagation approach and reduce the complexity of the inference algorithm to be linear rather than quadratic in the number of possible labels for each pixel, which is important for problems such as image restoration that have a large label set.

Globally optimal solutions for energy minimization in stereo vision using reweighted belief propagation

- Computer ScienceTenth IEEE International Conference on Computer Vision (ICCV'05) Volume 1
- 2005

It is shown that for standard benchmark stereo pairs, the global optimum can be found in about 30 minutes using a variant of the belief propagation (BP) algorithm.

Fast approximate energy minimization via graph cuts

- Computer ScienceProceedings of the Seventh IEEE International Conference on Computer Vision
- 1999

This paper proposes two algorithms that use graph cuts to compute a local minimum even when very large moves are allowed, and generates a labeling such that there is no expansion move that decreases the energy.

Tree-reweighted belief propagation algorithms and approximate ML estimation by pseudo-moment matching

- Computer ScienceAISTATS
- 2003

A class of local message-passing algorithms is developed, which is called tree-reweighted belief propagation, for efficiently computing the value of these upper bounds on the log partition function of an arbitrary undirected graphical model, as well as the associated pseudomarginals.

MAP estimation via agreement on trees: message-passing and linear programming

- Computer ScienceIEEE Transactions on Information Theory
- 2005

This work develops and analyze methods for computing provably optimal maximum a posteriori probability (MAP) configurations for a subclass of Markov random fields defined on graphs with cycles and establishes a connection between a certain LP relaxation of the mode-finding problem and a reweighted form of the max-product (min-sum) message-passing algorithm.

Multi-camera Scene Reconstruction via Graph Cuts

- Computer Science, MathematicsECCV
- 2002

This paper addresses the problem of computing the 3-dimensional shape of an arbitrary scene from a set of images taken at known viewpoints by giving an energy minimization formulation of the multi-camera scene reconstruction problem.

Constructing free-energy approximations and generalized belief propagation algorithms

- Computer ScienceIEEE Transactions on Information Theory
- 2005

This work explains how to obtain region-based free energy approximations that improve the Bethe approximation, and corresponding generalized belief propagation (GBP) algorithms, and describes empirical results showing that GBP can significantly outperform BP.

Approximation algorithms for the metric labeling problem via a new linear programming formulation

- Computer Science, MathematicsSODA '01
- 2001

A natural integer programming formulation is introduced and it is shown that the integrality gap of its linear relaxation either matches or improves the ratios known for several cases of the metric labeling problem studied until now, providing a unified approach to solving them.