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150
Fast approximate energy minimization via graph cuts
 IEEE Transactions on Pattern Analysis and Machine Intelligence
, 2001
"... In this paper we address the problem of minimizing a large class of energy functions that occur in early vision. The major restriction is that the energy function’s smoothness term must only involve pairs of pixels. We propose two algorithms that use graph cuts to compute a local minimum even when v ..."
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Cited by 1384 (51 self)
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In this paper we address the problem of minimizing a large class of energy functions that occur in early vision. The major restriction is that the energy function’s smoothness term must only involve pairs of pixels. We propose two algorithms that use graph cuts to compute a local minimum even when very large moves are allowed. The first move we consider is an αβswap: for a pair of labels α, β, this move exchanges the labels between an arbitrary set of pixels labeled α and another arbitrary set labeled β. Our first algorithm generates a labeling such that there is no swap move that decreases the energy. The second move we consider is an αexpansion: for a label α, this move assigns an arbitrary set of pixels the label α. Our second
Filters, Random Fields and Maximum Entropy . . .
 INTERNATIONAL JOURNAL OF COMPUTER VISION
, 1998
"... This article presents a statistical theory for texture modeling. This theory combines filtering theory and Markov random field modeling through the maximum entropy principle, and interprets and clarifies many previous concepts and methods for texture analysis and synthesis from a unified point of vi ..."
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Cited by 195 (17 self)
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This article presents a statistical theory for texture modeling. This theory combines filtering theory and Markov random field modeling through the maximum entropy principle, and interprets and clarifies many previous concepts and methods for texture analysis and synthesis from a unified point of view. Our theory characterizes the ensemble of images I with the same texture appearance by a probability distribution f (I) on a random field, and the objective of texture modeling is to make inference about f (I), given a set of observed texture examples. In our theory, texture modeling consists of two steps. (1) A set of filters is selected from a general filter bank to capture features of the texture, these filters are applied to observed texture images, and the histograms of the filtered images are extracted. These histograms are estimates of the marginal distributions of f (I). This step is called feature extraction. (2) The maximum entropy principle is employed to derive a distribution p(I), which is restricted to have the same marginal distributions as those in (1). This p(I) is considered as an estimate of f (I). This step is called feature fusion. A stepwise algorithm is proposed to choose filters from a general filter bank. The resulting model, called FRAME (Filters, Random fields And Maximum Entropy), is a Markov random field (MRF) model, but with a much enriched vocabulary and hence much stronger descriptive ability than the previous MRF models used for texture modeling. Gibbs sampler is adopted to synthesize texture images by drawing typical samples from p(I), thus the model is verified by seeing whether the synthesized texture images have similar visual appearances
Minimax Entropy Principle and Its Application to Texture Modeling
, 1997
"... This article proposes a general theory and methodology, called the minimax entropy principle, for building statistical models for images (or signals) in a variety of applications. This principle consists of two parts. The first is the maximum entropy principle for feature binding (or fusion): for a ..."
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Cited by 192 (39 self)
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This article proposes a general theory and methodology, called the minimax entropy principle, for building statistical models for images (or signals) in a variety of applications. This principle consists of two parts. The first is the maximum entropy principle for feature binding (or fusion): for a certain set of feature statistics, a distribution can be built to bind these feature statistics together by maximizing the entropy over all distributions that reproduce these feature statistics. The second part is the minimum entropy principle for feature selection: among all plausible sets of feature statistics, we choose the set whose maximum entropy distribution has the minimum entropy. Computational and inferential issues in both parts are addressed, in particular, a feature pursuit procedure is proposed for approximately selecting the optimal set of features. The model complexity is restricted because of the sample variation in the observed feature statistics. The minimax entropy principle is applied to texture modeling, where a novel Markov random field (MRF) model, called FRAME (Filter, Random field, And Minimax Entropy), is derived, and encouraging results are obtained in experiments on a variety of texture images. Relationship between our theory and the mechanisms of neural computation is also discussed.
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
Prior Learning and Gibbs ReactionDiffusion
, 1997
"... This article addresses two important themes in early visual computation: rst it presents a novel theory for learning the universal statistics of natural images { a prior model for typical cluttered scenes of the world { from a set of natural images, second it proposes a general framework of designi ..."
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Cited by 149 (18 self)
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This article addresses two important themes in early visual computation: rst it presents a novel theory for learning the universal statistics of natural images { a prior model for typical cluttered scenes of the world { from a set of natural images, second it proposes a general framework of designing reactiondiusion equations for image processing. We start by studying the statistics of natural images including the scale invariant properties, then generic prior models were learned to duplicate the observed statistics, based on the minimax entropy theory studied in two previous papers. The resulting Gibbs distributions have potentials of the form U(I; ; S) = P K I)(x; y)) with S = fF g being a set of lters and = f the potential functions. The learned Gibbs distributions con rm and improve the form of existing prior models such as lineprocess, but in contrast to all previous models, inverted potentials (i.e. (x) decreasing as a function of jxj) were found to be necessary. We nd that the partial dierential equations given by gradient descent on U(I; ; S) are essentially reactiondiusion equations, where the usual energy terms produce anisotropic diusion while the inverted energy terms produce reaction associated with pattern formation, enhancing preferred image features. We illustrate how these models can be used for texture pattern rendering, denoising, image enhancement and clutter removal by careful choice of both prior and data models of this type, incorporating the appropriate features. Song Chun Zhu is now with the Computer Science Department, Stanford University, Stanford, CA 94305, and David Mumford is with the Division of Applied Mathematics, Brown University, Providence, RI 02912. This work started when the authors were at ...
On Advances in Statistical Modeling of Natural Images
 Journal of Mathematical Imaging and Vision
, 2003
"... Statistical analysis of images reveals two interesting properties: (i) invariance of image statistics to scaling of images, and (ii) nonGaussian behavior of image statistics, i.e. high kurtosis, heavy tails, and sharp central cusps. In this paper we review some recent results in statistical modelin ..."
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Cited by 100 (5 self)
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Statistical analysis of images reveals two interesting properties: (i) invariance of image statistics to scaling of images, and (ii) nonGaussian behavior of image statistics, i.e. high kurtosis, heavy tails, and sharp central cusps. In this paper we review some recent results in statistical modeling of natural images that attempt to explain these patterns. Two categories of results are considered: (i) studies of probability models of images or image decompositions (such as Fourier or wavelet decompositions), and (ii) discoveries of underlying image manifolds while restricting to natural images. Applications of these models in areas such as texture analysis, image classification, compression, and denoising are also considered.
Accelerated training of conditional random fields with stochastic gradient methods
 In ICML
, 2006
"... We apply Stochastic MetaDescent (SMD), a stochastic gradient optimization method with gain vector adaptation, to the training of Conditional Random Fields (CRFs). On several large data sets, the resulting optimizer converges to the same quality of solution over an order of magnitude faster than lim ..."
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Cited by 95 (4 self)
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We apply Stochastic MetaDescent (SMD), a stochastic gradient optimization method with gain vector adaptation, to the training of Conditional Random Fields (CRFs). On several large data sets, the resulting optimizer converges to the same quality of solution over an order of magnitude faster than limitedmemory BFGS, the leading method reported to date. We report results for both exact and inexact inference techniques. 1.
Efficient GraphBased Energy Minimization Methods In Computer Vision
, 1999
"... ms (we show that exact minimization in NPhard in these cases). These algorithms produce a local minimum in interesting large move spaces. Furthermore, one of them nds a solution within a known factor from the optimum. The algorithms are iterative and compute several graph cuts at each iteration. Th ..."
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Cited by 82 (5 self)
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ms (we show that exact minimization in NPhard in these cases). These algorithms produce a local minimum in interesting large move spaces. Furthermore, one of them nds a solution within a known factor from the optimum. The algorithms are iterative and compute several graph cuts at each iteration. The running time at each iteration is eectively linear due to the special graph structure. In practice it takes just a few iterations to converge. Moreover most of the progress happens during the rst iteration. For a certain piecewise constant prior we adapt the algorithms developed for the piecewise smooth prior. One of them nds a solution within a factor of two from the optimum. In addition we develop a third algorithm which nds a local minimum in yet another move space. We demonstrate the eectiveness of our approach on image restoration, stereo, and motion. For the data with ground truth, our methods signicantly outperform standard methods. Biographical Sketch Olga