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      Markov Models for Image Labeling

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      Mathematical Problems in Engineering

      Hindawi Limited

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          Abstract

          Markov random field (MRF) is a widely used probabilistic model for expressing interaction of different events. One of the most successful applications is to solve image labeling problems in computer vision. This paper provides a survey of recent advances in this field. We give the background, basic concepts, and fundamental formulation of MRF. Two distinct kinds of discrete optimization methods, that is, belief propagation and graph cut, are discussed. We further focus on the solutions of two classical vision problems, that is, stereo and binary image segmentation using MRF model.

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          Most cited references 36

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          Constructing Free-Energy Approximations and Generalized Belief Propagation Algorithms

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            Convergent tree-reweighted message passing for energy minimization.

            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]--tree-reweighted max-product 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 tree-reweighted 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 tree-reweighted algorithm in [33]. In addition, on stereo problems with Potts interactions, we obtain a lower energy than graph cuts.
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              Efficient Belief Propagation for Early Vision

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                Author and article information

                Journal
                Mathematical Problems in Engineering
                Mathematical Problems in Engineering
                Hindawi Limited
                1024-123X
                1563-5147
                2012
                2012
                : 2012
                :
                : 1-18
                Article
                10.1155/2012/814356
                ab1f58df-e8f5-4c8d-a82c-e045037819d7
                © 2012

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