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      A Survey and Comparison of Discrete and Continuous Multi-label Optimization Approaches for the Potts Model

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      International Journal of Computer Vision

      Springer Nature

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          An experimental comparison of min-cut/max-flow algorithms for energy minimization in vision.

          After [15], [31], [19], [8], [25], [5], minimum cut/maximum flow algorithms on graphs emerged as an increasingly useful tool for exact or approximate energy minimization in low-level vision. The combinatorial optimization literature provides many min-cut/max-flow algorithms with different polynomial time complexity. Their practical efficiency, however, has to date been studied mainly outside the scope of computer vision. The goal of this paper is to provide an experimental comparison of the efficiency of min-cut/max flow algorithms for applications in vision. We compare the running times of several standard algorithms, as well as a new algorithm that we have recently developed. The algorithms we study include both Goldberg-Tarjan style "push-relabel" methods and algorithms based on Ford-Fulkerson style "augmenting paths." We benchmark these algorithms on a number of typical graphs in the contexts of image restoration, stereo, and segmentation. In many cases, our new algorithm works several times faster than any of the other methods, making near real-time performance possible. An implementation of our max-flow/min-cut algorithm is available upon request for research purposes.
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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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              MAP Estimation Via Agreement on Trees: Message-Passing and Linear Programming

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                Author and article information

                Journal
                International Journal of Computer Vision
                Int J Comput Vis
                Springer Nature
                0920-5691
                1573-1405
                September 2013
                April 19 2013
                September 2013
                : 104
                : 3
                : 223-240
                Article
                10.1007/s11263-013-0619-y
                76445490-56b7-473b-a3a1-1dc3fb2e222d
                © 2013
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