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83
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 386 (18 self)
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. 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 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 in low and high level computer vision. The unification is made possible due to a recent advance in MRF modeling for high level object recognition. Such unification provides a systematic approach for vision modeling based on sound mathematical principles. 1 Introduction Since its beginning in early 1960's, computer vision research has been evolving from heuristic design of algorithms to syste...
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 161 (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...
A local update strategy for iterative reconstruction from projections
 IEEE Tr. Sig. Proc
, 1993
"... Iterative methods for statisticallybased reconstruction from projections are computationally costly relative to convolution backprojection, but allow useful image reconstruction from sparse and noisy data. We present a method for Bayesian reconstruction which relies on updates of single pixel value ..."
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Cited by 120 (31 self)
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Iterative methods for statisticallybased reconstruction from projections are computationally costly relative to convolution backprojection, but allow useful image reconstruction from sparse and noisy data. We present a method for Bayesian reconstruction which relies on updates of single pixel values, rather than the entire image, at each iteration. The technique is similar to GaussSeidel (GS) iteration for the solution of differential equations on finite grids. The computational cost per iteration of the GS approach is found to be approximately equal to that of gradient methods. For continuously valued images, GS is found to have significantly better convergence at modes representing high spatial frequencies. In addition, GS is well suited to segmentation when the image is constrained to be discretely valued. We demonstrate that Bayesian segmentation using GS iteration produces useful estimates at much lower signaltonoise ratios than required for continuously valued reconstruction. This paper includes analysis of the convergence properties of gradient ascent and GS for reconstruction from integral projections, and simulations of both maximumlikelihood and maximum a posteriori cases.
Hybrid Image Segmentation Using Watersheds and Fast Region Merging
 IEEE transactions on Image Processing
, 1998
"... Abstract—A hybrid multidimensional image segmentation algorithm is proposed, which combines edge and regionbased techniques through the morphological algorithm of watersheds. An edgepreserving statistical noise reduction approach is used as a preprocessing stage in order to compute an accurate est ..."
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Cited by 88 (1 self)
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Abstract—A hybrid multidimensional image segmentation algorithm is proposed, which combines edge and regionbased techniques through the morphological algorithm of watersheds. An edgepreserving statistical noise reduction approach is used as a preprocessing stage in order to compute an accurate estimate of the image gradient. Then, an initial partitioning of the image into primitive regions is produced by applying the watershed transform on the image gradient magnitude. This initial segmentation is the input to a computationally efficient hierarchical (bottomup) region merging process that produces the final segmentation. The latter process uses the region adjacency graph (RAG) representation of the image regions. At each step, the most similar pair of regions is determined (minimum cost RAG edge), the regions are merged and the RAG is updated. Traditionally, the above is implemented by storing all RAG edges in a priority queue. We propose a significantly faster algorithm, which additionally maintains the socalled nearest neighbor graph, due to which the priority queue size and processing time are drastically reduced. The final segmentation provides, due to the RAG, onepixel wide, closed, and accurately localized contours/surfaces. Experimental results obtained with twodimensional/threedimensional (2D/3D) magnetic resonance images are presented. Index Terms — Image segmentation, nearest neighbor region merging, noise reduction, watershed transform. I.
Approximation Algorithms for the Metric Labeling Problem via a New Linear Programming Formulation
, 2000
"... We consider approximation algorithms for the metric labeling problem. Informally speaking, we are given a weighted graph that specifies relations between pairs of objects drawn from a given set of objects. The goal is to find a minimum cost labeling of these objects where the cost of a labeling is d ..."
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Cited by 66 (1 self)
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We consider approximation algorithms for the metric labeling problem. Informally speaking, we are given a weighted graph that specifies relations between pairs of objects drawn from a given set of objects. The goal is to find a minimum cost labeling of these objects where the cost of a labeling is determined by the pairwise relations between the objects and a distance function on labels; the distance function is assumed to be a metric. Each object also incurs an assignment cost that is label, and vertex dependent. The problem was introduced in a recent paper by Kleinberg and Tardos [19], and captures many classification problems that arise in computer vision and related fields. They gave an O(log k log log k) approximation for the general case where k is the number of labels and a 2approximation for the uniform metric case. More recently, Gupta and Tardos [14] gave a 4approximation for the truncated linear metric, a natural nonuniform metric motivated by practical applications to image restoration and visual correspondence. In this paper we introduce a new natural integer programming formulation and show that the integrality gap of its linear relaxation either matches or improves the ratios known for several cases of the metric labeling problem studied until now, providing a unified approach to solving them. Specifically, we show that the integrality gap of our LP is bounded by O(log k log log k) for general metric and 2 for the uniform metric thus matching the ratios in [19]. We also develop an algorithm based on our LP that achieves a ratio of 2 + p 2 ' 3:414 for the truncated linear metric improving the ratio provided by [14]. Our algorithm uses the fact that the integrality gap of our LP is 1 on a linear metric. We believe that our formulation h...
Estimation of Generalized Multisensor Hidden Markov Chains and Unsupervised Image Segmentation
, 1997
"... This paper attacks the problem of generalized multisensor mixture estimation. A distribution mixture is said to be generalized when the exact nature of components is not known, but each of them belongs to a finite known set of families of distributions. Estimating such a mixture entails a supplement ..."
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Cited by 57 (26 self)
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This paper attacks the problem of generalized multisensor mixture estimation. A distribution mixture is said to be generalized when the exact nature of components is not known, but each of them belongs to a finite known set of families of distributions. Estimating such a mixture entails a supplementary difficulty: one must label, for each class and each sensor, the exact nature of the corresponding distribution. Such generalized mixtures have been studied assuming that the components lie in the Pearson system. Adaptations of classical algorithms, such as ExpectationMaximization (EM), Stochastic ExpectationMaximization (SEM), or Iterative Conditional Estimation (ICE), can then be used to estimate such mixtures in the context of independent identically distributed data and hidden Markov random fields. We propose a more general procedure with applications to estimating generalized multisensor hidden Markov chains. Our proposed method is applied to the problem of unsupervised image segmen...
FrontalView Face Detection and Facial Feature Extraction using Color, Shape and Symmetry Based Cost Functions
, 1998
"... We describe an algorithm for detecting human faces and facial features, such as the location of the eyes, nose, and mouth. First, a supervised pixelbased color classifier is employed to mark all pixels that are within a prespecified distance of "skin color," which is computed from a training set of ..."
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Cited by 52 (0 self)
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We describe an algorithm for detecting human faces and facial features, such as the location of the eyes, nose, and mouth. First, a supervised pixelbased color classifier is employed to mark all pixels that are within a prespecified distance of "skin color," which is computed from a training set of skin patches. This colorclassification map is then smoothed by Gibbs random field modelbased filters to define skin regions. An ellipse model is fit to each disjoint skin region. Finally, we introduce symmetrybased cost functions to search the center of the eyes, tip of nose, and center of mouth within ellipses whose aspect ratio is similar to that of a face. Face detection facial feature detection image segmentation shape classification Gibbs random fields 1 Introduction Automatic detection and recognition of faces from still images and video is an active research area. A complete facial image analysis system should be able to localize faces in a given image, identify and pinpoint fac...
ContentBased Hierarchical Classification of Vacation Images
 In Proceedings of the IEEE International Conference on Multimedia Computing and Systems
, 1999
"... Grouping images into (semantically) meaningful categories using lowlevel visual features is a challenging and important problem in contentbased image retrieval. Using binary Bayesian classifiers, we show how highlevel concepts can be understood from lowlevel images under the constraint that the ..."
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Cited by 45 (4 self)
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Grouping images into (semantically) meaningful categories using lowlevel visual features is a challenging and important problem in contentbased image retrieval. Using binary Bayesian classifiers, we show how highlevel concepts can be understood from lowlevel images under the constraint that the image does belong to one of the classes in question. Specifically, we consider the hierarchical classification of vacation images; at the highest level, images are classified into indooroutdoor classes, outdoor images are further classified into citylandscape classes, and finally, a subset of landscape images is classified into sunset, forest, and mountain classes. We demonstrate that a small codebook (the optimal size of codebook is selected using MDL principle) extracted from a vector quantizer can be used to estimate the classconditional densities of the observed features needed for the Bayesian methodology. The classifiers have been built on a database of 6 � 931 vacation photographs. Our system achieved an accuracy of 90:8% for indooroutdoor classification, 94:3 % for city vs. landscape classification, 94:9 % for sunset vs. forest & mountain classification, and 93:6 % for forest vs. mountain classification. Our final goal is to combine multiple 2class classifiers into a single hierarchical classifier. Contentbased image organization and retrieval has emerged as an important area in computer vision and multimedia
Estimation of Generalized Mixtures and Its Application in Image Segmentation.
, 1997
"... We introduce in this work the notion of a generalised mixture and propose some methods for estimating it, along with applications to unsupervised statistical image segmentation. A distribution mixture is said to be "generalised" when the exact nature of components is not known, but each belongs to a ..."
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Cited by 45 (17 self)
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We introduce in this work the notion of a generalised mixture and propose some methods for estimating it, along with applications to unsupervised statistical image segmentation. A distribution mixture is said to be "generalised" when the exact nature of components is not known, but each belongs to a finite known set of families of distributions. For instance, we can consider a mixture of three distributions, each being exponential or Gaussian. The problem of estimating such a mixture contains thus a new difficulty : we have to label each of three components (there are eight possibilities). We show that the classical mixture estimation algorithms ExpectationMaximization (EM), Stochastic EM (SEM), and Iterative Conditional Estimation (ICE) can be adapted to such situations once as we dispose of a method of recognition of each component separately. That is, when we know that a sample proceeds from one family of the set considered, we have a decision rule for what family it belongs to. considering the Pearson system, which is a set of eight families, the decision rule above is defined by the use of "skewness" and "kurtosis". The different algorithms so obtained are then applied to the problem of unsupervised Bayesian image segmentation. We propose the adaptive versions of SEM, EM and ICE in the case of "blind", i.e., "pixel by pixel", segmentation. "Global" segmentation methods require modelling by Hidden Random Markov Fields and we propose adaptations of two traditional parameter estimation algorithms: Gibbsian EM (GEM) and ICE allowing the estimation of generalized mixtures corresponding to Pearson's system. The efficiency of different methods is compared via numerical studies and the results of unsupervised segmentation of three real radar images by different methods a...
A Markov Random Field modelbased approach to unsupervised texture segmentation using local and global spatial statistics
, 1993
"... The general problem of unsupervised textured image segmentation remains a fundamental but not entirely solved issue in image analysis. Many studies have proven that statistical modelbased texture segmentation algorithms yield good results provided that the model parameters and the number of region ..."
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Cited by 34 (4 self)
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The general problem of unsupervised textured image segmentation remains a fundamental but not entirely solved issue in image analysis. Many studies have proven that statistical modelbased texture segmentation algorithms yield good results provided that the model parameters and the number of regions be known a priori. In this paper, we present an unsupervised texture segmentation method which does not require a priori knowledge about the different texture regions, their parameters, or the number of available texture classes. The proposed algorithm relies on the analysis of local and global second and higher order spatial statistics of the original images. The segmentation map is modeled using an augmentedstate Markov Random Field, including an outlier class which enables dynamic creation of new regions during the optimization process. A bayesian estimate of this map is computed using a deterministic relaxation algorithm. The whole segmentation procedure is controlled by one single p...