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747
Exact Sampling with Coupled Markov Chains and Applications to Statistical Mechanics
, 1996
"... For many applications it is useful to sample from a finite set of objects in accordance with some particular distribution. One approach is to run an ergodic (i.e., irreducible aperiodic) Markov chain whose stationary distribution is the desired distribution on this set; after the Markov chain has ..."
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Cited by 402 (13 self)
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For many applications it is useful to sample from a finite set of objects in accordance with some particular distribution. One approach is to run an ergodic (i.e., irreducible aperiodic) Markov chain whose stationary distribution is the desired distribution on this set; after the Markov chain has run for M steps, with M sufficiently large, the distribution governing the state of the chain approximates the desired distribution. Unfortunately it can be difficult to determine how large M needs to be. We describe a simple variant of this method that determines on its own when to stop, and that outputs samples in exact accordance with the desired distribution. The method uses couplings, which have also played a role in other sampling schemes; however, rather than running the coupled chains from the present into the future, one runs from a distant point in the past up until the present, where the distance into the past that one needs to go is determined during the running of the al...
A generalized Gaussian image model for edgepreserving MAP estimation
 IEEE Trans. on Image Processing
, 1993
"... Absfrucf We present a Markov random field model which allows realistic edge modeling while providing stable maximum a posteriori MAP solutions. The proposed model, which we refer to as a generalized Gaussian Markov random field (GGMRF), is named for its similarity to the generalized Gaussian distri ..."
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Cited by 238 (34 self)
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Absfrucf We present a Markov random field model which allows realistic edge modeling while providing stable maximum a posteriori MAP solutions. The proposed model, which we refer to as a generalized Gaussian Markov random field (GGMRF), is named for its similarity to the generalized Gaussian distribution used in robust detection and estimation. The model satisifies several desirable analytical and computational properties for MAP estimation, including continuous dependence of the estimate on the data, invariance of the character of solutions to scaling of data, and a solution which lies at the unique global minimum of the U posteriori loglikeihood function. The GGMRF is demonstrated to be useful for image reconstruction in lowdosage transmission tomography. I.
A Multiscale Random Field Model for Bayesian Image Segmentation
, 1996
"... Many approaches to Bayesian image segmentation have used maximum a posteriori (MAP) estimation in conjunction with Markov random fields (MRF). While this approach performs well, it has a number of disadvantages. In particular, exact MAP estimates cannot be computed, approximate MAP estimates are com ..."
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Cited by 233 (18 self)
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Many approaches to Bayesian image segmentation have used maximum a posteriori (MAP) estimation in conjunction with Markov random fields (MRF). While this approach performs well, it has a number of disadvantages. In particular, exact MAP estimates cannot be computed, approximate MAP estimates are computationally expensive to compute, and unsupervised parameter estimation of the MRF is difficult. In this paper, we propose a new approach to Bayesian image segmentation which directly addresses these problems. The new method replaces the MRF model with a novel multiscale random field (MSRF), and replaces the MAP estimator with a sequential MAP (SMAP) estimator derived from a novel estimation criteria. Together, the proposed estimator and model result in a segmentation algorithm which is not iterative and can be computed in time proportional to MN where M is the number of classes and N is the number of pixels. We also develop a computationally effcient method for unsupervised estimation of m...
Deterministic edgepreserving regularization in computed imaging
 IEEE Trans. Image Processing
, 1997
"... Abstract—Many image processing problems are ill posed and must be regularized. Usually, a roughness penalty is imposed on the solution. The difficulty is to avoid the smoothing of edges, which are very important attributes of the image. In this paper, we first give conditions for the design of such ..."
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Cited by 228 (23 self)
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Abstract—Many image processing problems are ill posed and must be regularized. Usually, a roughness penalty is imposed on the solution. The difficulty is to avoid the smoothing of edges, which are very important attributes of the image. In this paper, we first give conditions for the design of such an edgepreserving regularization. Under these conditions, we show that it is possible to introduce an auxiliary variable whose role is twofold. First, it marks the discontinuities and ensures their preservation from smoothing. Second, it makes the criterion halfquadratic. The optimization is then easier. We propose a deterministic strategy, based on alternate minimizations on the image and the auxiliary variable. This leads to the definition of an original reconstruction algorithm, called ARTUR. Some theoretical properties of ARTUR are discussed. Experimental results illustrate the behavior of the algorithm. These results are shown in the field of tomography, but this method can be applied in a large number of applications in image processing. I.
A Probabilistic Framework for SemiSupervised Clustering
, 2004
"... Unsupervised clustering can be significantly improved using supervision in the form of pairwise constraints, i.e., pairs of instances labeled as belonging to same or different clusters. In recent years, a number of algorithms have been proposed for enhancing clustering quality by employing such supe ..."
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Cited by 183 (12 self)
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Unsupervised clustering can be significantly improved using supervision in the form of pairwise constraints, i.e., pairs of instances labeled as belonging to same or different clusters. In recent years, a number of algorithms have been proposed for enhancing clustering quality by employing such supervision. Such methods use the constraints to either modify the objective function, or to learn the distance measure. We propose a probabilistic model for semisupervised clustering based on Hidden Markov Random Fields (HMRFs) that provides a principled framework for incorporating supervision into prototypebased clustering. The model generalizes a previous approach that combines constraints and Euclidean distance learning, and allows the use of a broad range of clustering distortion measures, including Bregman divergences (e.g., Euclidean distance and Idivergence) and directional similarity measures (e.g., cosine similarity). We present an algorithm that performs partitional semisupervised clustering of data by minimizing an objective function derived from the posterior energy of the HMRF model. Experimental results on several text data sets demonstrate the advantages of the proposed framework. 1.
Discriminative random fields: A discriminative framework for contextual interaction in classification
 In ICCV
, 2003
"... ..."
Hidden Markov processes
 IEEE Trans. Inform. Theory
, 2002
"... Abstract—An overview of statistical and informationtheoretic aspects of hidden Markov processes (HMPs) is presented. An HMP is a discretetime finitestate homogeneous Markov chain observed through a discretetime memoryless invariant channel. In recent years, the work of Baum and Petrie on finite ..."
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Cited by 169 (3 self)
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Abstract—An overview of statistical and informationtheoretic aspects of hidden Markov processes (HMPs) is presented. An HMP is a discretetime finitestate homogeneous Markov chain observed through a discretetime memoryless invariant channel. In recent years, the work of Baum and Petrie on finitestate finitealphabet HMPs was expanded to HMPs with finite as well as continuous state spaces and a general alphabet. In particular, statistical properties and ergodic theorems for relative entropy densities of HMPs were developed. Consistency and asymptotic normality of the maximumlikelihood (ML) parameter estimator were proved under some mild conditions. Similar results were established for switching autoregressive processes. These processes generalize HMPs. New algorithms were developed for estimating the state, parameter, and order of an HMP, for universal coding and classification of HMPs, and for universal decoding of hidden Markov channels. These and other related topics are reviewed in this paper. Index Terms—Baum–Petrie algorithm, entropy ergodic theorems, finitestate channels, hidden Markov models, identifiability, Kalman filter, maximumlikelihood (ML) estimation, order estimation, recursive parameter estimation, switching autoregressive processes, Ziv inequality. I.
Approximation Algorithms for Classification Problems with Pairwise Relationships: Metric Labeling and Markov Random Fields
 IN IEEE SYMPOSIUM ON FOUNDATIONS OF COMPUTER SCIENCE
, 1999
"... In a traditional classification problem, we wish to assign one of k labels (or classes) to each of n objects, in a way that is consistent with some observed data that we have about the problem. An active line of research in this area is concerned with classification when one has information about pa ..."
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Cited by 158 (2 self)
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In a traditional classification problem, we wish to assign one of k labels (or classes) to each of n objects, in a way that is consistent with some observed data that we have about the problem. An active line of research in this area is concerned with classification when one has information about pairwise relationships among the objects to be classified; this issue is one of the principal motivations for the framework of Markov random fields, and it arises in areas such as image processing, biometry, and document analysis. In its most basic form, this style of analysis seeks a classification that optimizes a combinatorial function consisting of assignment costs  based on the individual choice of label we make for each object  and separation costs  based on the pair of choices we make for two "related" objects. We formulate a general classification problem of this type, the metric labeling problem; we show that it contains as special cases a number of standard classification f...
Interactive image segmentation using an adaptive GMMRF model
 in ECCV
, 2004
"... Abstract. The problem of interactive foreground/background segmentation in still images is of great practical importance in image editing. The state of the art in interactive segmentation is probably represented by the graph cut algorithm of Boykov and Jolly (ICCV 2001). Its underlying model uses bo ..."
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Cited by 153 (25 self)
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Abstract. The problem of interactive foreground/background segmentation in still images is of great practical importance in image editing. The state of the art in interactive segmentation is probably represented by the graph cut algorithm of Boykov and Jolly (ICCV 2001). Its underlying model uses both colour and contrast information, together with a strong prior for region coherence. Estimation is performed by solving a graph cut problem for which very efficient algorithms have recently been developed. However the model depends on parameters which must be set by hand and the aim of this work is for those constants to be learned from image data. First, a generative, probabilistic formulation of the model is set out in terms of a “Gaussian Mixture Markov Random Field ” (GMMRF). Secondly, a pseudolikelihood algorithm is derived which jointly learns the colour mixture and coherence parameters for foreground and background respectively. Error rates for GMMRF segmentation are calculated throughout using a new image database, available on the web, with ground truth provided by a human segmenter. The graph cut algorithm, using the learned parameters, generates good objectsegmentations with little interaction. However, pseudolikelihood learning proves to be frail, which limits the complexity of usable models, and hence also the achievable error rate. 1
Automated modelbased tissue classification of MR images of the brain
, 1999
"... We describe a fully automated method for modelbased tissue classification of Magnetic Resonance (MR) images of the brain. The method interleaves classification with estimation of the model parameters, improving the classification at each iteration. The algorithm is able to segment single and multi ..."
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Cited by 143 (13 self)
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We describe a fully automated method for modelbased tissue classification of Magnetic Resonance (MR) images of the brain. The method interleaves classification with estimation of the model parameters, improving the classification at each iteration. The algorithm is able to segment single and multispectral MR images, corrects for MR signal inhomogeneities and incorporates contextual information by means of Markov Random Fields. A digital brain atlas containing prior expectations about the spatial location of tissue classes is used to initialize the algorithm. This makes the method fully automated and therefore provides objective and reproducible segmentations. We have validated the technique on simulated as well as on real MR images of the brain.