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41
Recovering Occlusion Boundaries from a Single Image
"... Occlusion reasoning, necessary for tasks such as navigation and object search, is an important aspect of everyday life and a fundamental problem in computer vision. We believe that the amazing ability of humans to reason about occlusions from one image is based on an intrinsically 3D interpretation. ..."
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Cited by 58 (10 self)
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Occlusion reasoning, necessary for tasks such as navigation and object search, is an important aspect of everyday life and a fundamental problem in computer vision. We believe that the amazing ability of humans to reason about occlusions from one image is based on an intrinsically 3D interpretation. In this paper, our goal is to recover the occlusion boundaries and depth ordering of freestanding structures in the scene. Our approach is to learn to identify and label occlusion boundaries using the traditional edge and region cues together with 3D surface and depth cues. Since some of these cues require good spatial support (i.e., a segmentation), we gradually create larger regions and use them to improve inference over the boundaries. Our experiments demonstrate the power of a scenebased approach to occlusion reasoning. 1.
On the Uniqueness of Loopy Belief Propagation Fixed Points
, 2004
"... We derive sufficient conditions for the uniqueness of loopy belief propagation fixed points. These conditions depend on both the structure of the graph and the strength of the potentials and naturally extend those for convexity of the Bethe free energy. We compare them with (a strengthened version o ..."
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Cited by 57 (2 self)
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We derive sufficient conditions for the uniqueness of loopy belief propagation fixed points. These conditions depend on both the structure of the graph and the strength of the potentials and naturally extend those for convexity of the Bethe free energy. We compare them with (a strengthened version of) conditions derived elsewhere for pairwise potentials. We discuss possible implications for convergent algorithms, as well as for other approximate free energies.
Estimating the "Wrong" Graphical Model: Benefits in the ComputationLimited Setting
 Journal of Machine Learning Research
, 2006
"... Consider the problem of joint parameter estimation and prediction in a Markov random field: that is, the model parameters are estimated on the basis of an initial set of data, and then the fitted model is used to perform prediction (e.g., smoothing, denoising, interpolation) on a new noisy observa ..."
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Cited by 36 (2 self)
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Consider the problem of joint parameter estimation and prediction in a Markov random field: that is, the model parameters are estimated on the basis of an initial set of data, and then the fitted model is used to perform prediction (e.g., smoothing, denoising, interpolation) on a new noisy observation.
libDAI: A free/open source C++ library for discrete approximate inference methods
, 2008
"... This paper describes the software package libDAI, a free & open source C++ library that provides implementations of various exact and approximate inference methods for graphical models with discretevalued variables. libDAI supports directed graphical models (Bayesian networks) as well as undirected ..."
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Cited by 32 (1 self)
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This paper describes the software package libDAI, a free & open source C++ library that provides implementations of various exact and approximate inference methods for graphical models with discretevalued variables. libDAI supports directed graphical models (Bayesian networks) as well as undirected ones (Markov random fields and factor graphs). It offers various approximations of the partition sum, marginal probability distributions and maximum probability states. Parameter learning is also supported. A feature comparison with other open source software packages for approximate inference is given. libDAI is licensed under the GPL v2+ license and is available at
Sufficient conditions for convergence of the sumproduct algorithm
 IEEE Trans. IT
, 2007
"... Abstract—Novel conditions are derived that guarantee convergence ..."
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Cited by 28 (2 self)
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Abstract—Novel conditions are derived that guarantee convergence
LogDeterminant Relaxation for Approximate Inference in Discrete Markov Random Fields
, 2006
"... Graphical models are well suited to capture the complex and nonGaussian statistical dependencies that arise in many realworld signals. A fundamental problem common to any signal processing application of a graphical model is that of computing approximate marginal probabilities over subsets of nod ..."
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Cited by 27 (3 self)
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Graphical models are well suited to capture the complex and nonGaussian statistical dependencies that arise in many realworld signals. A fundamental problem common to any signal processing application of a graphical model is that of computing approximate marginal probabilities over subsets of nodes. This paper proposes a novel method, applicable to discretevalued Markov random fields (MRFs) on arbitrary graphs, for approximately solving this marginalization problem. The foundation of our method is a reformulation of the marginalization problem as the solution of a lowdimensional convex optimization problem over the marginal polytope. Exactly solving this problem for general graphs is intractable; for binary Markov random fields, we describe how to relax it by using a Gaussian bound on the discrete entropy and a semidefinite outer bound on the marginal polytope. This combination leads to a logdeterminant maximization problem that can be solved efficiently by interior point methods, thereby providing approximations to the exact marginals. We show how a slightly weakened logdeterminant relaxation can be solved even more efficiently by a dual reformulation. When applied to denoising problems in a coupled mixtureofGaussian model defined on a binary MRF with cycles, we find that the performance of this logdeterminant relaxation is comparable or superior to the widely used sumproduct algorithm over a range of experimental conditions.
Convexity Arguments for Efficient Minimization of the Bethe and Kikuchi Free Energies
"... Loopy and generalized belief propagation are popular algorithms for approximate inference in Markov random fields and Bayesian networks. Fixed points of these algorithms have been shown to correspond to extrema of the Bethe and Kikuchi free energy, both of which are approximations of the exact Helmh ..."
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Cited by 26 (0 self)
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Loopy and generalized belief propagation are popular algorithms for approximate inference in Markov random fields and Bayesian networks. Fixed points of these algorithms have been shown to correspond to extrema of the Bethe and Kikuchi free energy, both of which are approximations of the exact Helmholtz free energy. However, belief propagation does not always converge, which motivates approaches that explicitly minimize the Kikuchi/Bethe free energy, such as CCCP and UPS. Here we describe a class of algorithms that solves this typically nonconvex constrained minimization problem through a sequence of convex constrained minimizations of upper bounds on the Kikuchi free energy. Intuitively one would expect tighter bounds to lead to faster algorithms, which is indeed convincingly demonstrated in our simulations. Several ideas are applied to obtain tight convex bounds that yield dramatic speedups over CCCP.
Efficient belief propagation for vision using linear constraint nodes
 in CVPR
, 2007
"... Belief propagation over pairwise connected Markov Random Fields has become a widely used approach, and has been successfully applied to several important computer vision problems. However, pairwise interactions are often insufficient to capture the full statistics of the problem. Higherorder intera ..."
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Cited by 25 (4 self)
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Belief propagation over pairwise connected Markov Random Fields has become a widely used approach, and has been successfully applied to several important computer vision problems. However, pairwise interactions are often insufficient to capture the full statistics of the problem. Higherorder interactions are sometimes required. Unfortunately, the complexity of belief propagation is exponential in the size of the largest clique. In this paper, we introduce a new technique to compute belief propagation messages in time linear with respect to clique size for a large class of potential functions over realvalued variables. We demonstrate this technique in two applications. First, we perform efficient inference in graphical models where the spatial prior of natural images is captured by 2 × 2 cliques. This approach shows significant improvement over the commonly used pairwiseconnected models, and may benefit a variety of applications using belief propagation to infer images or range images. Finally, we apply these techniques to shapefromshading and demonstrate significant improvement over previous methods, both in quality and in flexibility. 1.
Learning to find object boundaries using motion cues
 In IEEE international conference on computer vision (ICCV
, 2007
"... While great strides have been made in detecting and localizing specific objects in natural images, the bottomup segmentation of unknown, generic objects remains a difficult challenge. We believe that occlusion can provide a strong cue for object segmentation and “popout”, but detecting an object’s ..."
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Cited by 21 (4 self)
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While great strides have been made in detecting and localizing specific objects in natural images, the bottomup segmentation of unknown, generic objects remains a difficult challenge. We believe that occlusion can provide a strong cue for object segmentation and “popout”, but detecting an object’s occlusion boundaries using appearance alone is a difficult problem in itself. If the camera or the scene is moving, however, that motion provides an additional powerful indicator of occlusion. Thus, we use standard appearance cues (e.g. brightness/color gradient) in addition to motion cues that capture subtle differences in the relative surface motion (i.e. parallax) on either side of an occlusion boundary. We describe a learned local classifier and global inference approach which provide a framework for combining and reasoning about these appearance and motion cues to estimate which region boundaries of an initial oversegmentation correspond to object/occlusion boundaries in the scene. Through results on a dataset which contains short videos with labeled boundaries, we demonstrate the effectiveness of motion cues for this task. 1.
Sufficient conditions for convergence of loopy belief propagation
 In Proc. Conference on Uncertainty in Artificial Intelligence (UAI
, 2005
"... We derive novel conditions that guarantee convergence of Loopy Belief Propagation (also known as the SumProduct algorithm) to a unique fixed point. Our results are provably stronger than existing sufficient conditions. We show that the improvement can be quite substantial; in particular, for binary ..."
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Cited by 20 (3 self)
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We derive novel conditions that guarantee convergence of Loopy Belief Propagation (also known as the SumProduct algorithm) to a unique fixed point. Our results are provably stronger than existing sufficient conditions. We show that the improvement can be quite substantial; in particular, for binary variables with (anti)ferromagnetic interactions, our conditions seem to be sharp.