Results 1 - 10
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241
Learning low-level vision
- International Journal of Computer Vision
, 2000
"... We show a learning-based method for low-level vision problems. We set-up 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 ..."
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Cited by 579 (30 self)
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We show a learning-based method for low-level vision problems. We set-up 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 \super-resolution " problem (estimating high frequency details from a low-resolution image), showing good results. For the motion estimation problem, we show resolution of the aperture problem and lling-in arising from application of the same probabilistic machinery.
A comparative study of energy minimization methods for Markov random fields
- IN ECCV
, 2006
"... 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 Ran ..."
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Cited by 415 (36 self)
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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 top-performing 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 tree-reweighted message passing—as well as the well-known 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 general-purpose 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
MAP estimation via agreement on trees: Message-passing and linear programming
, 2002
"... We develop and analyze methods for computing provably optimal maximum a posteriori (MAP) configurations for a subclass of Markov random fields defined on graphs with cycles. By decomposing the original distribution into a convex combination of tree-structured distributions, we obtain an upper bound ..."
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Cited by 191 (9 self)
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We develop and analyze methods for computing provably optimal maximum a posteriori (MAP) configurations for a subclass of Markov random fields defined on graphs with cycles. By decomposing the original distribution into a convex combination of tree-structured distributions, we obtain an upper bound on the optimal value of the original problem (i.e., the log probability of the MAP assignment) in terms of the combined optimal values of the tree problems. We prove that this upper bound is tight if and only if all the tree distributions share an optimal configuration in common. An important implication is that any such shared configuration must also be a MAP configuration for the original distribution. Next we develop two approaches to attempting to obtain tight upper bounds: (a) a tree-relaxed linear program (LP), which is derived from the Lagrangian dual of the upper bounds; and (b) a tree-reweighted max-product messagepassing algorithm that is related to but distinct from the max-product algorithm. In this way, we establish a connection between a certain LP relaxation of the modefinding problem, and a reweighted form of the max-product (min-sum) message-passing algorithm.
Multiresolution markov models for signal and image processing
- Proceedings of the IEEE
, 2002
"... This paper reviews a significant component of the rich field of statistical multiresolution (MR) modeling and processing. These MR methods have found application and permeated the literature of a widely scattered set of disciplines, and one of our principal objectives is to present a single, coheren ..."
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Cited by 153 (17 self)
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This paper reviews a significant component of the rich field of statistical multiresolution (MR) modeling and processing. These MR methods have found application and permeated the literature of a widely scattered set of disciplines, and one of our principal objectives is to present a single, coherent picture of this framework. A second goal is to describe how this topic fits into the even larger field of MR methods and concepts–in particular making ties to topics such as wavelets and multigrid methods. A third is to provide several alternate viewpoints for this body of work, as the methods and concepts we describe intersect with a number of other fields. The principle focus of our presentation is the class of MR Markov processes defined on pyramidally organized trees. The attractiveness of these models stems from both the very efficient algorithms they admit and their expressive power and broad applicability. We show how a variety of methods and models relate to this framework including models for self-similar and 1/f processes. We also illustrate how these methods have been used in practice. We discuss the construction of MR models on trees and show how questions that arise in this context make contact with wavelets, state space modeling of time series, system and parameter identification, and hidden
MAP estimation via agreement on (hyper)trees: Message-passing and linear programming approaches
- IEEE Transactions on Information Theory
, 2002
"... We develop an approach for computing provably exact maximum a posteriori (MAP) configurations for a subclass of problems on graphs with cycles. By decomposing the original problem into a convex combination of tree-structured problems, we obtain an upper bound on the optimal value of the original ..."
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Cited by 147 (10 self)
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We develop an approach for computing provably exact maximum a posteriori (MAP) configurations for a subclass of problems on graphs with cycles. By decomposing the original problem into a convex combination of tree-structured problems, we obtain an upper bound on the optimal value of the original problem (i.e., the log probability of the MAP assignment) in terms of the combined optimal values of the tree problems. We prove that this upper bound is met with equality if and only if the tree problems share an optimal configuration in common. An important implication is that any such shared configuration must also be a MAP configuration for the original problem. Next we present and analyze two methods for attempting to obtain tight upper bounds: (a) a tree-reweighted messagepassing algorithm that is related to but distinct from the max-product (min-sum) algorithm; and (b) a tree-relaxed linear program (LP), which is derived from the Lagrangian dual of the upper bounds. Finally, we discuss the conditions that govern when the relaxation is tight, in which case the MAP configuration can be obtained. The analysis described here generalizes naturally to convex combinations of hypertree-structured distributions.
Image completion with structure propagation
- ACM Transactions on Graphics
, 2005
"... two intersecting lines (green) specified by the user, (c) intermediate result after propagating structure and texture information along the user-specified lines, and (d) final result after filling in the remaining unknown regions by texture propagation. In this paper, we introduce a novel approach t ..."
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Cited by 133 (4 self)
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two intersecting lines (green) specified by the user, (c) intermediate result after propagating structure and texture information along the user-specified lines, and (d) final result after filling in the remaining unknown regions by texture propagation. In this paper, we introduce a novel approach to image completion, which we call structure propagation. In our system, the user manually specifies important missing structure information by extending a few curves or line segments from the known to the unknown regions. Our approach synthesizes image patches along these user-specified curves in the unknown region using patches selected around the curves in the known region. Structure propagation is formulated as a global optimization problem by enforcing structure and consistency constraints. If only a single curve is specified, structure propagation is solved using Dynamic Programming. When multiple intersecting curves are specified, we adopt the Belief Propagation algorithm to find the optimal patches. After completing structure propagation, we fill in the remaining unknown regions using patch-based texture synthesis. We show that our approach works well on a number of examples that are challenging to state-of-the-art techniques.
Stereo Matching with Color-Weighted Correlation, Hierarchical BELIEF PROPAGATION AND OCCLUSION HANDLING
, 2009
"... In this paper, we formulate a stereo matching algorithm with careful handling of disparity, discontinuity, and occlusion. The algorithm works with a global matching stereo model based on an energy-minimization framework. The global energy contains two terms, the data term and the smoothness term. T ..."
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Cited by 126 (10 self)
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In this paper, we formulate a stereo matching algorithm with careful handling of disparity, discontinuity, and occlusion. The algorithm works with a global matching stereo model based on an energy-minimization framework. The global energy contains two terms, the data term and the smoothness term. The data term is first approximated by a color-weighted correlation, then refined in occluded and low-texture areas in a repeated application of a hierarchical loopy belief propagation algorithm. The experimental results are evaluated on the Middlebury data sets, showing that our algorithm is the top performer among all the algorithms listed there.
Residual belief propagation: Informed scheduling for asynchronous message passing
- in Proceedings of the Twenty-second Conference on Uncertainty in AI (UAI
, 2006
"... Inference for probabilistic graphical models is still very much a practical challenge in large domains. The commonly used and effective belief propagation (BP) algorithm and its generalizations often do not converge when applied to hard, real-life inference tasks. While it is widely recognized that ..."
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Cited by 110 (3 self)
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Inference for probabilistic graphical models is still very much a practical challenge in large domains. The commonly used and effective belief propagation (BP) algorithm and its generalizations often do not converge when applied to hard, real-life inference tasks. While it is widely recognized that the scheduling of messages in these algorithms may have significant consequences, this issue remains largely unexplored. In this work, we address the question of how to schedule messages for asynchronous propagation so that a fixed point is reached faster and more often. We first show that any reasonable asynchronous BP converges to a unique fixed point under conditions similar to those that guarantee convergence of synchronous BP. In addition, we show that the convergence rate of a simple roundrobin schedule is at least as good as that of synchronous propagation. We then propose residual belief propagation (RBP), a novel, easy-toimplement, asynchronous propagation algorithm that schedules messages in an informed way, that pushes down a bound on the distance from the fixed point. Finally, we demonstrate the superiority of RBP over state-of-the-art methods for a variety of challenging synthetic and real-life problems: RBP converges significantly more often than other methods; and it significantly reduces running time until convergence, even when other methods converge. 1
MRF energy minimization and beyond via dual decomposition
- IN: IEEE PAMI. (2011
"... This paper introduces a new rigorous theoretical framework to address discrete MRF-based optimization in computer vision. Such a framework exploits the powerful technique of Dual Decomposition. It is based on a projected subgradient scheme that attempts to solve an MRF optimization problem by first ..."
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Cited by 105 (9 self)
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This paper introduces a new rigorous theoretical framework to address discrete MRF-based optimization in computer vision. Such a framework exploits the powerful technique of Dual Decomposition. It is based on a projected subgradient scheme that attempts to solve an MRF optimization problem by first decomposing it into a set of appropriately chosen subproblems and then combining their solutions in a principled way. In order to determine the limits of this method, we analyze the conditions that these subproblems have to satisfy and we demonstrate the extreme generality and flexibility of such an approach. We thus show that, by appropriately choosing what subproblems to use, one can design novel and very powerful MRF optimization algorithms. For instance, in this manner we are able to derive algorithms that: 1) generalize and extend state-of-the-art message-passing methods, 2) optimize very tight LP-relaxations to MRF optimization, 3) and take full advantage of the special structure that may exist in particular MRFs, allowing the use of efficient inference techniques such as, e.g, graph-cut based methods. Theoretical analysis on the bounds related with the different algorithms derived from our framework and experimental results/comparisons using synthetic and real data for a variety of tasks in computer vision demonstrate the extreme potentials of our approach.