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67
Convergent Treereweighted Message Passing for Energy Minimization
 ACCEPTED TO IEEE TRANSACTIONS ON PATTERN ANALYSIS AND MACHINE INTELLIGENCE (PAMI), 2006. ABSTRACTACCEPTED TO IEEE TRANSACTIONS ON PATTERN ANALYSIS AND MACHINE INTELLIGENCE (PAMI)
, 2006
"... 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. [33] treereweighted maxproduct message passing (TRW). It was inspired by the problem of maximizing a lower bound on the energy ..."
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Cited by 491 (16 self)
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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. [33] treereweighted maxproduct 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 call sequential treereweighted message passing. Its main property is that the bound is guaranteed not to decrease. We also give a weak tree agreement condition which characterizes local maxima of the bound with respect to TRW algorithms. We prove that our algorithm has a limit point that achieves weak tree agreement. Finally, we show that our algorithm requires half as much memory as traditional message passing approaches. Experimental results demonstrate that on certain synthetic and real problems our algorithm outperforms both the ordinary belief propagation and treereweighted algorithm in [33]. In addition, on stereo problems with Potts interactions we obtain a lower energy than graph cuts.
Optimizing binary MRFs via extended roof duality
 In Proc. CVPR
, 2007
"... Many computer vision applications rely on the efficient optimization of challenging, socalled nonsubmodular, binary pairwise MRFs. A promising graph cut based approach for optimizing such MRFs known as “roof duality” was recently introduced into computer vision. We study two methods which extend t ..."
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Cited by 171 (12 self)
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Many computer vision applications rely on the efficient optimization of challenging, socalled nonsubmodular, binary pairwise MRFs. A promising graph cut based approach for optimizing such MRFs known as “roof duality” was recently introduced into computer vision. We study two methods which extend this approach. First, we discuss an efficient implementation of the “probing ” technique introduced recently by Boros et al. [5]. It simplifies the MRF while preserving the global optimum. Our code is 400700 faster on some graphs than the implementation of [5]. Second, we present a new technique which takes an arbitrary input labeling and tries to improve its energy. We give theoretical characterizations of local minima of this procedure. We applied both techniques to many applications, including image segmentation, new view synthesis, superresolution, diagram recognition, parameter learning, texture restoration, and image deconvolution. For several applications we see that we are able to find the global minimum very efficiently, and considerably outperform the original roof duality approach. In comparison to existing techniques, such as graph cut, TRW, BP, ICM, and simulated annealing, we nearly always find a lower energy. 1.
Fixing MaxProduct: Convergent Message Passing Algorithms for MAP LPRelaxations
"... We present a novel message passing algorithm for approximating the MAP problem in graphical models. The algorithm is similar in structure to maxproduct but unlike maxproduct it always converges, and can be proven to find the exact MAP solution in various settings. The algorithm is derived via bloc ..."
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Cited by 162 (16 self)
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We present a novel message passing algorithm for approximating the MAP problem in graphical models. The algorithm is similar in structure to maxproduct but unlike maxproduct it always converges, and can be proven to find the exact MAP solution in various settings. The algorithm is derived via block coordinate descent in a dual of the LP relaxation of MAP, but does not require any tunable parameters such as step size or tree weights. We also describe a generalization of the method to cluster based potentials. The new method is tested on synthetic and realworld problems, and compares favorably with previous approaches. Graphical models are an effective approach for modeling complex objects via local interactions. In such models, a distribution over a set of variables is assumed to factor according to cliques of a graph with potentials assigned to each clique. Finding the assignment with highest probability in these models is key to using them in practice, and is often referred to as the MAP (maximum aposteriori) assignment problem. In the general case the problem is NP hard, with complexity exponential in the treewidth of the underlying graph.
Minimizing nonsubmodular functions with graph cuts  a review
 TPAMI
, 2007
"... Optimization techniques based on graph cuts have become a standard tool for many vision applications. These techniques allow to minimize efficiently certain energy functions corresponding to pairwise Markov Random Fields (MRFs). Currently, there is an accepted view within the computer vision communi ..."
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Cited by 148 (8 self)
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Optimization techniques based on graph cuts have become a standard tool for many vision applications. These techniques allow to minimize efficiently certain energy functions corresponding to pairwise Markov Random Fields (MRFs). Currently, there is an accepted view within the computer vision community that graph cuts can only be used for optimizing a limited class of MRF energies (e.g. submodular functions). In this survey we review some results that show that graph cuts can be applied to a much larger class of energy functions (in particular, nonsubmodular functions). While these results are wellknown in the optimization community, to our knowledge they were not used in the context of computer vision and MRF optimization. We demonstrate the relevance of these results to vision on the problem of binary texture restoration.
MRF optimization via dual decomposition: Messagepassing revisited
 In ICCV
, 2007
"... A new messagepassing scheme for MRF optimization is proposed in this paper. This scheme inherits better theoretical properties than all other stateoftheart message passing methods and in practice performs equally well/outperforms them. It is based on the very powerful technique of Dual Decomposi ..."
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Cited by 118 (11 self)
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A new messagepassing scheme for MRF optimization is proposed in this paper. This scheme inherits better theoretical properties than all other stateoftheart message passing methods and in practice performs equally well/outperforms them. It is based on the very powerful technique of Dual Decomposition [1] and leads to an elegant and general framework for understanding/designing messagepassing algorithms that can provide new insights into existing techniques. Promising experimental results and comparisons with the state of the art demonstrate the extreme theoretical and practical potentials of our approach. 1.
Tightening LP Relaxations for MAP using Message Passing
, 2008
"... Linear Programming (LP) relaxations have become powerful tools for finding the most probable (MAP) configuration in graphical models. These relaxations can be solved efficiently using messagepassing algorithms such as belief propagation and, when the relaxation is tight, provably find the MAP confi ..."
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Cited by 109 (18 self)
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Linear Programming (LP) relaxations have become powerful tools for finding the most probable (MAP) configuration in graphical models. These relaxations can be solved efficiently using messagepassing algorithms such as belief propagation and, when the relaxation is tight, provably find the MAP configuration. The standard LP relaxation is not tight enough in many realworld problems, however, and this has lead to the use of higher order clusterbased LP relaxations. The computational cost increases exponentially with the size of the clusters and limits the number and type of clusters we can use. We propose to solve the cluster selection problem monotonically in the dual LP, iteratively selecting clusters with guaranteed improvement, and quickly resolving with the added clusters by reusing the existing solution. Our dual messagepassing algorithm finds the MAP configuration in protein sidechain placement, protein design, and stereo problems, in cases where the standard LP relaxation fails.
MRF energy minimization and beyond via dual decomposition
 IN: IEEE PAMI. (2011
"... This paper introduces a new rigorous theoretical framework to address discrete MRFbased optimization in computer vision. Such a framework exploits the powerful technique of Dual Decomposition. It is based on a projected subgradient scheme that attempts to solve an MRF optimization problem by first ..."
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Cited by 107 (9 self)
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This paper introduces a new rigorous theoretical framework to address discrete MRFbased optimization in computer vision. Such a framework exploits the powerful technique of Dual Decomposition. It is based on a projected subgradient scheme that attempts to solve an MRF optimization problem by first decomposing it into a set of appropriately chosen subproblems and then combining their solutions in a principled way. In order to determine the limits of this method, we analyze the conditions that these subproblems have to satisfy and we demonstrate the extreme generality and flexibility of such an approach. We thus show that, by appropriately choosing what subproblems to use, one can design novel and very powerful MRF optimization algorithms. For instance, in this manner we are able to derive algorithms that: 1) generalize and extend stateoftheart messagepassing methods, 2) optimize very tight LPrelaxations to MRF optimization, 3) and take full advantage of the special structure that may exist in particular MRFs, allowing the use of efficient inference techniques such as, e.g, graphcut based methods. Theoretical analysis on the bounds related with the different algorithms derived from our framework and experimental results/comparisons using synthetic and real data for a variety of tasks in computer vision demonstrate the extreme potentials of our approach.
Linear programming relaxations and belief propagation – an empirical study
 Jourmal of Machine Learning Research
, 2006
"... The problem of finding the most probable (MAP) configuration in graphical models comes up in a wide range of applications. In a general graphical model this problem is NP hard, but various approximate algorithms have been developed. Linear programming (LP) relaxations are a standard method in comput ..."
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Cited by 88 (4 self)
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The problem of finding the most probable (MAP) configuration in graphical models comes up in a wide range of applications. In a general graphical model this problem is NP hard, but various approximate algorithms have been developed. Linear programming (LP) relaxations are a standard method in computer science for approximating combinatorial problems and have been used for finding the most probable assignment in small graphical models. However, applying this powerful method to realworld problems is extremely challenging due to the large numbers of variables and constraints in the linear program. TreeReweighted Belief Propagation is a promising recent algorithm for solving LP relaxations, but little is known about its running time on large problems. In this paper we compare treereweighted belief propagation (TRBP) and powerful generalpurpose LP solvers (CPLEX) on relaxations of realworld graphical models from the fields of computer vision and computational biology. We find that TRBP almost always finds the solution significantly faster than all the solvers in CPLEX and more importantly, TRBP can be applied to large scale problems for which the solvers in CPLEX cannot be applied. Using TRBP we can find the MAP configurations in a matter of minutes for a large range of real world problems. 1.