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On the statistical analysis of dirty pictures
 JOURNAL OF THE ROYAL STATISTICAL SOCIETY B
, 1986
"... ..."
Factor Graphs and the SumProduct Algorithm
 IEEE TRANSACTIONS ON INFORMATION THEORY
, 1998
"... A factor graph is a bipartite graph that expresses how a "global" function of many variables factors into a product of "local" functions. Factor graphs subsume many other graphical models including Bayesian networks, Markov random fields, and Tanner graphs. Following one simple c ..."
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Cited by 1787 (72 self)
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A factor graph is a bipartite graph that expresses how a "global" function of many variables factors into a product of "local" functions. Factor graphs subsume many other graphical models including Bayesian networks, Markov random fields, and Tanner graphs. Following one simple computational rule, the sumproduct algorithm operates in factor graphs to computeeither exactly or approximatelyvarious marginal functions by distributed messagepassing in the graph. A wide variety of algorithms developed in artificial intelligence, signal processing, and digital communications can be derived as specific instances of the sumproduct algorithm, including the forward/backward algorithm, the Viterbi algorithm, the iterative "turbo" decoding algorithm, Pearl's belief propagation algorithm for Bayesian networks, the Kalman filter, and certain fast Fourier transform algorithms.
Graphical models, exponential families, and variational inference
, 2008
"... The formalism of probabilistic graphical models provides a unifying framework for capturing complex dependencies among random variables, and building largescale multivariate statistical models. Graphical models have become a focus of research in many statistical, computational and mathematical fiel ..."
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Cited by 800 (26 self)
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The formalism of probabilistic graphical models provides a unifying framework for capturing complex dependencies among random variables, and building largescale multivariate statistical models. Graphical models have become a focus of research in many statistical, computational and mathematical fields, including bioinformatics, communication theory, statistical physics, combinatorial optimization, signal and image processing, information retrieval and statistical machine learning. Many problems that arise in specific instances — including the key problems of computing marginals and modes of probability distributions — are best studied in the general setting. Working with exponential family representations, and exploiting the conjugate duality between the cumulant function and the entropy for exponential families, we develop general variational representations of the problems of computing likelihoods, marginal probabilities and most probable configurations. We describe how a wide varietyof algorithms — among them sumproduct, cluster variational methods, expectationpropagation, mean field methods, maxproduct and linear programming relaxation, as well as conic programming relaxations — can all be understood in terms of exact or approximate forms of these variational representations. The variational approach provides a complementary alternative to Markov chain Monte Carlo as a general source of approximation methods for inference in largescale statistical models.
Energy Minimization for Linear Envelope MRFs
"... Markov random fields with higher order potentials have emerged as a powerful model for several problems in computer vision. In order to facilitate their use, we propose a new representation for higher order potentials as upper and lower envelopes of linear functions. Our representation concisely mod ..."
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Cited by 25 (7 self)
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. This allows us to minimize energy functions with lower envelope potentials using conventional algorithms such as BP, TRW and αexpansion. Furthermore, we show how the minimization of energy functions with upper envelope potentials leads to a difficult minmax problem. We address this difficulty by proposing a
Dynamic Hybrid Algorithms for MAP Inference in Discrete MRFs
"... In this paper, we present novel techniques that improve the computational and memory efficiency of algorithms for solving multilabel energy functions arising from discrete MRFs or CRFs. These methods are motivated by the observations that the performance of minimization algorithms depends on: (a) t ..."
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Cited by 16 (4 self)
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In this paper, we present novel techniques that improve the computational and memory efficiency of algorithms for solving multilabel energy functions arising from discrete MRFs or CRFs. These methods are motivated by the observations that the performance of minimization algorithms depends on: (a
Optimizing binary MRFS with higher order cliques
, 2008
"... Abstract. Widespread use of efficient and successful solutions of Computer Vision problems based on pairwise Markov Random Field (MRF) models raises a question: does any link exist between the pairwise and higher order MRFs such that the like solutions can be applied to the latter models? This work ..."
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Cited by 12 (0 self)
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Abstract. Widespread use of efficient and successful solutions of Computer Vision problems based on pairwise Markov Random Field (MRF) models raises a question: does any link exist between the pairwise and higher order MRFs such that the like solutions can be applied to the latter models
Shape priors and discrete mrfs for knowledgebased segmentation
, 2009
"... In this paper we introduce a new approach to knowledgebased segmentation. Our method consists of a novel representation to model shape variations as well as an efficient inference procedure to fit the model to new data. The considered shape model is similarityinvariant and refers to an incomplete g ..."
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Cited by 15 (5 self)
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In this paper we introduce a new approach to knowledgebased segmentation. Our method consists of a novel representation to model shape variations as well as an efficient inference procedure to fit the model to new data. The considered shape model is similarityinvariant and refers to an incomplete graph that consists of intra and intercluster connections representing the interdependencies of control points. The clusters are determined according to the codependencies of the deformations of the control points within the training set. The connections between the components of a cluster represent the local structure while the connections between the clusters account for the global structure. The distributions of the normalized distances between the connected control points encode the prior model. During search, this model is used together with a discrete markov random field (MRF) based segmentation, where the unknown variables are the positions of the control points in the image domain. To encode the image support, a Voronoi decomposition of the domain is considered and regional based statistics are used. The resulting model is computationally efficient, can encode complex statistical models of shape variations and benefits from the image support of the entire spatial domain. 1.
Mean Field for Continuous HighOrder MRFs
"... Abstract. Probabilistic inference beyond MAP estimation is of interest in computer vision, both for learning appropriate models and in applications. Yet, common approximate inference techniques, such as belief propagation, have largely been limited to discretevalued Markov random fields (MRFs) and ..."
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Cited by 1 (0 self)
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Abstract. Probabilistic inference beyond MAP estimation is of interest in computer vision, both for learning appropriate models and in applications. Yet, common approximate inference techniques, such as belief propagation, have largely been limited to discretevalued Markov random fields (MRFs
Image Segmentation using MRFs and Statistical Shape Modeling
, 2010
"... In this thesis, we introduce a new statistical shape model and use it for knowledgebased image segmentation. The model is represented by a Markov Random Field (MRF). The vertices of the graph correspond to landmarks lying on the shape boundary, whereas the edges of the graph encode the dependencie ..."
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Cited by 1 (0 self)
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In this thesis, we introduce a new statistical shape model and use it for knowledgebased image segmentation. The model is represented by a Markov Random Field (MRF). The vertices of the graph correspond to landmarks lying on the shape boundary, whereas the edges of the graph encode the dependencies between the landmarks. The MRF structure is determined from a training set of shapes using manifold learning and unsupervised clustering techniques. The interpoint constraints are enforced using the learned probability distribution function of the normalized chord lengths. This model is used as a basis for knowledgebased segmentation. We adopt two approaches to incorporate the data support: one is based on landmark correspondences and the other one uses image region information. In the first case, correspondences between the model and the image are obtained through detectors and the optimal configuration is achieved through combination of detector responses and prior knowledge. The second approach consists of minimizing an energy that discriminates the object from the background while
Results 1  10
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1,681