Results 1  10
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164
Learning lowlevel vision
 International Journal of Computer Vision
, 2000
"... We show a learningbased method for lowlevel vision problems. We setup a Markov network of patches of the image and the underlying scene. A factorization approximation allows us to easily learn the parameters of the Markov network from synthetic examples of image/scene pairs, and to e ciently prop ..."
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Cited by 468 (25 self)
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We show a learningbased method for lowlevel vision problems. We setup a Markov network of patches of the image and the underlying scene. A factorization approximation allows us to easily learn the parameters of the Markov network from synthetic examples of image/scene pairs, and to e ciently propagate image information. Monte Carlo simulations justify this approximation. We apply this to the \superresolution " problem (estimating high frequency details from a lowresolution image), showing good results. For the motion estimation problem, we show resolution of the aperture problem and llingin arising from application of the same probabilistic machinery.
MAP estimation via agreement on trees: Messagepassing and linear programming
, 2002
"... We develop and analyze methods for computing provably optimal maximum a posteriori (MAP) configurations for a subclass of Markov random fields defined on graphs with cycles. By decomposing the original distribution into a convex combination of treestructured distributions, we obtain an upper bound ..."
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Cited by 132 (8 self)
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We develop and analyze methods for computing provably optimal maximum a posteriori (MAP) configurations for a subclass of Markov random fields defined on graphs with cycles. By decomposing the original distribution into a convex combination of treestructured distributions, we obtain an upper bound on the optimal value of the original problem (i.e., the log probability of the MAP assignment) in terms of the combined optimal values of the tree problems. We prove that this upper bound is tight if and only if all the tree distributions share an optimal configuration in common. An important implication is that any such shared configuration must also be a MAP configuration for the original distribution. Next we develop two approaches to attempting to obtain tight upper bounds: (a) a treerelaxed linear program (LP), which is derived from the Lagrangian dual of the upper bounds; and (b) a treereweighted maxproduct messagepassing algorithm that is related to but distinct from the maxproduct algorithm. In this way, we establish a connection between a certain LP relaxation of the modefinding problem, and a reweighted form of the maxproduct (minsum) messagepassing algorithm.
Multiresolution markov models for signal and image processing
 Proceedings of the IEEE
, 2002
"... This paper reviews a significant component of the rich field of statistical multiresolution (MR) modeling and processing. These MR methods have found application and permeated the literature of a widely scattered set of disciplines, and one of our principal objectives is to present a single, coheren ..."
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Cited by 122 (18 self)
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This paper reviews a significant component of the rich field of statistical multiresolution (MR) modeling and processing. These MR methods have found application and permeated the literature of a widely scattered set of disciplines, and one of our principal objectives is to present a single, coherent picture of this framework. A second goal is to describe how this topic fits into the even larger field of MR methods and concepts–in particular making ties to topics such as wavelets and multigrid methods. A third is to provide several alternate viewpoints for this body of work, as the methods and concepts we describe intersect with a number of other fields. The principle focus of our presentation is the class of MR Markov processes defined on pyramidally organized trees. The attractiveness of these models stems from both the very efficient algorithms they admit and their expressive power and broad applicability. We show how a variety of methods and models relate to this framework including models for selfsimilar and 1/f processes. We also illustrate how these methods have been used in practice. We discuss the construction of MR models on trees and show how questions that arise in this context make contact with wavelets, state space modeling of time series, system and parameter identification, and hidden
MAP estimation via agreement on (hyper)trees: Messagepassing and linear programming approaches
 IEEE Transactions on Information Theory
, 2002
"... We develop an approach for computing provably exact maximum a posteriori (MAP) configurations for a subclass of problems on graphs with cycles. By decomposing the original problem into a convex combination of treestructured problems, we obtain an upper bound on the optimal value of the original ..."
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Cited by 107 (11 self)
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We develop an approach for computing provably exact maximum a posteriori (MAP) configurations for a subclass of problems on graphs with cycles. By decomposing the original problem into a convex combination of treestructured problems, we obtain an upper bound on the optimal value of the original problem (i.e., the log probability of the MAP assignment) in terms of the combined optimal values of the tree problems. We prove that this upper bound is met with equality if and only if the tree problems share an optimal configuration in common. An important implication is that any such shared configuration must also be a MAP configuration for the original problem. Next we present and analyze two methods for attempting to obtain tight upper bounds: (a) a treereweighted messagepassing algorithm that is related to but distinct from the maxproduct (minsum) algorithm; and (b) a treerelaxed linear program (LP), which is derived from the Lagrangian dual of the upper bounds. Finally, we discuss the conditions that govern when the relaxation is tight, in which case the MAP configuration can be obtained. The analysis described here generalizes naturally to convex combinations of hypertreestructured distributions.
Residual belief propagation: Informed scheduling for asynchronous message passing
 in Proceedings of the Twentysecond Conference on Uncertainty in AI (UAI
, 2006
"... Inference for probabilistic graphical models is still very much a practical challenge in large domains. The commonly used and effective belief propagation (BP) algorithm and its generalizations often do not converge when applied to hard, reallife inference tasks. While it is widely recognized that ..."
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Cited by 81 (3 self)
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Inference for probabilistic graphical models is still very much a practical challenge in large domains. The commonly used and effective belief propagation (BP) algorithm and its generalizations often do not converge when applied to hard, reallife inference tasks. While it is widely recognized that the scheduling of messages in these algorithms may have significant consequences, this issue remains largely unexplored. In this work, we address the question of how to schedule messages for asynchronous propagation so that a fixed point is reached faster and more often. We first show that any reasonable asynchronous BP converges to a unique fixed point under conditions similar to those that guarantee convergence of synchronous BP. In addition, we show that the convergence rate of a simple roundrobin schedule is at least as good as that of synchronous propagation. We then propose residual belief propagation (RBP), a novel, easytoimplement, asynchronous propagation algorithm that schedules messages in an informed way, that pushes down a bound on the distance from the fixed point. Finally, we demonstrate the superiority of RBP over stateoftheart methods for a variety of challenging synthetic and reallife problems: RBP converges significantly more often than other methods; and it significantly reduces running time until convergence, even when other methods converge. 1
Image completion with structure propagation
 ACM Transactions on Graphics
, 2005
"... two intersecting lines (green) specified by the user, (c) intermediate result after propagating structure and texture information along the userspecified lines, and (d) final result after filling in the remaining unknown regions by texture propagation. In this paper, we introduce a novel approach t ..."
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Cited by 81 (2 self)
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two intersecting lines (green) specified by the user, (c) intermediate result after propagating structure and texture information along the userspecified lines, and (d) final result after filling in the remaining unknown regions by texture propagation. In this paper, we introduce a novel approach to image completion, which we call structure propagation. In our system, the user manually specifies important missing structure information by extending a few curves or line segments from the known to the unknown regions. Our approach synthesizes image patches along these userspecified curves in the unknown region using patches selected around the curves in the known region. Structure propagation is formulated as a global optimization problem by enforcing structure and consistency constraints. If only a single curve is specified, structure propagation is solved using Dynamic Programming. When multiple intersecting curves are specified, we adopt the Belief Propagation algorithm to find the optimal patches. After completing structure propagation, we fill in the remaining unknown regions using patchbased texture synthesis. We show that our approach works well on a number of examples that are challenging to stateoftheart techniques.
Stereo Matching with ColorWeighted Correlation, Hierarchical BELIEF PROPAGATION AND OCCLUSION HANDLING
, 2009
"... In this paper, we formulate a stereo matching algorithm with careful handling of disparity, discontinuity, and occlusion. The algorithm works with a global matching stereo model based on an energyminimization framework. The global energy contains two terms, the data term and the smoothness term. T ..."
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Cited by 77 (8 self)
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In this paper, we formulate a stereo matching algorithm with careful handling of disparity, discontinuity, and occlusion. The algorithm works with a global matching stereo model based on an energyminimization framework. The global energy contains two terms, the data term and the smoothness term. The data term is first approximated by a colorweighted correlation, then refined in occluded and lowtexture areas in a repeated application of a hierarchical loopy belief propagation algorithm. The experimental results are evaluated on the Middlebury data sets, showing that our algorithm is the top performer among all the algorithms listed there.
Bethe free energy, Kikuchi approximations and belief propagation algorithms
, 2000
"... Belief propagation (BP) was only supposed to work for treelike networks but works surprisingly well in many applications involving networks with loops, including turbo codes. However, there has been little understanding of the algorithm or the nature of the solutions it nds for general graphs. ..."
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Cited by 70 (2 self)
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Belief propagation (BP) was only supposed to work for treelike networks but works surprisingly well in many applications involving networks with loops, including turbo codes. However, there has been little understanding of the algorithm or the nature of the solutions it nds for general graphs. We show that BP can only converge to a stationary point of an approximate free energy, known as the Bethe free energy in statistical physics. This result characterizes BP xedpoints and makes connections with variational approaches to approximate inference. More importantly, our analysis lets us build on the progress made in statistical physics since Bethe's approximation was introduced in 1935. Kikuchi and others have shown how to construct more accurate free energy approximations, of which Bethe's approximation is the simplest. Exploiting the insights from our analysis, we derive generalized belief propagation (GBP) versions of these Kikuchi approximations. These new message passing algorithms can be signicantly more accurate than ordinary BP, at an adjustable increase in complexity. We illustrate such a new GBP algorithm on a grid Markov network and show that it gives much more accurate marginal probabilities than those found using ordinary BP.
Approximate inference and protein folding
 Advances in Neural Information Processing Systems
, 2002
"... Sidechain prediction is an important subtask in the proteinfolding problem. We show that finding a minimal energy sidechain configuration is equivalent to performing inference in an undirected graphical model. The graphical model is relatively sparse yet has many cycles. We used this equivalence ..."
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Cited by 60 (7 self)
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Sidechain prediction is an important subtask in the proteinfolding problem. We show that finding a minimal energy sidechain configuration is equivalent to performing inference in an undirected graphical model. The graphical model is relatively sparse yet has many cycles. We used this equivalence to assess the performance of approximate inference algorithms in a realworld setting. Specifically we compared belief propagation (BP), generalized BP (GBP) and naive mean field (MF). In cases where exact inference was possible, maxproduct BP always found the global minimum of the energy (except in few cases where it failed to converge), while other approximation algorithms of similar complexity did not. In the full protein data set, maxproduct BP always found a lower energy configuration than the other algorithms, including a widely used proteinfolding software (SCWRL). 1