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21
Learning lowlevel vision
 International Journal of Computer Vision
, 2000
"... We show a learningbased method for lowlevel vision problems. We setup a Markov network of patches of the image and the underlying scene. A factorization approximation allows us to easily learn the parameters of the Markov network from synthetic examples of image/scene pairs, and to e ciently prop ..."
Abstract

Cited by 468 (25 self)
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We show a learningbased method for lowlevel vision problems. We setup a Markov network of patches of the image and the underlying scene. A factorization approximation allows us to easily learn the parameters of the Markov network from synthetic examples of image/scene pairs, and to e ciently propagate image information. Monte Carlo simulations justify this approximation. We apply this to the \superresolution " problem (estimating high frequency details from a lowresolution image), showing good results. For the motion estimation problem, we show resolution of the aperture problem and llingin arising from application of the same probabilistic machinery.
The Computation of Optical Flow
, 1995
"... Twodimensional image motion is the projection of the threedimensional motion of objects, relative to a visual sensor, onto its image plane. Sequences of timeordered images allow the estimation of projected twodimensional image motion as either instantaneous image velocities or discrete image dis ..."
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Cited by 216 (10 self)
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Twodimensional image motion is the projection of the threedimensional motion of objects, relative to a visual sensor, onto its image plane. Sequences of timeordered images allow the estimation of projected twodimensional image motion as either instantaneous image velocities or discrete image displacements. These are usually called the optical flow field or the image velocity field. Provided that optical flow is a reliable approximation to twodimensional image motion, it may then be used to recover the threedimensional motion of the visual sensor (to within a scale factor) and the threedimensional surface structure (shape or relative depth) through assumptions concerning the structure of the optical flow field, the threedimensional environment and the motion of the sensor. Optical flow may also be used to perform motion detection, object segmentation, timetocollision and focus of expansion calculations, motion compensated encoding and stereo disparity measurement. We investiga...
Distributed Representation and Analysis of Visual Motion
, 1993
"... This thesis describes some new approaches to the representation and analysis of visual motion, as perceived by a biological or machine visual system. We begin by discussing the computation of image motion fields, the projection of motion in the threedimensional world onto the twodimensional image ..."
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Cited by 61 (4 self)
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This thesis describes some new approaches to the representation and analysis of visual motion, as perceived by a biological or machine visual system. We begin by discussing the computation of image motion fields, the projection of motion in the threedimensional world onto the twodimensional image plane. This computation is notoriously difficult, and there are a wide variety of approaches that have been developed for use in image processing, machine vision, and biological modeling. We show that a large number of the basic techniques are quite similar in nature, differing primarily in conceptual motivation, and that they each fail to handle a set of situations that occur commonly in natural scenery. The central theme of the thesis is that the failure of these algorithms is due primarily to the use of vector fields as a representation for visual motion. We argue that the translational vector field representation is inherently impoverished and errorprone. Furthermore, there is evidence that a ...
Interpreting images by propagating Bayesian beliefs
 Advances in Neural Information Processing Systems 9
, 1996
"... A central theme of computational vision research has been the realization that reliable estimation of local scene properties requires propagating measurements across the image. Many authors have therefore suggested solving vision problems using architectures of locally connected units updating their ..."
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Cited by 43 (4 self)
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A central theme of computational vision research has been the realization that reliable estimation of local scene properties requires propagating measurements across the image. Many authors have therefore suggested solving vision problems using architectures of locally connected units updating their activity in parallel. Unfortunately, the convergence of traditional relaxation methods on such architectures has proven to be excruciatingly slow and in general they do not guarantee that the stable point will be a global minimum. In this paper we show that an architecture in which Bayesian Beliefs about image properties are propagated between neighboring units yields convergence times which are several orders of magnitude faster than traditional methods and avoids local minima. In particular our architecture is noniterative in the sense of Marr [5]: at every time step, the local estimates at a given location are optimal given the information which has already been propagated to that loc...
Beyond independent components: trees and clusters
 Journal of Machine Learning Research
, 2003
"... We present a generalization of independent component analysis (ICA), where instead of looking for a linear transform that makes the data components independent, we look for a transform that makes the data components well fit by a treestructured graphical model. This treedependent component analysi ..."
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Cited by 42 (0 self)
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We present a generalization of independent component analysis (ICA), where instead of looking for a linear transform that makes the data components independent, we look for a transform that makes the data components well fit by a treestructured graphical model. This treedependent component analysis (TCA) provides a tractable and flexible approach to weakening the assumption of independence in ICA. In particular, TCA allows the underlying graph to have multiple connected components, and thus the method is able to find “clusters ” of components such that components are dependent within a cluster and independent between clusters. Finally, we make use of a notion of graphical models for time series due to Brillinger (1996) to extend these ideas to the temporal setting. In particular, we are able to fit models that incorporate treestructured dependencies among multiple time series.
Learning to estimate scenes from images
 Adv. Neural Information Processing Systems 11
, 1999
"... We seek the scene interpretation that best explains image data. ..."
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Cited by 38 (6 self)
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We seek the scene interpretation that best explains image data.
Embedded Trees: Estimation of Gaussian Processes on Graphs with Cycles
 IEEE Transactions on Signal Processing
, 2002
"... Graphical models provide a powerful general framework for encoding the structure of largescale estimation problems. However, the graphs describing typical realworld phenomena contain many cycles, making direct estimation procedures prohibitively costly. In this paper, we develop an iterative infer ..."
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Cited by 36 (13 self)
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Graphical models provide a powerful general framework for encoding the structure of largescale estimation problems. However, the graphs describing typical realworld phenomena contain many cycles, making direct estimation procedures prohibitively costly. In this paper, we develop an iterative inference algorithm for general Gaussian graphical models. It operates by exactly solving a series of modified estimation problems on spanning trees embedded within the original cyclic graph. When these subproblems are suitably chosen, the algorithm converges to the correct conditional means. Moreover, and in contrast to many other iterative methods, the treebased procedures we propose can also be used to calculate exact error variances. Although the conditional mean iteration is effective for quite densely connected graphical models, the error variance computation is most efficient for sparser graphs. In this context, we present a modeling example which suggests that very sparsely connected graphs with cycles may provide significant advantages relative to their treestructured counterparts, thanks both to the expressive power of these models and to the efficient inference algorithms developed herein.
Image modeling with positionencoding dynamic trees
 IEEE Trans. Pattern Anal. Machine Intell
, 2003
"... Abstract This paper describes the PositionEncoding Dynamic Tree (PEDT). The PEDT is a probabilistic model for images which improves on the Dynamic Tree by allowing the positions of objects to play a part in the model. This increases the flexibility of the model over the Dynamic Tree and allows the ..."
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Cited by 30 (0 self)
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Abstract This paper describes the PositionEncoding Dynamic Tree (PEDT). The PEDT is a probabilistic model for images which improves on the Dynamic Tree by allowing the positions of objects to play a part in the model. This increases the flexibility of the model over the Dynamic Tree and allows the positions of objects to be located and manipulated. The paper motivates and defines this form of probabilistic model using the belief network formalism. A structured variational approach for inference and learning in the PEDT is developed, and the resulting variational updates are obtained, along with additional implementation considerations which ensure the computational cost scales linearly in the number of nodes of the belief network. The PEDT model is demonstrated and compared with the dynamic tree and fixed tree. The structured variational learning method is compared with mean field approaches.
Comparing the mean field method and belief propagation for approximate inference in MRFs
, 2001
"... re the \beliefs") while in the physics setting mean eld approximations may be used to predict the macroscopic behavior of the system (e.g. critical temperature, correlation lengths etc.). I will therefore start this chapter reformulating both methods in a common language. I will then show simulatio ..."
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Cited by 30 (0 self)
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re the \beliefs") while in the physics setting mean eld approximations may be used to predict the macroscopic behavior of the system (e.g. critical temperature, correlation lengths etc.). I will therefore start this chapter reformulating both methods in a common language. I will then show simulation results on some toy problems. I tried to set up the toy problems such that they are small enough to make exact inference possible yet capture some of the qualities of the MRFs that occur in vision applications. I hope more head to head comparisons will be done in dierent graphs with dierent parameter regimes. Figure 1: An example of a MRF with pairwise potentials. The hidden nodes x i are denoted with open circles and observed nodes y i are denoted with lled circles. 1 The setting: undirected graphs with pairwise potentials I will assume we are dealing with pairwise Markov Random Fields (MRFs) of the form shown
Markov random fields and images
 CWI Quarterly
, 1998
"... At the intersection of statistical physics and probability theory, Markov random elds and Gibbs distributions have emerged in the early eighties as powerful tools for modeling images and coping with highdimensional inverse problems from lowlevel vision. Since then, they have been used in many studi ..."
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Cited by 25 (0 self)
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At the intersection of statistical physics and probability theory, Markov random elds and Gibbs distributions have emerged in the early eighties as powerful tools for modeling images and coping with highdimensional inverse problems from lowlevel vision. Since then, they have been used in many studies from the image processing and computer vision community. Abrief and simple introduction to the basics of the domain is proposed. 1. Introduction and