메뉴 건너뛰기




Volumn 157, Issue 16, 2009, Pages 3412-3423

Global optimization for first order Markov Random Fields with submodular priors

Author keywords

Global optimization; Maximum flow s, t minimum cut; Submodular functions

Indexed keywords

ARBITRARY GRAPHS; BINARY VARIABLES; CARDINALITIES; FIRST ORDER; GLOBAL OPTIMIZER; INTERACTION TERM; LEVEL SET; MARKOV RANDOM FIELDS; MARKOVIAN; MAXIMUM FLOW/S, T MINIMUM CUT; NUMERICAL RESULTS; PAIRWISE INTERACTION; SUBMODULAR; SUBMODULAR FUNCTIONS; SUBMODULARITY; SUFFICIENT CONDITIONS;

EID: 70249141267     PISSN: 0166218X     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.dam.2009.02.026     Document Type: Article
Times cited : (14)

References (65)
  • 1
    • 21044452195 scopus 로고    scopus 로고
    • A cut-based algorithm for the nonlinear dual of the minimum cost network flow problem
    • Ahuja R.K., Hochbaum D.S., and Orlin J.B. A cut-based algorithm for the nonlinear dual of the minimum cost network flow problem. Algorithmica 39 3 (2004) 189-208
    • (2004) Algorithmica , vol.39 , Issue.3 , pp. 189-208
    • Ahuja, R.K.1    Hochbaum, D.S.2    Orlin, J.B.3
  • 2
    • 0042266794 scopus 로고    scopus 로고
    • Solving the convex cost integer dual network flow problem
    • Ahuja R.K., Hochbaum D.S., and Orlin J.B. Solving the convex cost integer dual network flow problem. Management Science 49 7 (2003) 950-964
    • (2003) Management Science , vol.49 , Issue.7 , pp. 950-964
    • Ahuja, R.K.1    Hochbaum, D.S.2    Orlin, J.B.3
  • 5
    • 4243117834 scopus 로고
    • Finding ground states in random-field Ising ferromagnets
    • Barahona F. Finding ground states in random-field Ising ferromagnets. Journal of Physics A 18 (1985) 673-675
    • (1985) Journal of Physics A , vol.18 , pp. 673-675
    • Barahona, F.1
  • 6
    • 0000013152 scopus 로고
    • On the statistical analysis of dirty pictures
    • Besag J. On the statistical analysis of dirty pictures. Journal of the Royal Statistics Society 48 (1986) 259-302
    • (1986) Journal of the Royal Statistics Society , vol.48 , pp. 259-302
    • Besag, J.1
  • 11
    • 4344598245 scopus 로고    scopus 로고
    • An experimental comparison of min-cut/max-flow algorithms for energy minimization in vision
    • Boykov Y., and Kolmogorov V. An experimental comparison of min-cut/max-flow algorithms for energy minimization in vision. IEEE Transactions on Pattern Analysis and Machine Interaction 26 9 (2004) 1124-1137
    • (2004) IEEE Transactions on Pattern Analysis and Machine Interaction , vol.26 , Issue.9 , pp. 1124-1137
    • Boykov, Y.1    Kolmogorov, V.2
  • 14
    • 33646554193 scopus 로고    scopus 로고
    • Total variation minimization and a class of binary mrf models
    • Energy Minimization Methods in Computer Vision and Pattern Recognition, St. Augustine, Florida, USA
    • Chambolle A. Total variation minimization and a class of binary mrf models. Energy Minimization Methods in Computer Vision and Pattern Recognition. LNCS vol. 3757 (2005), St. Augustine, Florida, USA
    • (2005) LNCS , vol.3757
    • Chambolle, A.1
  • 15
    • 69049120393 scopus 로고    scopus 로고
    • On total variation minimization and surface evolution using parametric maximum flows
    • Tech. Rep, UCLA, 2008
    • A. Chambolle, J. Darbon, On total variation minimization and surface evolution using parametric maximum flows, Tech. Rep., UCLA, 2008
    • Chambolle, A.1    Darbon, J.2
  • 17
    • 25144513305 scopus 로고    scopus 로고
    • Algorithms for finding global minimizers of image segmentation and denoising models
    • Tech. Rep, UCLA, 2004
    • T. Chan, S. Esedoglu, M. Nikolova, Algorithms for finding global minimizers of image segmentation and denoising models, Tech. Rep., UCLA, 2004
    • Chan, T.1    Esedoglu, S.2    Nikolova, M.3
  • 19
    • 0031213363 scopus 로고    scopus 로고
    • Global minimum for active contour models: A minimal path approach
    • Cohen L., and Kimmel R. Global minimum for active contour models: A minimal path approach. International Journal of Computer Vision 24 1 (1997) 57-78
    • (1997) International Journal of Computer Vision , vol.24 , Issue.1 , pp. 57-78
    • Cohen, L.1    Kimmel, R.2
  • 20
    • 0142095169 scopus 로고    scopus 로고
    • A comparison of mixed-integer programming models for nonconvex piecewise linear cost minimization problem
    • Croxton K., Gendron B., and Magnanti T. A comparison of mixed-integer programming models for nonconvex piecewise linear cost minimization problem. Management Science 49 9 (2003) 1268-1273
    • (2003) Management Science , vol.49 , Issue.9 , pp. 1268-1273
    • Croxton, K.1    Gendron, B.2    Magnanti, T.3
  • 22
    • 70249118868 scopus 로고    scopus 로고
    • J. Darbon, Composants logiciels et algorithmes de minimisation exacte d'énergies dédiés au traitement des images, Ph.D. thesis, Ecole Nationale Supérieure des Télécommunications, 2005
    • J. Darbon, Composants logiciels et algorithmes de minimisation exacte d'énergies dédiés au traitement des images, Ph.D. thesis, Ecole Nationale Supérieure des Télécommunications, 2005
  • 23
    • 70249100926 scopus 로고    scopus 로고
    • Global optimization for first order Markov Random Fields with submodular priors
    • Combinatorial Image Analysis. Brimkov V., Barneva R., and Hauptman H. (Eds), Springer, Berlin
    • Darbon J. Global optimization for first order Markov Random Fields with submodular priors. In: Brimkov V., Barneva R., and Hauptman H. (Eds). Combinatorial Image Analysis. Lecture Notes in Computer Science Series vol. 4958 (2008), Springer, Berlin
    • (2008) Lecture Notes in Computer Science Series , vol.4958
    • Darbon, J.1
  • 25
    • 33845478943 scopus 로고    scopus 로고
    • Image restoration with discrete constrained total variation part II: Levelable functions, convex priors and non-convex cases
    • Darbon J., and Sigelle M. Image restoration with discrete constrained total variation part II: Levelable functions, convex priors and non-convex cases. Journal of Mathematical Imaging and Vision 26 3 (2006) 277-291
    • (2006) Journal of Mathematical Imaging and Vision , vol.26 , Issue.3 , pp. 277-291
    • Darbon, J.1    Sigelle, M.2
  • 26
    • 33845482689 scopus 로고    scopus 로고
    • Image restoration with discrete constrained total variation part I: Fast and exact optimization
    • Darbon J., and Sigelle M. Image restoration with discrete constrained total variation part I: Fast and exact optimization. Journal of Mathematical Imaging and Vision 26 3 (2006) 261-276
    • (2006) Journal of Mathematical Imaging and Vision , vol.26 , Issue.3 , pp. 261-276
    • Darbon, J.1    Sigelle, M.2
  • 27
    • 70249124513 scopus 로고    scopus 로고
    • Sar image regularization with fast approximate discrete minimization
    • Tech. Rep. CAM-07-38, UCLA, 2007
    • L. Denis, F. Tupin, J. Darbon, M. Sigelle, Sar image regularization with fast approximate discrete minimization, Tech. Rep. CAM-07-38, UCLA, 2007
    • Denis, L.1    Tupin, F.2    Darbon, J.3    Sigelle, M.4
  • 28
    • 32944467806 scopus 로고    scopus 로고
    • Stability of the minimizers of least squares with a non-convex regularization. Part I: Local behavior
    • Durand S., and Nikolova M. Stability of the minimizers of least squares with a non-convex regularization. Part I: Local behavior. Journal of Applied Mathematics and Optimization 53 2 (2006) 185-208
    • (2006) Journal of Applied Mathematics and Optimization , vol.53 , Issue.2 , pp. 185-208
    • Durand, S.1    Nikolova, M.2
  • 29
    • 33646419033 scopus 로고    scopus 로고
    • Stability of the minimizers of least squares with a non-convex regularization. Part II: Global behavior
    • Durand S., and Nikolova M. Stability of the minimizers of least squares with a non-convex regularization. Part II: Global behavior. Journal of Applied Mathematics and Optimization 53 3 (2006) 259-277
    • (2006) Journal of Applied Mathematics and Optimization , vol.53 , Issue.3 , pp. 259-277
    • Durand, S.1    Nikolova, M.2
  • 32
    • 0021518209 scopus 로고
    • Stochastic relaxation, Gibbs distributions, and the Bayesian restoration of images
    • Geman S., and Geman D. Stochastic relaxation, Gibbs distributions, and the Bayesian restoration of images. IEEE Transactions on Pattern Analysis and Machine Interaction 6 6 (1984) 721-741
    • (1984) IEEE Transactions on Pattern Analysis and Machine Interaction , vol.6 , Issue.6 , pp. 721-741
    • Geman, S.1    Geman, D.2
  • 34
    • 51849127184 scopus 로고    scopus 로고
    • Parametric maximum flow algorithms for fast total variation minimization
    • Tech. Rep, Rice University
    • D. Goldfarb, Y. Yin, Parametric maximum flow algorithms for fast total variation minimization, Tech. Rep., Rice University, 2007
    • (2007)
    • Goldfarb, D.1    Yin, Y.2
  • 36
    • 0004248801 scopus 로고    scopus 로고
    • Image iterative smoothing and PDE s., downloadable
    • manuscript: please write email to fguichard@poseidon-tech.com
    • F. Guichard, J.-M. Morel, Image iterative smoothing and PDE s., downloadable manuscript: please write email to fguichard@poseidon-tech.com, 2000
    • (2000)
    • Guichard, F.1    Morel, J.-M.2
  • 38
    • 0000571009 scopus 로고
    • Exact determination of all ground states of random field systems in polynomial time
    • Hartmann A., and Usadel K. Exact determination of all ground states of random field systems in polynomial time. Physica A 214 2 (1995) 141-152
    • (1995) Physica A , vol.214 , Issue.2 , pp. 141-152
    • Hartmann, A.1    Usadel, K.2
  • 39
    • 0008821575 scopus 로고    scopus 로고
    • An efficient algorithm for image segmentation, Markov Random Fields and related problems
    • Hochbaum D. An efficient algorithm for image segmentation, Markov Random Fields and related problems. Journal of the ACM 48 2 (2001) 686-701
    • (2001) Journal of the ACM , vol.48 , Issue.2 , pp. 686-701
    • Hochbaum, D.1
  • 40
    • 0025496223 scopus 로고
    • Convex separable optimization is not much harder than linear optimization
    • Hochbaum D., and Shanthikumar J. Convex separable optimization is not much harder than linear optimization. Journal of the ACM 37 (1990) 843-862
    • (1990) Journal of the ACM , vol.37 , pp. 843-862
    • Hochbaum, D.1    Shanthikumar, J.2
  • 42
    • 0000335630 scopus 로고    scopus 로고
    • A combinatorial strongly polynomial algorithm for minimizing submodular functions
    • Iwata S., Fleischer L., and Fujishige S. A combinatorial strongly polynomial algorithm for minimizing submodular functions. Journal of the ACM 48 4 (2001) 761-777
    • (2001) Journal of the ACM , vol.48 , Issue.4 , pp. 761-777
    • Iwata, S.1    Fleischer, L.2    Fujishige, S.3
  • 44
    • 33947213194 scopus 로고    scopus 로고
    • Primal-dual algorithm for convex Markov random fields
    • Tech. Rep, Microsoft Research
    • V. Kolmogorov, Primal-dual algorithm for convex Markov random fields, Tech. Rep., Microsoft Research, 2005
    • (2005)
    • Kolmogorov, V.1
  • 52
    • 70249106676 scopus 로고    scopus 로고
    • SIAM Society for Industrial and Applied Mathematics
    • Murota K. Discrete Convex Analyis (2003), SIAM Society for Industrial and Applied Mathematics
    • (2003) Discrete Convex Analyis
    • Murota, K.1
  • 53
    • 33748416181 scopus 로고    scopus 로고
    • Analysis of the recovery of edges in images and signals by minimizing nonconvex regularized least-squares
    • Nikolova M. Analysis of the recovery of edges in images and signals by minimizing nonconvex regularized least-squares. SIAM Journal on Multiscale Modeling and Simulation 4 3 (2005) 960-991
    • (2005) SIAM Journal on Multiscale Modeling and Simulation , vol.4 , Issue.3 , pp. 960-991
    • Nikolova, M.1
  • 54
  • 55
    • 0000888388 scopus 로고
    • Integer optimization and zero-fixed point in Ising random-field systems
    • Ogielski A. Integer optimization and zero-fixed point in Ising random-field systems. Physical Review Letters 57 10 (1986) 1251-1254
    • (1986) Physical Review Letters , vol.57 , Issue.10 , pp. 1251-1254
    • Ogielski, A.1
  • 56
    • 0016565825 scopus 로고
    • Minimum cuts and related problem
    • Picard J., and Ratliff H. Minimum cuts and related problem. Networks 5 (1975) 357-370
    • (1975) Networks , vol.5 , pp. 357-370
    • Picard, J.1    Ratliff, H.2
  • 57
    • 44049111982 scopus 로고
    • Nonlinear total variation based noise removal algorithms
    • Rudin L., Osher S., and Fatemi E. Nonlinear total variation based noise removal algorithms. Physica D 60 (1992) 259-268
    • (1992) Physica D , vol.60 , pp. 259-268
    • Rudin, L.1    Osher, S.2    Fatemi, E.3
  • 58
    • 35148886004 scopus 로고    scopus 로고
    • Transforming an arbitrary minsum problem into a binary one
    • Tech. Rep, Dresden University of Technology
    • D. Schlesinger, B. Flach, Transforming an arbitrary minsum problem into a binary one, Tech. Rep., Dresden University of Technology, 2008
    • (2008)
    • Schlesinger, D.1    Flach, B.2
  • 60
    • 0034311821 scopus 로고    scopus 로고
    • A combinatorial algorithm minimizing submodular functions in strongly polynomial time
    • Schrijver A. A combinatorial algorithm minimizing submodular functions in strongly polynomial time. Journal of Combinatorial Theory Series B 80 2 (2000) 346-355
    • (2000) Journal of Combinatorial Theory Series B , vol.80 , Issue.2 , pp. 346-355
    • Schrijver, A.1
  • 62
    • 27744456278 scopus 로고    scopus 로고
    • MAP estimation via agreement on (hyper)trees: Message-passing and linear-programming approaches
    • Wainwright M.J., Jaakkola T.S., and Willsky A.S. MAP estimation via agreement on (hyper)trees: Message-passing and linear-programming approaches. IEEE Transactions on Information Theory 51 11 (2005) 3697-3717
    • (2005) IEEE Transactions on Information Theory , vol.51 , Issue.11 , pp. 3697-3717
    • Wainwright, M.J.1    Jaakkola, T.S.2    Willsky, A.S.3
  • 63
    • 0003455701 scopus 로고    scopus 로고
    • Image Analysis, Random Fields and Dynamic Monte Carlo Methods. A Mathematical Introduction
    • Springer-Verlag
    • Winkler G. Image Analysis, Random Fields and Dynamic Monte Carlo Methods. A Mathematical Introduction. Applications of Mathematics. 3rd ed. (2006), Springer-Verlag
    • (2006) Applications of Mathematics. 3rd ed.
    • Winkler, G.1
  • 64
    • 70249115520 scopus 로고    scopus 로고
    • Efficient determination of Gibbs estimator with submodular energy functions
    • Tech. Rep, United Institution of Information Problem
    • B. Zalesky, Efficient determination of Gibbs estimator with submodular energy functions, Tech. Rep., United Institution of Information Problem, 2005
    • (2005)
    • Zalesky, B.1
  • 65
    • 20444410464 scopus 로고    scopus 로고
    • Network flow optimization for restoration of images
    • Zalesky B. Network flow optimization for restoration of images. Journal of Applied Mathematics 2 4 (2002) 199-218
    • (2002) Journal of Applied Mathematics , vol.2 , Issue.4 , pp. 199-218
    • Zalesky, B.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.