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376
Dynamic Bayesian Networks: Representation, Inference and Learning
, 2002
"... Modelling sequential data is important in many areas of science and engineering. Hidden Markov models (HMMs) and Kalman filter models (KFMs) are popular for this because they are simple and flexible. For example, HMMs have been used for speech recognition and biosequence analysis, and KFMs have bee ..."
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Cited by 564 (3 self)
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Modelling sequential data is important in many areas of science and engineering. Hidden Markov models (HMMs) and Kalman filter models (KFMs) are popular for this because they are simple and flexible. For example, HMMs have been used for speech recognition and biosequence analysis, and KFMs have been used for problems ranging from tracking planes and missiles to predicting the economy. However, HMMs
and KFMs are limited in their “expressive power”. Dynamic Bayesian Networks (DBNs) generalize HMMs by allowing the state space to be represented in factored form, instead of as a single discrete random variable. DBNs generalize KFMs by allowing arbitrary probability distributions, not just (unimodal) linearGaussian. In this thesis, I will discuss how to represent many different kinds of models as DBNs, how to perform exact and approximate inference in DBNs, and how to learn DBN models from sequential data.
In particular, the main novel technical contributions of this thesis are as follows: a way of representing
Hierarchical HMMs as DBNs, which enables inference to be done in O(T) time instead of O(T 3), where T is the length of the sequence; an exact smoothing algorithm that takes O(log T) space instead of O(T); a simple way of using the junction tree algorithm for online inference in DBNs; new complexity bounds on exact online inference in DBNs; a new deterministic approximate inference algorithm called factored frontier; an analysis of the relationship between the BK algorithm and loopy belief propagation; a way of
applying RaoBlackwellised particle filtering to DBNs in general, and the SLAM (simultaneous localization
and mapping) problem in particular; a way of extending the structural EM algorithm to DBNs; and a variety of different applications of DBNs. However, perhaps the main value of the thesis is its catholic presentation of the field of sequential data modelling.
Generalized Belief Propagation
 IN NIPS 13
, 2000
"... Belief propagation (BP) was only supposed to work for treelike networks but works surprisingly well in many applications involving networks with loops, including turbo codes. However, there has been little understanding of the algorithm or the nature of the solutions it finds for general graphs ..."
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Cited by 400 (9 self)
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Belief propagation (BP) was only supposed to work for treelike networks but works surprisingly well in many applications involving networks with loops, including turbo codes. However, there has been little understanding of the algorithm or the nature of the solutions it finds for general graphs. We show that
Image analogies
, 2001
"... Figure 1 An image analogy. Our problem is to compute a new “analogous ” image B ′ that relates to B in “the same way ” as A ′ relates to A. Here, A, A ′ , and B are inputs to our algorithm, and B ′ is the output. The fullsize images are shown in Figures 10 and 11. This paper describes a new framewo ..."
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Cited by 353 (8 self)
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Figure 1 An image analogy. Our problem is to compute a new “analogous ” image B ′ that relates to B in “the same way ” as A ′ relates to A. Here, A, A ′ , and B are inputs to our algorithm, and B ′ is the output. The fullsize images are shown in Figures 10 and 11. This paper describes a new framework for processing images by example, called “image analogies. ” The framework involves two stages: a design phase, in which a pair of images, with one image purported to be a “filtered ” version of the other, is presented as “training data”; and an application phase, in which the learned filter is applied to some new target image in order to create an “analogous” filtered result. Image analogies are based on a simple multiscale autoregression, inspired primarily by recent results in texture synthesis. By choosing different types of source image pairs as input, the framework supports a wide variety of “image filter ” effects, including traditional image filters, such as blurring or embossing; improved texture synthesis, in which some textures are synthesized with higher quality than by previous approaches; superresolution, in which a higherresolution image is inferred from a lowresolution source; texture transfer, in which images are “texturized ” with some arbitrary source texture; artistic filters, in which various drawing and painting styles are synthesized based on scanned realworld examples; and texturebynumbers, in which realistic scenes, composed of a variety of textures, are created using a simple painting interface.
Limits on superresolution and how to break them
 IEEE Transactions on Pattern Analysis and Machine Intelligence
, 2002
"... AbstractÐNearly all superresolution algorithms are based on the fundamental constraints that the superresolution image should generate the low resolution input images when appropriately warped and downsampled to model the image formation process. �These reconstruction constraints are normally com ..."
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Cited by 304 (8 self)
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AbstractÐNearly all superresolution algorithms are based on the fundamental constraints that the superresolution image should generate the low resolution input images when appropriately warped and downsampled to model the image formation process. �These reconstruction constraints are normally combined with some form of smoothness prior to regularize their solution.) In the first part of this paper, we derive a sequence of analytical results which show that the reconstruction constraints provide less and less useful information as the magnification factor increases. We also validate these results empirically and show that, for large enough magnification factors, any smoothness prior leads to overly smooth results with very little highfrequency content �however, many low resolution input images are used). In the second part of this paper, we propose a superresolution algorithm that uses a different kind of constraint, in addition to the reconstruction constraints. The algorithm attempts to recognize local features in the lowresolution images and then enhances their resolution in an appropriate manner. We call such a superresolution algorithm a hallucination or recogstruction algorithm. We tried our hallucination algorithm on two different data sets, frontal images of faces and printed Roman text. We obtained significantly better results than existing reconstructionbased algorithms, both qualitatively and in terms of RMS pixel error. Index TermsÐSuperresolution, analysis of reconstruction constraints, learning, faces, text, hallucination, recogstruction. 1
Convergent TreeReweighted Message Passing for Energy Minimization
 Proc. Int’l Workshop Artificial Intelligence and Statistics
, 2005
"... Abstract—Algorithms for discrete energy minimization are of fundamental importance in computer vision. In this paper, we focus on the recent technique proposed by Wainwright et al. [33]—treereweighted maxproduct message passing (TRW). It was inspired by the problem of maximizing a lower bound on t ..."
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Cited by 299 (10 self)
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Abstract—Algorithms for discrete energy minimization are of fundamental importance in computer vision. In this paper, we focus on the recent technique proposed by Wainwright et al. [33]—treereweighted maxproduct message passing (TRW). It was inspired by the problem of maximizing a lower bound on the energy. However, the algorithm is not guaranteed to increase this bound—it may actually go down. In addition, TRW does not always converge. We develop a modification of this algorithm which we call sequential treereweighted message passing. Its main property is that the bound is guaranteed not to decrease. We also give a weak tree agreement condition which characterizes local maxima of the bound with respect to TRW algorithms. We prove that our algorithm has a limit point that achieves weak tree agreement. Finally, we show that, our algorithm requires half as much memory as traditional message passing approaches. Experimental results demonstrate that on certain synthetic and real problems, our algorithm outperforms both the ordinary belief propagation and treereweighted algorithm in [33]. In addition, on stereo problems with Potts interactions, we obtain a lower energy than graph cuts. Index Terms—Energy minimization, graph algorithms, message passing, belief propagation, early vision, Markov random fields, stereo. Ç 1
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 253 (3 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, and a binary process for occlusion. After eliminating the line process and the binary process by introducing two robust functions, we apply the belief propagation algorithm to obtain the maximum a posteriori (MAP) estimation in the Markov network. Other lowlevel visual cues (e.g., image segmentation) can also be easily incorporated in our stereo model to obtain better stereo results. Experiments demonstrate that our methods are comparable to the stateoftheart stereo algorithms for many test cases.
A comparative study of energy minimization methods for Markov random fields
 In ECCV
, 2006
"... Abstract. 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 Ma ..."
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Cited by 245 (26 self)
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Abstract. 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 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. Unfortunately, most papers define their own energy function, which is minimized with a specific algorithm of their choice. As a result, the tradeoffs among different energy minimization algorithms are not well understood. In this paper we describe a set of energy minimization benchmarks, which we use to compare the solution quality and running time of several common energy minimization algorithms. We investigate three promising recent methods—graph cuts, LBP, and treereweighted message passing—as well as the wellknown older iterated conditional modes (ICM) algorithm. Our benchmark problems are drawn from published energy functions used for stereo, image stitching and interactive segmentation. We also provide a generalpurpose software interface that allows vision researchers to easily switch between optimization methods with minimal overhead. We expect that the availability of our benchmarks and interface will make it significantly easier for vision researchers to adopt the best method for their specific problems. Benchmarks, code, results and images are available at
Fields of experts: A framework for learning image priors
 In CVPR
, 2005
"... We develop a framework for learning generic, expressive image priors that capture the statistics of natural scenes and can be used for a variety of machine vision tasks. The approach extends traditional Markov Random Field (MRF) models by learning potential functions over extended pixel neighborhood ..."
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Cited by 229 (3 self)
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We develop a framework for learning generic, expressive image priors that capture the statistics of natural scenes and can be used for a variety of machine vision tasks. The approach extends traditional Markov Random Field (MRF) models by learning potential functions over extended pixel neighborhoods. Field potentials are modeled using a ProductsofExperts framework that exploits nonlinear functions of many linear filter responses. In contrast to previous MRF approaches all parameters, including the linear filters themselves, are learned from training data. We demonstrate the capabilities of this Field of Experts model with two example applications, image denoising and image inpainting, which are implemented using a simple, approximate inference scheme. While the model is trained on a generic image database and is not tuned toward a specific application, we obtain results that compete with and even outperform specialized techniques. 1.
Examplebased superresolution
 IEEE Comput. Graph. Appl
"... The Problem: Pixel representations for images do not have resolution independence. When we zoom into a bitmapped image, we get a blurred image. Figure 1 shows the problem for a teapot image, rich with realworld detail. We know the teapot’s features should remain sharp as we zoom in on them, yet sta ..."
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Cited by 228 (5 self)
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The Problem: Pixel representations for images do not have resolution independence. When we zoom into a bitmapped image, we get a blurred image. Figure 1 shows the problem for a teapot image, rich with realworld detail. We know the teapot’s features should remain sharp as we zoom in on them, yet standard pixel interpolation methods, such as pixel replication (b, c) and cubic spline interpolation (d, e), introduce artifacts or blurring of edges. For images zoomed 3 octaves, such as these, sharpening the interpolated result has little useful effect (f, g). Many applications in graphics or image processing could benefit from such pixel resolution independence, such as texture mapping, enlarging consumer photographs, and converting NTSC video content to HDTV. We don’t expect perfect resolution independence—even the polygon representation doesn’t have that—but increasing the resolution independence of pixelbased representations is an important task for imagebased rendering. Our examplebased superresolution algorithm yields Fig. 1 (h, i). Previous Work: Researchers have long studied image interpolation, although only recently using machine learning or sampling approaches, which offer much power. Cubic spline interpolation [5] is a very common image interpolation function, but suffers from blurring of edges and image details. Recent attempts to improve on cubic spline interpolation [6, 8, 2] have met with limited success. Schreiber and collaborators [6] proposed a sharpened Gaussian interpolator function to minimize information
Nonparametric Belief Propagation
 IN CVPR
, 2002
"... In applications of graphical models arising in fields such as computer vision, the hidden variables of interest are most naturally specified by continuous, nonGaussian distributions. However, due to the limitations of existing inf#6F6F3 algorithms, it is of#]k necessary tof#3# coarse, ..."
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Cited by 208 (25 self)
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In applications of graphical models arising in fields such as computer vision, the hidden variables of interest are most naturally specified by continuous, nonGaussian distributions. However, due to the limitations of existing inf#6F6F3 algorithms, it is of#]k necessary tof#3# coarse, discrete approximations to such models. In this paper, we develop a nonparametric belief propagation (NBP) algorithm, which uses stochastic methods to propagate kernelbased approximations to the true continuous messages. Each NBP message update is based on an efficient sampling procedure which can accomodate an extremely broad class of potentialf#l3]k[[z3 allowing easy adaptation to new application areas. We validate our method using comparisons to continuous BP for Gaussian networks, and an application to the stereo vision problem.