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241
Graph Cut based Inference with Cooccurrence Statistics
"... Abstract. Markov and Conditional random fields (CRFs) used in computer vision typically model only local interactions between variables, as this is computationally tractable. In this paper we consider a class of global potentials defined over all variables in the CRF. We show how they can be readily ..."
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Cited by 98 (13 self)
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Abstract. Markov and Conditional random fields (CRFs) used in computer vision typically model only local interactions between variables, as this is computationally tractable. In this paper we consider a class of global potentials defined over all variables in the CRF. We show how they can be readily optimised using standard graph cut algorithms at little extra expense compared to a standard pairwise field. This result can be directly used for the problem of class based image segmentation which has seen increasing recent interest within computer vision. Here the aim is to assign a label to each pixel of a given image from a set of possible object classes. Typically these methods use random fields to model local interactions between pixels or superpixels. One of the cues that helps recognition is global object cooccurrence statistics, a measure of which classes (such as chair or motorbike) are likely to occur in the same image together. There have been several approaches proposed to exploit this property, but all of them suffer from different limitations and typically carry a high computational cost, preventing their application on large images. We find that the new model we propose produces an improvement in the labelling compared to just using a pairwise model. 1
Bethe free energy, Kikuchi approximations and belief propagation algorithms
, 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 nds for general graphs. ..."
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Cited by 95 (2 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 nds for general graphs. We show that BP can only converge to a stationary point of an approximate free energy, known as the Bethe free energy in statistical physics. This result characterizes BP xedpoints and makes connections with variational approaches to approximate inference. More importantly, our analysis lets us build on the progress made in statistical physics since Bethe's approximation was introduced in 1935. Kikuchi and others have shown how to construct more accurate free energy approximations, of which Bethe's approximation is the simplest. Exploiting the insights from our analysis, we derive generalized belief propagation (GBP) versions of these Kikuchi approximations. These new message passing algorithms can be signicantly more accurate than ordinary BP, at an adjustable increase in complexity. We illustrate such a new GBP algorithm on a grid Markov network and show that it gives much more accurate marginal probabilities than those found using ordinary BP.
Decentralised Coordination of LowPower Embedded Devices Using the MaxSum Algorithm
 In: 7 th International Conference on Autonomous Agents and MultiAgent Systems (AAMAS08
, 2008
"... This paper considers the problem of performing decentralised coordination of lowpower embedded devices (as is required within many environmental sensing and surveillance applications). Specifically, we address the generic problem of maximising social welfare within a group of interacting agents. We ..."
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Cited by 93 (29 self)
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This paper considers the problem of performing decentralised coordination of lowpower embedded devices (as is required within many environmental sensing and surveillance applications). Specifically, we address the generic problem of maximising social welfare within a group of interacting agents. We propose a novel representation of the problem, as a cyclic bipartite factor graph, composed of variable and function nodes (representing the agents’ states and utilities respectively). We show that such representation allows us to use an extension of the maxsum algorithm to generate approximate solutions to this global optimisation problem through local decentralised message passing. We empirically evaluate this approach on a canonical coordination problem (graph colouring), and benchmark it against state of the art approximate and complete algorithms (DSA and DPOP). We show that our approach is robust to lossy communication, that it generates solutions closer to those of DPOP than DSA is able to, and that it does so with a communication cost (in terms of total messages size) that scales very well with the number of agents in the system (compared to the exponential increase of DPOP). Finally, we describe a hardware implementation of our algorithm operating on lowpower Chipcon CC2431 SystemonChip sensor nodes.
Minimizing Sparse Higher Order Energy Functions of Discrete Variables
"... Higher order energy functions have the ability to encode high level structural dependencies between pixels, which have been shown to be extremely powerful for image labeling problems. Their use, however, is severely hampered in practice by the intractable complexity of representing and minimizing su ..."
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Cited by 74 (13 self)
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Higher order energy functions have the ability to encode high level structural dependencies between pixels, which have been shown to be extremely powerful for image labeling problems. Their use, however, is severely hampered in practice by the intractable complexity of representing and minimizing such functions. We observed that higher order functions encountered in computer vision are very often “sparse”, i.e. many labelings of a higher order clique are equally unlikely and hence have the same high cost. In this paper, we address the problem of minimizing such sparse higher order energy functions. Our method works by transforming the problem into an equivalent quadratic function minimization problem. The resulting quadratic function can be minimized using popular message passing or graph cut based algorithms for MAP inference. Although this is primarily a theoretical paper, it also shows how higher order functions can be used to obtain impressive results for the binary texture restoration problem.
Approximate inference and protein folding
 Proceedings of NIPS 2002
, 2002
"... Sidechain prediction is an important subtask in the proteinfolding problem. We show that finding a minimal energy sidechain configuration is equivalent to performing inference in an undirected graphical model. The graphical model is relatively sparse yet has many cycles. We used this equivalence ..."
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Cited by 73 (8 self)
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Sidechain prediction is an important subtask in the proteinfolding problem. We show that finding a minimal energy sidechain configuration is equivalent to performing inference in an undirected graphical model. The graphical model is relatively sparse yet has many cycles. We used this equivalence to assess the performance of approximate inference algorithms in a realworld setting. Specifically we compared belief propagation (BP), generalized BP (GBP) and naive mean field (MF). In cases where exact inference was possible, maxproduct BP always found the global minimum of the energy (except in few cases where it failed to converge), while other approximation algorithms of similar complexity did not. In the full protein data set, maxproduct BP always found a lower energy configuration than the other algorithms, including a widely used proteinfolding software (SCWRL). 1
A comparison of algorithms for inference and learning in probabilistic graphical models
 IEEE Transactions on Pattern Analysis and Machine Intelligence
, 2005
"... Computer vision is currently one of the most exciting areas of artificial intelligence research, largely because it has recently become possible to record, store and process large amounts of visual data. While impressive achievements have been made in pattern classification problems such as handwr ..."
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Cited by 70 (4 self)
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Computer vision is currently one of the most exciting areas of artificial intelligence research, largely because it has recently become possible to record, store and process large amounts of visual data. While impressive achievements have been made in pattern classification problems such as handwritten character recognition and face detection, it is even more exciting that researchers may be on the verge of introducing computer vision systems that perform scene analysis, decomposing image input into its constituent objects, lighting conditions, motion patterns, and so on. Two of the main challenges in computer vision are finding efficient models of the physics of visual scenes and finding efficient algorithms for inference and learning in these models. In this paper, we advocate the use of graphbased probability models and their associated inference and learning algorithms for computer vision and scene analysis. We review exact techniques and various approximate, computationally efficient techniques, including iterative conditional modes, the expectation maximization (EM) algorithm, the mean field method, variational techniques, structured variational techniques, Gibbs sampling, the sumproduct algorithm and “loopy ” belief propagation. We describe how each technique can be applied in a model of multiple, occluding objects, and contrast the behaviors and performances of the techniques using a unifying cost function, free energy.
On the optimality of treereweighted maxproduct message passing
 In UAI
, 2005
"... Treereweighted maxproduct (TRW) message passing [9] is a modified form of the ordinary maxproduct algorithm for attempting to find minimal energy configurations in Markov random field with cycles. For a TRW fixed point satisfying the strong tree agreement condition, the algorithm outputs a config ..."
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Cited by 68 (5 self)
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Treereweighted maxproduct (TRW) message passing [9] is a modified form of the ordinary maxproduct algorithm for attempting to find minimal energy configurations in Markov random field with cycles. For a TRW fixed point satisfying the strong tree agreement condition, the algorithm outputs a configuration that is provably optimal. In this paper, we focus on the case of binary variables with pairwise couplings, and establish stronger properties of TRW fixed points that satisfy only the milder condition of weak tree agreement (WTA). First, we demonstrate how it is possible to identify part of the optimal solution—i.e., a provably optimal solution for a subset of nodes — without knowing a complete solution. Second, we show that for submodular functions, a WTA fixed point always yields a globally optimal solution. We establish that for binary variables, any WTA fixed point always achieves the global maximum of the linear programming relaxation underlying the TRW method. 1
Tree Consistency and Bounds on the Performance of the MaxProduct Algorithm and Its Generalizations
, 2002
"... Finding the maximum a posteriori (MAP) assignment of a discretestate distribution specified by a graphical model requires solving an integer program. The maxproduct algorithm, also known as the maxplus or minsum algorithm, is an iterative method for (approximately) solving such a problem on gr ..."
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Cited by 67 (5 self)
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Finding the maximum a posteriori (MAP) assignment of a discretestate distribution specified by a graphical model requires solving an integer program. The maxproduct algorithm, also known as the maxplus or minsum algorithm, is an iterative method for (approximately) solving such a problem on graphs with cycles.
Measuring uncertainty in graph cut solutions  efficiently computing minmarginal energies using dynamic graph cuts
 In ECCV
, 2006
"... Abstract. In recent years the use of graphcuts has become quite popular in computer vision. However, researchers have repeatedly asked the question whether it might be possible to compute a measure of uncertainty associated with the graphcut solutions. In this paper we answer this particular questi ..."
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Cited by 66 (10 self)
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Abstract. In recent years the use of graphcuts has become quite popular in computer vision. However, researchers have repeatedly asked the question whether it might be possible to compute a measure of uncertainty associated with the graphcut solutions. In this paper we answer this particular question by showing how the minmarginals associated with the label assignments in a MRF can be efficiently computed using a new algorithm based on dynamic graph cuts. We start by reporting the discovery of a novel relationship between the minmarginal energy corresponding to a latent variable label assignment, and the flow potentials of the node representing that variable in the graph used in the energy minimization procedure. We then proceed to show how the minmarginal energy can be computed by minimizing a projection of the energy function defined by the MRF. We propose a fast and novel algorithm based on dynamic graph cuts to efficiently minimize these energy projections. The minmarginal energies obtained by our proposed algorithm are exact, as opposed to the ones obtained from other inference algorithms like loopy belief propagation and generalized belief propagation. We conclude by showing how minmarginals can be used to compute a confidence measure for label assignments in labelling problems such as image segmentation. 1
Maximum weight matching via maxproduct belief propagation
 in International Symposium of Information Theory
, 2005
"... Abstract — The maxproduct “belief propagation ” algorithm is an iterative, local, message passing algorithm for finding the maximum a posteriori (MAP) assignment of a discrete probability distribution specified by a graphical model. Despite the spectacular success of the algorithm in many applicati ..."
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Cited by 64 (12 self)
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Abstract — The maxproduct “belief propagation ” algorithm is an iterative, local, message passing algorithm for finding the maximum a posteriori (MAP) assignment of a discrete probability distribution specified by a graphical model. Despite the spectacular success of the algorithm in many application areas such as iterative decoding and computer vision which involve graphs with many cycles, theoretical convergence results are only known for graphs which are treelike or have a single cycle. In this paper, we consider a weighted complete bipartite graph and define a probability distribution on it whose MAP assignment corresponds to the maximum weight matching (MWM) in that graph. We analyze the fixed points of the maxproduct algorithm when run on this graph and prove the surprising result that even though the underlying graph has many short cycles, the maxproduct assignment converges to the correct MAP assignment. We also provide a bound on the number of iterations required by the algorithm. I.