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Volumn 33, Issue 3, 2011, Pages 531-552

MRF energy minimization and beyond via dual decomposition

Author keywords

Discrete optimization; graph cuts; graphical models; linear programming; Markov random fields; message passing

Indexed keywords

CAN DESIGN; DISCRETE OPTIMIZATION; DUAL DECOMPOSITION; ENERGY MINIMIZATION; GRAPH-CUT; GRAPH-CUTS; GRAPHICAL MODELS; INFERENCE TECHNIQUES; MARKOV RANDOM FIELDS; OPTIMIZATION ALGORITHMS; OPTIMIZATION PROBLEMS; SPECIAL STRUCTURE; SUB-PROBLEMS; SUBGRADIENT; SYNTHETIC AND REAL DATA; THEORETICAL FRAMEWORK;

EID: 79551518880     PISSN: 01628828     EISSN: None     Source Type: Journal    
DOI: 10.1109/TPAMI.2010.108     Document Type: Article
Times cited : (239)

References (57)
  • 1
    • 0013152010 scopus 로고    scopus 로고
    • The Volume algorithm: Producing primal solutions with a subgradient method
    • F. Barahona and R. Anbil, "The Volume Algorithm: Producing Primal Solutions with a Subgradient Method," Math. Programming, vol. 87, pp. 385-399, 2000.
    • (2000) Math. Programming , vol.87 , pp. 385-399
    • Barahona, F.1    Anbil, R.2
  • 3
    • 0006565946 scopus 로고
    • A Descent numerical method for optimization problems with nondifferentiable cost functionals
    • D.P. Bertsekas and S.K. Mitter, "A Descent Numerical Method for Optimization Problems with Nondifferentiable Cost Functionals," SIAM J. Control, vol. 11, pp. 637-652, 1973.
    • (1973) SIAM J. Control , vol.11 , pp. 637-652
    • Bertsekas, D.P.1    Mitter, S.K.2
  • 5
  • 6
    • 0016601948 scopus 로고
    • On Improving relaxation methods by modifying gradient techniques
    • P. Camerini, L. Fratta, and F. Maffioli, "On Improving Relaxation Methods by Modifying Gradient Techniques," Math. Programming Study, vol. 3, pp. 26-34, 1975.
    • (1975) Math. Programming Study , vol.3 , pp. 26-34
    • Camerini, P.1    Fratta, L.2    Maffioli, F.3
  • 7
  • 9
    • 77958077320 scopus 로고    scopus 로고
    • Residual belief propagation: Informed scheduling for asynchronous message passing
    • G. Elidan, I. McGraw, and D. Koller, "Residual Belief Propagation: Informed Scheduling for Asynchronous Message Passing," Proc. 22nd Conf. Uncertainty in AI, 2006.
    • (2006) Proc. 22nd Conf. Uncertainty in AI
    • Elidan, G.1    McGraw, I.2    Koller, D.3
  • 14
    • 85162019740 scopus 로고    scopus 로고
    • Fixing max-product: Convergent message passing algorithms for map lp-relaxations
    • MIT Press
    • A. Globerson and T. Jaakkola, "Fixing Max-Product: Convergent Message Passing Algorithms for Map LP-Relaxations," Advances in Neural Information Processing Systems, pp. 553-560, MIT Press, 2008.
    • (2008) Advances in Neural Information Processing Systems , pp. 553-560
    • Globerson, A.1    Jaakkola, T.2
  • 15
    • 84898959007 scopus 로고    scopus 로고
    • Stable fixed points of loopy belief propagation are minima of the bethe free energy
    • MIT Press
    • T. Heskes, "Stable Fixed Points of Loopy Belief Propagation Are Minima of the Bethe Free Energy," Advances in Neural Information Processing Systems, pp. 359-366, MIT Press, 2003.
    • (2003) Advances in Neural Information Processing Systems , pp. 359-366
    • Heskes, T.1
  • 16
    • 33749029684 scopus 로고    scopus 로고
    • Convexity arguments for efficient minimization of the bethe and kikuchi free energies
    • T. Heskes, "Convexity Arguments for Efficient Minimization of the Bethe and Kikuchi Free Energies," J. Artificial Intelligence Research, vol. 26, pp. 153-190, 2006.
    • (2006) J. Artificial Intelligence Research , vol.26 , pp. 153-190
    • Heskes, T.1
  • 20
    • 36249013608 scopus 로고    scopus 로고
    • Dynamic graph cuts for efficient inference in markov random fields
    • Dec.
    • P. Kohli and P. Torr, "Dynamic Graph Cuts for Efficient Inference in Markov Random Fields," IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 29, no. 12, pp. 2079-2088, Dec. 2007.
    • (2007) IEEE Trans. Pattern Analysis and Machine Intelligence , vol.29 , Issue.12 , pp. 2079-2088
    • Kohli, P.1    Torr, P.2
  • 21
    • 33750129298 scopus 로고    scopus 로고
    • Convergent tree-reweighted message passing for energy minimization
    • Oct.
    • V. Kolmogorov, "Convergent Tree-Reweighted Message Passing for Energy Minimization," IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 28, no. 10, pp. 1568-1583, Oct. 2006.
    • (2006) IEEE Trans. Pattern Analysis and Machine Intelligence , vol.28 , Issue.10 , pp. 1568-1583
    • Kolmogorov, V.1
  • 30
    • 0037876458 scopus 로고    scopus 로고
    • Ergodic primal convergence in dual subgradient schemes for convex programming
    • T. Larsson, M. Patriksson, and A. Stromberg, "Ergodic Primal Convergence in Dual Subgradient Schemes for Convex Programming," Math. Programming, vol. 86, pp. 283-312, 1999.
    • (1999) Math. Programming , vol.86 , pp. 283-312
    • Larsson, T.1    Patriksson, M.2    Stromberg, A.3
  • 31
    • 33745933877 scopus 로고    scopus 로고
    • Globally optimal solutions for energy minimization in stereo vision using reweighted belief propagation
    • T. Meltzer, C. Yanover, and Y. Weiss, "Globally Optimal Solutions for Energy Minimization in Stereo Vision Using Reweighted Belief Propagation," Proc. IEEE Int'l Conf. Computer Vision, 2005.
    • (2005) Proc. IEEE Int'l Conf. Computer Vision
    • Meltzer, T.1    Yanover, C.2    Weiss, Y.3
  • 32
    • 0036342213 scopus 로고    scopus 로고
    • Incremental subgradient methods for nondifferentiable optimization
    • A. Nedic and D.P. Bertsekas, "Incremental Subgradient Methods for Nondifferentiable Optimization," SIAM J. Optimization, vol. 12, pp. 109-138, 2001.
    • (2001) SIAM J. Optimization , vol.12 , pp. 109-138
    • Nedic, A.1    Bertsekas, D.P.2
  • 33
    • 70349668835 scopus 로고    scopus 로고
    • Approximate primal solutions and rate analysis for dual subgradient methods
    • A. Nedic and A. Ozdaglar, "Approximate Primal Solutions and Rate Analysis for Dual Subgradient Methods," SIAM J. Optimization, vol. 19, pp. 1757-1780, 2009.
    • (2009) SIAM J. Optimization , vol.19 , pp. 1757-1780
    • Nedic, A.1    Ozdaglar, A.2
  • 36
    • 56449095463 scopus 로고    scopus 로고
    • Message-Passing for graph-structured linear programs: Proximal projections, convergence and rounding schemes
    • P. Ravikumar, A. Agarwal, and M. Wainwright, "Message-Passing for Graph-Structured Linear Programs: Proximal Projections, Convergence and Rounding Schemes," Proc. Int'l Conf. Machine Learning, pp. 800-807, 2008.
    • (2008) Proc. Int'l Conf. Machine Learning , pp. 800-807
    • Ravikumar, P.1    Agarwal, A.2    Wainwright, M.3
  • 39
    • 51949102883 scopus 로고    scopus 로고
    • Solution to structural recognition (max,+)-problems by their equivalent transformations
    • M. Schlesinger and V. Giginyak, "Solution to Structural Recognition (MAX,+)-Problems by Their Equivalent Transformations," Control Systems and Computers, vol. 1, pp. 3-15, 2007.
    • (2007) Control Systems and Computers , vol.1 , pp. 3-15
    • Schlesinger, M.1    Giginyak, V.2
  • 40
    • 33947143988 scopus 로고
    • Syntactic analysis of two-dimensional visual signals in noisy conditions
    • M.I. Schlesinger, "Syntactic Analysis of Two-Dimensional Visual Signals in Noisy Conditions," Kybernetica, vol. 4, pp. 113-130, 1976.
    • (1976) Kybernetica , vol.4 , pp. 113-130
    • Schlesinger, M.I.1
  • 41
    • 0009734492 scopus 로고    scopus 로고
    • Recovery of primal solutions when using subgradient optimization methods to solve lagrangian duals of linear programs
    • H. Sherali and G. Choi, "Recovery of Primal Solutions When Using Subgradient Optimization Methods to Solve Lagrangian Duals of Linear Programs," Operations Research Letters, vol. 19, pp. 105-113, 1996.
    • (1996) Operations Research Letters , vol.19 , pp. 105-113
    • Sherali, H.1    Choi, G.2
  • 47
    • 0344983321 scopus 로고    scopus 로고
    • Comparison of graph cuts with belief propagation for stereo, using identical mrf parameters
    • M.F. Tappen and W.T. Freeman, "Comparison of Graph Cuts with Belief Propagation for Stereo, Using Identical mrf Parameters," Proc. IEEE Int'l Conf. Computer Vision, pp. 900-907, 2003.
    • (2003) Proc. IEEE Int'l Conf. Computer Vision , pp. 900-907
    • Tappen, M.F.1    Freeman, W.T.2
  • 49
    • 27744456278 scopus 로고    scopus 로고
    • Map Estimation via agreement on trees: Message-passing and linear programming
    • M. Wainwright, T. Jaakkola, and A. Willsky, "Map Estimation via Agreement on Trees: Message-Passing and Linear Programming," IEEE Trans. Information Theory, vol. 51, no. 11, pp. 3697-3717, 2005.
    • (2005) IEEE Trans. Information Theory , vol.51 , Issue.11 , pp. 3697-3717
    • Wainwright, M.1    Jaakkola, T.2    Willsky, A.3
  • 50
    • 0011952756 scopus 로고    scopus 로고
    • Correctness of belief propagation in gaussian graphical models of arbitrary topology
    • Y. Weiss and W.T. Freeman, "Correctness of Belief Propagation in Gaussian Graphical Models of Arbitrary Topology," Neural Computation, vol. 13, no. 10, pp. 2173-2200, 2001.
    • (2001) Neural Computation , vol.13 , Issue.10 , pp. 2173-2200
    • Weiss, Y.1    Freeman, W.T.2
  • 51
    • 0035246323 scopus 로고    scopus 로고
    • On the Optimality of solutions of the max-product belief-propagation algorithm in arbitrary graphs
    • Y. Weiss and W.T. Freeman, "On the Optimality of Solutions of the Max-Product Belief-Propagation Algorithm in Arbitrary Graphs," IEEE Trans. Information Theory, vol. 47, no. 2, pp. 736-744, 2001.
    • (2001) IEEE Trans. Information Theory , vol.47 , Issue.2 , pp. 736-744
    • Weiss, Y.1    Freeman, W.T.2
  • 52
    • 80053218745 scopus 로고    scopus 로고
    • MAP Estimation, linear programming and belief propagation with convex free energies
    • Y. Weiss, C. Yanover, and T. Meltzer, "MAP Estimation, Linear Programming and Belief Propagation with Convex Free Energies," Proc. 22nd Conf. Uncertainty in AI, 2007.
    • (2007) Proc. 22nd Conf. Uncertainty in AI
    • Weiss, Y.1    Yanover, C.2    Meltzer, T.3
  • 53
    • 34249652006 scopus 로고    scopus 로고
    • A Linear programming approach to max-sum problem: A review
    • July
    • T. Werner, "A Linear Programming Approach to Max-Sum Problem: A Review," IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 29, no. 7, pp. 1165-1179, July 2007.
    • (2007) IEEE Trans. Pattern Analysis and Machine Intelligence , vol.29 , Issue.7 , pp. 1165-1179
    • Werner, T.1
  • 54
    • 51949116660 scopus 로고    scopus 로고
    • High-Arity interactions, polyhedral relaxations, and cutting plane algorithm for soft constraint optimisation (Map-mrf)
    • T. Werner, "High-Arity Interactions, Polyhedral Relaxations, and Cutting Plane Algorithm for Soft Constraint Optimisation (Map-mrf)," Proc. IEEE Conf. Computer Vision and Pattern Recognition, 2008.
    • (2008) Proc. IEEE Conf. Computer Vision and Pattern Recognition
    • Werner, T.1
  • 56
    • 33745778496 scopus 로고    scopus 로고
    • Linear programming relaxations and belief propagation-an empirical study
    • C. Yanover, T. Meltzer, and Y. Weiss, "Linear Programming Relaxations and Belief Propagation-An Empirical Study," J. Machine Learning Research, vol. 7, pp. 1887-1907, 2006.
    • (2006) J. Machine Learning Research , vol.7 , pp. 1887-1907
    • Yanover, C.1    Meltzer, T.2    Weiss, Y.3
  • 57
    • 23744513375 scopus 로고    scopus 로고
    • Constructing free energy approximations and generalized belief propagation algorithms
    • July
    • J. Yedidia, W. Freeman, and Y. Weiss, "Constructing Free Energy Approximations and Generalized Belief Propagation Algorithms," IEEE Trans. Information Theory, vol. 51, no. 7, pp. 2282-2312, July 2005.
    • (2005) IEEE Trans. Information Theory , vol.51 , Issue.7 , pp. 2282-2312
    • Yedidia, J.1    Freeman, W.2    Weiss, Y.3


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.