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Global optimization for first order Markov Random Fields with submodular priors

Jérôme Darbon
2009 Discrete Applied Mathematics  
The label set is assumed to be linearly ordered and of finite cardinality, while each interaction term (prior) shall be a submodular function.  ...  This paper copes with the global optimization of Markovian energies. Energies are defined on an arbitrary graph and pairwise interactions are considered.  ...  The author deeply thanks Marc Sigelle (Telecom ParisTech) for fruitful discussions and  ... 
doi:10.1016/j.dam.2009.02.026 fatcat:jaav5cy3grab7elupjztqhuqmq

Statistical Priors for Efficient Combinatorial Optimization Via Graph Cuts [chapter]

Daniel Cremers, Leo Grady
2006 Lecture Notes in Computer Science  
While the Bayesian approach has been successfully applied in the Markov random field literature, the resulting combinatorial optimization problems have been commonly treated with rather inefficient and  ...  As an illustration, we demonstrate that one can optimally restore binary textures from very noisy images with runtimes on the order of a second while imposing hundreds of statistically learned constraints  ...  Ishikawa [14] provided constructive results showing how Graph Cuts may be applied to optimize Markov random fields for convex expressions.  ... 
doi:10.1007/11744078_21 fatcat:rtndbjam5zdozajvnxv6vg5tem

Higher-order gradient descent by fusion-move graph cut

Hiroshi Ishikawa
2009 2009 IEEE 12th International Conference on Computer Vision  
Markov Random Field is now ubiquitous in many formulations of various vision problems.  ...  to first-order, and iii) the QPBO algorithm.  ...  Acknowledgments This work was partially supported by the Kayamori Foundation and the Grant-in-Aid for Scientific Research 19650065 from the Japan Society for the Promotion of Science.  ... 
doi:10.1109/iccv.2009.5459187 dblp:conf/iccv/Ishikawa09 fatcat:cq6pd6ttqvaxzaoo2gi7vvkijm

Inference for order reduction in Markov random fields

Andrew C. Gallagher, Dhruv Batra, Devi Parikh
2011 CVPR 2011  
This paper presents an algorithm for order reduction of factors in High-Order Markov Random Fields (HOMRFs).  ...  Standard techniques for transforming arbitrary high-order factors into pairwise ones have been known for a long time.  ...  Introduction The introduction of sophisticated discrete optimization tools for inference in Markov Random Fields (MRFs) over the last two decades has brought about a paradigm shift in the way we think  ... 
doi:10.1109/cvpr.2011.5995452 dblp:conf/cvpr/GallagherBP11 fatcat:ka45pojctzd7jemnbri45wtjum

Σ-Optimality for Active Learning on Gaussian Random Fields

Yifei Ma, Roman Garnett, Jeff G. Schneider
2013 Neural Information Processing Systems  
We further show that GRFs satisfy the suppressor-free condition in addition to the conditional independence inherited from Markov random fields.  ...  V-optimality satisfies a submodularity property showing that greedy reduction produces a (1 − 1/e) globally optimal solution.  ...  It is well known for Markov random fields that the labels of two nodes on a graph become independent given labels of their Markov blanket.  ... 
dblp:conf/nips/MaGS13 fatcat:ts42pggfobbw3acnqq7qznwpvm

A graph cut algorithm for higher-order Markov Random Fields

Alexander Fix, Aritanan Gruber, Endre Boros, Ramin Zabih
2011 2011 International Conference on Computer Vision  
Higher-order Markov Random Fields, which can capture important properties of natural images, have become increasingly important in computer vision.  ...  His method transforms an arbitrary higher-order MRF with binary labels into a first-order one with the same minima.  ...  This avoids the distracting sawtooth pattern visible in [8, 9] , due to his alternation between random fusion moves and blurred fusion moves. Schwartz for helpful comments.  ... 
doi:10.1109/iccv.2011.6126347 dblp:conf/iccv/FixGBZ11 fatcat:ynnurxbgbnalxgv55uoxfeg63i

Higher-order clique reduction in binary graph cut

H. Ishikawa
2009 2009 IEEE Conference on Computer Vision and Pattern Recognition  
We introduce a new technique that can reduce any higher-order Markov random field with binary labels into a first-order one that has the same minima as the original.  ...  The problem uses the Fields of Experts model, a learned spatial prior of natural images that has been used to test two belief propagation algorithms capable of optimizing higher-order energies.  ...  Acknowledgments We thank Stefan Roth for providing the test images and the FoE models, Brian Potetz for providing his results, and Vladimir Kolmogorov for making his QPBO code publicly available.  ... 
doi:10.1109/cvprw.2009.5206689 fatcat:cvptk3jvlvfgznzs2qfdvi5p54

Higher-order clique reduction in binary graph cut

Hiroshi Ishikawa
2009 2009 IEEE Conference on Computer Vision and Pattern Recognition  
We introduce a new technique that can reduce any higher-order Markov random field with binary labels into a first-order one that has the same minima as the original.  ...  The problem uses the Fields of Experts model, a learned spatial prior of natural images that has been used to test two belief propagation algorithms capable of optimizing higher-order energies.  ...  Acknowledgments We thank Stefan Roth for providing the test images and the FoE models, Brian Potetz for providing his results, and Vladimir Kolmogorov for making his QPBO code publicly available.  ... 
doi:10.1109/cvpr.2009.5206689 dblp:conf/cvpr/Ishikawa09 fatcat:rng4csnxkjhnpomrlio2vrryga

Markov Chain Monte Carlo combined with deterministic methods for Markov random field optimization

Wonsik Kim, Kyoung Mu Lee
2009 2009 IEEE Conference on Computer Vision and Pattern Recognition  
Although they have obtained good results, they are still unsatisfactory when it comes to more difficult MRF problems such as non-submodular energy functions, highly connected MRFs, and high-order clique  ...  There have also been other approaches, known as stochastic sampling-based algorithms, which include Simulated Annealing, Markov Chain Monte Carlo and Populationbased Markov Chain Monte Carlo.  ...  Introduction Markov Random Field (MRF) models are of fundamental importance in computer vision. Many vision problems have been successfully formulated in MRF optimization.  ... 
doi:10.1109/cvprw.2009.5206504 fatcat:ysrjskucpvgoxiyjobb3dd2n7y

Markov Chain Monte Carlo combined with deterministic methods for Markov random field optimization

Wonsik Kim, Kyoung Mu Lee
2009 2009 IEEE Conference on Computer Vision and Pattern Recognition  
Although they have obtained good results, they are still unsatisfactory when it comes to more difficult MRF problems such as non-submodular energy functions, highly connected MRFs, and high-order clique  ...  There have also been other approaches, known as stochastic sampling-based algorithms, which include Simulated Annealing, Markov Chain Monte Carlo and Populationbased Markov Chain Monte Carlo.  ...  Introduction Markov Random Field (MRF) models are of fundamental importance in computer vision. Many vision problems have been successfully formulated in MRF optimization.  ... 
doi:10.1109/cvpr.2009.5206504 dblp:conf/cvpr/KimL09 fatcat:cm3bj5sy7rdebammistyxhjjsi

Submodular decomposition framework for inference in associative Markov networks with global constraints

Anton Osokin, Dmitry Vetrov, Vladimir Kolmogorov
2011 CVPR 2011  
In this paper we address the problem of finding the most probable state of discrete Markov random field (MRF) with associative pairwise terms.  ...  We propose a new type of MRF decomposition, submodular decomposition (SMD).  ...  Acknowledgements This work was supported by the Russian Foundation for Basic Research (projects 10-01-00131 and 10-01-90419), Russian President Grant MK-3827.2010.9, and Royal Academy of Engineering/EPSRC  ... 
doi:10.1109/cvpr.2011.5995361 dblp:conf/cvpr/OsokinVK11 fatcat:ajjgbzyjhvbzji57xtcic2rqbi

A hybrid approach for MRF optimization problems: Combination of stochastic sampling and deterministic algorithms

Wonsik Kim, Kyoung Mu Lee
2011 Computer Vision and Image Understanding  
In computer vision, many applications have been formulated as Markov Random Field (MRF) optimization or energy minimization problems.  ...  MRFs, and high-order clique potentials.  ...  Consequently, this will encourage the design of better yet more complex energy models for practical vision applications.  ... 
doi:10.1016/j.cviu.2011.05.015 fatcat:7cjzcigtarbwvcedasn442bprm

Transformation of General Binary MRF Minimization to the First-Order Case

H Ishikawa
2011 IEEE Transactions on Pattern Analysis and Machine Intelligence  
We introduce a transformation of general higher-order Markov random field with binary labels into a first-order one that has the same minima as the original.  ...  This is because of the lack of efficient algorithms to optimize energies with higher-order interactions.  ...  ACKNOWLEDGMENTS The author thanks Stefan Roth for providing the test images and the FoE models, Brian Potetz for providing his results, and Vladimir Kolmogorov for making his QPBO code publicly available  ... 
doi:10.1109/tpami.2010.91 pmid:20421673 fatcat:vchkur2jo5ab5adcrnxz7ywzcm

Markov Random Field modeling, inference & learning in computer vision & image understanding: A survey

Chaohui Wang, Nikos Komodakis, Nikos Paragios
2013 Computer Vision and Image Understanding  
In this paper, we present a comprehensive survey of Markov Random Fields (MRFs) in computer vision and image understanding, with respect to the modeling, the inference and the learning.  ...  While most of the literature concerns pairwise MRFs, in recent years we have also witnessed signi cant progress in higher-order MRFs, which substantially enhances the expressiveness of graph-based models  ...  Acknowledgments The authors would like to thank the anonymous reviewers for their constructive comments. Part of the work was done while C. Wang was with the Vision Lab at  ... 
doi:10.1016/j.cviu.2013.07.004 fatcat:d4ruu3u4gvg3dmud7xhni5gpbq

A Primal-Dual Algorithm for Higher-Order Multilabel Markov Random Fields

Alexander Fix, Chen Wang, Ramin Zabih
2014 2014 IEEE Conference on Computer Vision and Pattern Recognition  
Higher-order Markov Random Fields (MRF's), which are important for numerous applications, have proven to be very difficult, especially for multilabel MRF's (i.e. more than 2 labels).  ...  Our algorithm generalizes the PD3 [19] technique for first-order MRFs, and relies on a variant of max-flow that can exactly optimize certain higher-order binary MRF's [14] .  ...  Field of Experts denoising Field of Experts (FoE) for image denoising has been used as a benchmark in several higher-order optimization papers [10, 6, 11] .  ... 
doi:10.1109/cvpr.2014.149 dblp:conf/cvpr/FixWZ14 fatcat:jbbiuqqnebhclin5fm3zmmultu
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