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148
A comparative study of energy minimization methods for Markov random fields
 IN ECCV
, 2006
"... One of the most exciting advances in early vision has been the development of efficient energy minimization algorithms. Many early vision tasks require labeling each pixel with some quantity such as depth or texture. While many such problems can be elegantly expressed in the language of Markov Ran ..."
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Cited by 414 (36 self)
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One of the most exciting advances in early vision has been the development of efficient energy minimization algorithms. Many early vision tasks require labeling each pixel with some quantity such as depth or texture. While many such problems can be elegantly expressed in the language of Markov Random Fields (MRF’s), the resulting energy minimization problems were widely viewed as intractable. Recently, algorithms such as graph cuts and loopy belief propagation (LBP) have proven to be very powerful: for example, such methods form the basis for almost all the topperforming stereo methods. Unfortunately, most papers define their own energy function, which is minimized with a specific algorithm of their choice. As a result, the tradeoffs among different energy minimization algorithms are not well understood. In this paper we describe a set of energy minimization benchmarks, which we use to compare the solution quality and running time of several common energy minimization algorithms. We investigate three promising recent methods—graph cuts, LBP, and treereweighted message passing—as well as the wellknown older iterated conditional modes (ICM) algorithm. Our benchmark problems are drawn from published energy functions used for stereo, image stitching and interactive segmentation. We also provide a generalpurpose software interface that allows vision researchers to easily switch between optimization methods with minimal overhead. We expect that the availability of our benchmarks and interface will make it significantly easier for vision researchers to adopt the best method for their specific problems. Benchmarks, code, results and images are available at
A family of algorithms for approximate Bayesian inference
, 2001
"... One of the major obstacles to using Bayesian methods for pattern recognition has been its computational expense. This thesis presents an approximation technique that can perform Bayesian inference faster and more accurately than previously possible. This method, "Expectation Propagation," ..."
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Cited by 369 (11 self)
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One of the major obstacles to using Bayesian methods for pattern recognition has been its computational expense. This thesis presents an approximation technique that can perform Bayesian inference faster and more accurately than previously possible. This method, "Expectation Propagation," unifies and generalizes two previous techniques: assumeddensity filtering, an extension of the Kalman filter, and loopy belief propagation, an extension of belief propagation in Bayesian networks. The unification shows how both of these algorithms can be viewed as approximating the true posterior distribution with a simpler distribution, which is close in the sense of KLdivergence. Expectation Propagation exploits the best of both algorithms: the generality of assumeddensity filtering and the accuracy of loopy belief propagation. Loopy belief propagation, because it propagates exact belief states, is useful for limited types of belief networks, such as purely discrete networks. Expectation Propagati...
The generalized distributive law
 Information Theory, IEEE Transactions on
"... Abstract—In this semitutorial paper we discuss a general message passing algorithm, which we call the generalized distributive law (GDL). The GDL is a synthesis of the work of many authors in the information theory, digital communications, signal processing, statistics, and artificial intelligence ..."
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Cited by 364 (2 self)
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Abstract—In this semitutorial paper we discuss a general message passing algorithm, which we call the generalized distributive law (GDL). The GDL is a synthesis of the work of many authors in the information theory, digital communications, signal processing, statistics, and artificial intelligence communities. It includes as special cases the Baum–Welch algorithm, the fast Fourier transform (FFT) on any finite Abelian group, the Gallager–Tanner–Wiberg decoding algorithm, Viterbi’s algorithm, the BCJR algorithm, Pearl’s “belief propagation ” algorithm, the Shafer–Shenoy probability propagation algorithm, and the turbo decoding algorithm. Although this algorithm is guaranteed to give exact answers only in certain cases (the “junction tree ” condition), unfortunately not including the cases of GTW with cycles or turbo decoding, there is much experimental evidence, and a few theorems, suggesting that it often works approximately even when it is not supposed to. Index Terms—Belief propagation, distributive law, graphical models, junction trees, turbo codes. I.
Bayesian compressive sensing via belief propagation
 IEEE Trans. Signal Processing
, 2010
"... Compressive sensing (CS) is an emerging field based on the revelation that a small collection of linear projections of a sparse signal contains enough information for stable, subNyquist signal acquisition. When a statistical characterization of the signal is available, Bayesian inference can comple ..."
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Cited by 129 (19 self)
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Compressive sensing (CS) is an emerging field based on the revelation that a small collection of linear projections of a sparse signal contains enough information for stable, subNyquist signal acquisition. When a statistical characterization of the signal is available, Bayesian inference can complement conventional CS methods based on linear programming or greedy algorithms. We perform approximate Bayesian inference using belief propagation (BP) decoding, which represents the CS encoding matrix as a graphical model. Fast encoding and decoding is provided using sparse encoding matrices, which also improve BP convergence by reducing the presence of loops in the graph. To decode a lengthN signal containing K large coefficients, our CSBP decoding algorithm uses O(K log(N)) measurements and O(N log 2 (N)) computation. Finally, sparse encoding matrices and the CSBP decoding algorithm can be modified to support a variety of signal models and measurement noise. 1
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.
Locationbased activity recognition
 In Advances in Neural Information Processing Systems (NIPS
, 2005
"... Learning patterns of human behavior from sensor data is extremely important for highlevel activity inference. We show how to extract and label a person’s activities and significant places from traces of GPS data. In contrast to existing techniques, our approach simultaneously detects and classifies ..."
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Cited by 79 (8 self)
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Learning patterns of human behavior from sensor data is extremely important for highlevel activity inference. We show how to extract and label a person’s activities and significant places from traces of GPS data. In contrast to existing techniques, our approach simultaneously detects and classifies the significant locations of a person and takes the highlevel context into account. Our system uses relational Markov networks to represent the hierarchical activity model that encodes the complex relations among GPS readings, activities and significant places. We apply FFTbased message passing to perform efficient summation over large numbers of nodes in the networks. We present experiments that show significant improvements over existing techniques. 1
Divergence Measures and Message Passing
, 2005
"... This paper presents a unifying view of messagepassing algorithms, as methods to approximate a complex Bayesian network by a simpler network with minimum information divergence. In this view, the difference between meanfield methods and belief propagation is not the amount of structure they model, b ..."
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Cited by 75 (2 self)
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This paper presents a unifying view of messagepassing algorithms, as methods to approximate a complex Bayesian network by a simpler network with minimum information divergence. In this view, the difference between meanfield methods and belief propagation is not the amount of structure they model, but only the measure of loss they minimize (‘exclusive ’ versus ‘inclusive’ KullbackLeibler divergence). In each case, messagepassing arises by minimizing a localized version of the divergence, local to each factor. By examining these divergence measures, we can intuit the types of solution they prefer (symmetrybreaking, for example) and their suitability for different tasks. Furthermore, by considering a wider variety of divergence measures (such as alphadivergences), we can achieve different complexity and performance goals. 1
A comparison of algorithms for inference and learning in probabilistic graphical models
 IEEE Transactions on Pattern Analysis and Machine Intelligence
, 2005
"... Computer vision is currently one of the most exciting areas of artificial intelligence research, largely because it has recently become possible to record, store and process large amounts of visual data. While impressive achievements have been made in pattern classification problems such as handwr ..."
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Cited by 70 (4 self)
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Computer vision is currently one of the most exciting areas of artificial intelligence research, largely because it has recently become possible to record, store and process large amounts of visual data. While impressive achievements have been made in pattern classification problems such as handwritten character recognition and face detection, it is even more exciting that researchers may be on the verge of introducing computer vision systems that perform scene analysis, decomposing image input into its constituent objects, lighting conditions, motion patterns, and so on. Two of the main challenges in computer vision are finding efficient models of the physics of visual scenes and finding efficient algorithms for inference and learning in these models. In this paper, we advocate the use of graphbased probability models and their associated inference and learning algorithms for computer vision and scene analysis. We review exact techniques and various approximate, computationally efficient techniques, including iterative conditional modes, the expectation maximization (EM) algorithm, the mean field method, variational techniques, structured variational techniques, Gibbs sampling, the sumproduct algorithm and “loopy ” belief propagation. We describe how each technique can be applied in a model of multiple, occluding objects, and contrast the behaviors and performances of the techniques using a unifying cost function, free energy.
Belief Optimization for Binary Networks: A Stable Alternative to Loopy Belief Propagation
 In Proceedings of the Conference on Uncertainty in Artificial Intelligence
, 2001
"... We present a novel inference algorithm for arbitrary, binary, undirected graphs.Unlike loopy belief propagation, which iterates fixed point equations, we directly descend on the Bethe free energy. The algorithm consists of two phases,first we update the pairwise probabilities, given the marginal pro ..."
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Cited by 66 (6 self)
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We present a novel inference algorithm for arbitrary, binary, undirected graphs.Unlike loopy belief propagation, which iterates fixed point equations, we directly descend on the Bethe free energy. The algorithm consists of two phases,first we update the pairwise probabilities, given the marginal probabilities at each unit, using an analytic expression. Next, we update the marginal probabilities, by following the negative gradient of the Bethe free energy. Both steps are guaranteed to decrease the Bethe free energy, and since it is lower bounded, the algorithm is guaranteed to converge to a local minimum. We also show that the Bethe free energy is equal to the TAP free energy up to second order in the weights. In experiments we confirm that when belief propagation converges it usually finds identical solutions as our belief optimization method. The stable nature of belief optimization makes it ideally suited for learning graphical models from data.