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Markov Random Field Models in Computer Vision
, 1994
"... . A variety of computer vision problems can be optimally posed as Bayesian labeling in which the solution of a problem is defined as the maximum a posteriori (MAP) probability estimate of the true labeling. The posterior probability is usually derived from a prior model and a likelihood model. The l ..."
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Cited by 516 (18 self)
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. The latter relates to how data is observed and is problem domain dependent. The former depends on how various prior constraints are expressed. Markov Random Field Models (MRF) theory is a tool to encode contextual constraints into the prior probability. This paper presents a unified approach for MRF modeling
Segmentation of brain MR images through a hidden Markov random field model and the expectationmaximization algorithm
 IEEE TRANSACTIONS ON MEDICAL. IMAGING
, 2001
"... The finite mixture (FM) model is the most commonly used model for statistical segmentation of brain magnetic resonance (MR) images because of its simple mathematical form and the piecewise constant nature of ideal brain MR images. However, being a histogrambased model, the FM has an intrinsic limi ..."
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Cited by 639 (15 self)
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based methods produce unreliable results. In this paper, we propose a novel hidden Markov random field (HMRF) model, which is a stochastic process generated by a MRF whose state sequence cannot be observed directly but which can be indirectly estimated through observations. Mathematically, it can be shown
Conditional random fields: Probabilistic models for segmenting and labeling sequence data
, 2001
"... We present conditional random fields, a framework for building probabilistic models to segment and label sequence data. Conditional random fields offer several advantages over hidden Markov models and stochastic grammars for such tasks, including the ability to relax strong independence assumptions ..."
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Cited by 3485 (85 self)
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We present conditional random fields, a framework for building probabilistic models to segment and label sequence data. Conditional random fields offer several advantages over hidden Markov models and stochastic grammars for such tasks, including the ability to relax strong independence assumptions
Discriminative Training Methods for Hidden Markov Models: Theory and Experiments with Perceptron Algorithms
, 2002
"... We describe new algorithms for training tagging models, as an alternative to maximumentropy models or conditional random fields (CRFs). The algorithms rely on Viterbi decoding of training examples, combined with simple additive updates. We describe theory justifying the algorithms through a modific ..."
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Cited by 660 (13 self)
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We describe new algorithms for training tagging models, as an alternative to maximumentropy models or conditional random fields (CRFs). The algorithms rely on Viterbi decoding of training examples, combined with simple additive updates. We describe theory justifying the algorithms through a
Probabilistic Inference Using Markov Chain Monte Carlo Methods
, 1993
"... Probabilistic inference is an attractive approach to uncertain reasoning and empirical learning in artificial intelligence. Computational difficulties arise, however, because probabilistic models with the necessary realism and flexibility lead to complex distributions over highdimensional spaces. R ..."
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Cited by 736 (24 self)
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. Related problems in other fields have been tackled using Monte Carlo methods based on sampling using Markov chains, providing a rich array of techniques that can be applied to problems in artificial intelligence. The "Metropolis algorithm" has been used to solve difficult problems in statistical
Stereo matching using belief propagation
, 2003
"... In this paper, we formulate the stereo matching problem as a Markov network and solve it using Bayesian belief propagation. The stereo Markov network consists of three coupled Markov random fields that model the following: a smooth field for depth/disparity, a line process for depth discontinuity, ..."
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Cited by 350 (4 self)
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In this paper, we formulate the stereo matching problem as a Markov network and solve it using Bayesian belief propagation. The stereo Markov network consists of three coupled Markov random fields that model the following: a smooth field for depth/disparity, a line process for depth discontinuity
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 415 (36 self)
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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
Fast texture synthesis using treestructured vector quantization
, 2000
"... Figure 1: Our texture generation process takes an example texture patch (left) and a random noise (middle) as input, and modifies this random noise to make it look like the given example texture. The synthesized texture (right) can be of arbitrary size, and is perceived as very similar to the given ..."
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Cited by 561 (12 self)
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, but runs two orders of magnitude faster. This permits us to apply texture synthesis to problems where it has traditionally been considered impractical. In particular, we have applied it to constrained synthesis for image editing and temporal texture generation. Our algorithm is derived from Markov Random
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 1791 (69 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
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 819 (28 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
Results 1  10
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